metadata: authors: 0: author: Strand,Jon
count: World
docna: 0: docna: Prospects for Markets for Internationally
            Transferred Mitigation Outcomes under the Paris Agreement
docty: Policy Research Working Paper
abstracts: cdata!: The Paris Agreement provides for parties
            to use internationally transferred mitigation outcomes in
            implementing their Nationally Determined Contributions. This
            paper analyzes forward trading of these outcomes in the
            presence of two forms of uncertainty: (1) uncertainty about
            the fulfillment of Nationally Determined Contribution
            targets, and (2) uncertainty about the existence and
            functioning of the forward, options, and future spot markets
            markets for internationally transferred mitigation outcomes.
            When parties can sell and buy internationally transferred
            mitigation outcomes forward, access to call options for late
            purchases leads to correspondingly larger forward sales, or
            less current mitigation. Access to put options for late
            internationally transferred mitigation outcome sales does
            not affect forward trading outcomes but increases late sales
            for net sellers. Access to options markets is welfare
            enhancing for all parties, and call options help parties
            stay in compliance with their Nationally Determined
            Contributions at the Paris Agreement end point, 2030. The
            existence of internationally transferred mitigation outcome
            markets may be in peril, however, as banking beyond 2030 is
            not allowed. The availability and functioning of
            internationally transferred mitigation outcome markets can
            be enabled or improved by increased climate finance provided
            by donors. With no options markets, host countries will
            still sell internationally transferred mitigation outcomes
            forward, albeit less so, and rely on access to more
            expensive “backstop” mitigation for ex-post compliance with
            their Nationally Determined Contributions. Closed-form
            solutions are derived for trading and its welfare impacts in
            all the option contract alternatives, given that parties’
            uncertainties about fulfilling their commitments are
            uniformly distributed. The welfare impact of the
            availability of put and call option contracts is then
            strongly increasing in uncertainty, and in ex-post and
            forward outcome prices.
display_title: Prospects for Markets for
            Internationally Transferred Mitigation Outcomes under the
            Paris Agreement
listing_relative_url: /research/2022/05/33819706/prospects-markets-internationally-transferred-mitigation-outcomes-under-paris-agreement
topicv3: Climate Change Mitigation m1327079 579,Carbon Pricing m1327308 1846,Climate Finance m1327548 1847,Carbon Trading m1327771 1776
publishtoextweb_dt: 2022-05-16T00:00:00Z
dois: 10.1596/1813-9450-10045
origu: Off of Sr VP Dev Econ/Chief Econ (DECVP)
author_keys: 0: author_key: 1008099
model_extractions: Policy Research Working Paper 10045 Prospects for Markets for Internationally Transferred Mitigation Outcomes under the Paris Agreement _Jon Strand_ Development Economics Development Research Group May 2022
Policy Research Working Paper 10045

# **Abstract**

The Paris Agreement provides for parties to use internationally transferred mitigation outcomes in implementing their Nationally Determined Contributions. This paper analyzes forward trading of these outcomes in the presence of two forms of uncertainty: (1) uncertainty about the fulfillment of Nationally Determined Contribution targets, and (2) uncertainty about the existence and functioning of the forward, options, and future spot markets markets for internationally transferred mitigation outcomes. When parties can sell and buy internationally transferred mitigation outcomes forward, access to call options for late purchases leads to correspondingly larger forward sales, or less current mitigation. Access to put options for late internationally transferred mitigation outcome sales does not affect forward trading outcomes but increases late sales for net sellers. Access to options markets is welfare enhancing for all parties, and call options help parties stay in compliance with their Nationally Determined Contributions at the Paris Agreement end point, 2030. The existence of internationally transferred mitigation outcome markets may be in peril, however, as banking beyond 2030 is not allowed. The availability and functioning of internationally transferred mitigation outcome markets can be enabled or improved by increased climate finance provided by donors. With no options markets, host countries will still sell internationally transferred mitigation outcomes forward, albeit less so, and rely on access to more expensive “backstop” mitigation for ex-post compliance with their Nationally Determined Contributions. Closed-form solutions are derived for trading and its welfare impacts in all the option contract alternatives, given that parties’ uncertainties about fulfilling their commitments are uniformly distributed. The welfare impact of the availability of put and call option contracts is then strongly increasing in uncertainty, and in ex-post and forward outcome prices.

This paper is a product of the Development Research Group, Development Economics. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The author may be contacted at Jstrand1344@gmail.com.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# **Prospects for Markets for Internationally Transferred Mitigation Outcomes under the Paris Agreement**

# **By**

# **Jon Strand**

**Development Research Group, Sustainability and Infrastructure Team**

**The World Bank**

**<u>Jstrand1344@gmail.com</u>**

**JEL Codes:** G15; G23; Q54; Q56

**Key words:** Paris Agreement; Nationally Determined Contributions; Uncertainty; Climate Finance; ITMOs; Options contracts; Forward contracting.
# **Prospects for Markets for Internationally Transferred Mitigation Outcomes under the Paris Agreement**<sup>**1**</sup>

# **1. Introduction and Background**

A topical question on today’s climate policy agenda is whether markets and infrastructure under the Paris Agreement (PA) will support trading of internationally transferred mitigation outcomes (ITMOs). ITMOs are defined and made precise in relation to Article 6 of the PA. This instrument opens up for participating countries to fulfill their (unconditional) Nationally Determined Contributions (NDCs) toward the PA by trading ITMOs, between selling parties which “overfulfill” their PA NDCs, and other parties which do not themselves fulfill their NDC targets. ITMOs must be considered in the context of two trading mechanisms under the PA: one mechanism for bilateral trade in mitigation outcomes under Article 6.2; and a new global market mechanism for ITMO trading under Article 6.4. A growing number of parties seem interested in using these mechanisms, although (so far) more parties have expressed interest in selling ITMOs than potentially buying them. Brandemann, Kreibich and Obergassell (2021) found that, by October 2021, 102 of 124 parties analyzed state a willingness to use these market mechanisms in their NDC implementation. See also Michaelowa et al. (2021a). More parties may have become positive after the Article 6 Rulebook was completed at the Glasgow COP-26 in November 2021. Some large parties, notably the United States and the European Union, have however (at this point) expressed a lack of willingness to use these mechanisms.

A final approval and rulebook for the Article 6 mechanisms were produced at the COP 26 in Glasgow, implying that there are now no formal barriers to ITMO trading under these mechanisms; see Michaelowa (2021). Note however that these mechanisms, and ITMO trading, do not themselves lead to reduced targeted emission rates, nor reduced actual emissions given that targets are achieved. Instead, the Article 6 mechanisms imply that costs of reaching the targets are reduced, perhaps dramatically. The markets for selling and buying of ITMOs thus open up for very large potential welfare gains, through reductions in GHG mitigation costs across countries, and corresponding increases in participating countries’ mitigation ambitions (by tightening their NDC

> 1 The author thanks Gabriela Mundaca, Klaus Oppermann, Billy Pizer and Govinda Timilsina for helpful discussions and comments to the various versions of this paper. The author also thanks the World Bank Climate Change Group for supporting this research. Views and ideas expressed in the paper are solely those of the author and cannot be ascribed to the World Bank, its management or member countries.

2
targets), which can result in similar reductions in GHG emissions by 2030 and beyond that date. Edmonds et al. (2021) have estimated that ITMO trading through the Article 6 mechanisms can reduce the costs of achieving the 2030 NDC targets by $300 billion (or about one-third of the total potential ITMO transaction value), which in turn could reduce GHG emissions by an additional 9 billion tons CO2e per year if reinvested fully in emissions reducing capital and activities. Similar conclusions were drawn in an earlier study by the World Bank (2016). See also the seminal and even earlier study by Metcalf and Weisbach (2012), and more recent work by Mehling, Metcalf and Stavins (2018, 2019), Parry et al. (2021), and Black et al. (2021) for further analysis and discussions.

When selling an ITMO to another party of the PA, the seller must perform a “corresponding adjustment” (CA) exempting the underlying emission reduction from accounting against its own NDC emissions target, to avoid double counting of mitigation outcomes that can be claimed to the parties’ NDCs, and attribute the transferred ITMO to the buying party.<sup>2</sup> A main objective of this paper is to discuss principal and analytical issues related to the functioning of ITMO markets, their impacts on potential ITMO-supplying countries, and their potential for reducing the cost of global GHG mitigation activity, and increase the global ambition in climate policy. Our focus in this discussion will be on impacts of uncertainty, on parties’ strategies and activities, and on the functioning of the carbon markets which form the fundaments for these trading mechanisms. A background is a widespread worry that the Article 6 trading mechanisms may not be widely used for PA implementation, due to several factors but with uncertainty as one central issue. The objective of these mechanisms is to facilitate more efficient, effective and broadbased global GHG mitigation for a maximum number of countries. The objective is to make it easier and less expensive for the parties to reach their NDC targets, and to give these countries incentives to set more ambitious NDC targets. As vividly illustrated in Edmonds et al. (2021), when the Article 6 mechanisms are not used (or used only sparingly and inefficiently), overall costs of implementing the required emissions reductions can be (much) higher than necessary, and also make it harder for all countries to reach their NDC targets.

> 2 Correct CA accounting requires that strict book-keeping principles are followed by all PA parties; see Schneider et al. (2017).

3
A reason for this skepticism is a widespread worry among parties about their ability to fulfill their NDC pledges. There is also a worry about whether parties can over-fulfill their NDC targets and do not find countries to which to sell their surpluses. A high degree of uncertainty about a party’s mitigation outcome at or close to 2030 could make a participating country highly conservative in its activity to sell ITMOs forward (which must be paired with a CA), given that NDC fulfillment at the end point has high priority for the party. This might severely curtail the supply side of the ITMO market. The anticipation of future supply limitations could in turn have serious knock-on impacts for the demand side. Potential future demanders of ITMOs, who are highly concerned about fulfilling their future NDC requirements, will tend to anticipate the availability of ITMOs required for NDC fulfillment when uncertain variables take their most adverse values, and ITMOs at the same time may not be available for purchase in the ex-post market. When ITMOs are expected to not be available near 2030, these countries may respond by assuring that their NDC requirements will be fulfilled in the absence of late ITMO trading, thus making the ITMO markets redundant. Such behavior among a large number of potential ITMO demanders could thin the market and lead to an unfortunate situation with no or only marginal trading opportunities during the PA implementation period. We might end up with a self-fulfilling belief that such markets will not exist as demand fails due to lack of supply, and supply fails due to lack of demand. Greater uncertainty with respect to future NDC fulfillment could make such problems more likely.

Certain institutional issues related to the PA compound and magnify these worries. The institutional setup of the PA trading system based on Article 6 is problematic, as it does not allow for banking of ITMOs from one NDC period to subsequent ones. This can cause severe problems for the very existence of an ITMO market near the end point. “Nobody” (in particular, no low- or middle-income country) will want to be left with idle ITMOs at the end point (under current rules for the PA, these ITMOs will then be worthless). To guard against this possibility, parties may seek to end trading and achieve ITMO balance relative to their NDCs, in ample time before the end point. This may cause the markets to fail near the end point, which may push back further the time at which a party will decide to stop trading.<sup>3</sup>

> 3 It appears that these clauses have been inserted into the PA rulebook to prevent a situation similar to that experienced at the end of the contract period for the KP, which was not suffering from these problems. But under that agreement, some countries were left with substantial amounts of surplus mitigation at the end point which could later be cashed out. Rule makers for the PA wanted to avoid such situations under the current agreement.

4
A natural question here is whether this problem can be rectified or ameliorated by “soon” altering this institutional setup. Policy makers and other relevant actors need to be alerted about the importance of such rule changes for successful treaty implementation.

There however do exist potentially fruitful responses to problems raised by uncertainty for the functioning of ITMO markets. Which response(s) will turn out as (most) viable depend on several factors, including the participating countries’ preferences, their policy options and choices, the costs involved, and institutional details of the PA, to the extent that these can be modified. Assume that a potential ITMO-selling country has already set its NDC target for 2030, and that this country is highly committed to its target. According to the PA rulebook, this target can be tightened but not relaxed. The natural way to respond to greater uncertainty about goal fulfillment is to increase GHG mitigation above its “normal” or “planned” level, to create a “mitigation buffer” that makes target fulfillment more resilient to uncertainty. From that perspective, greater uncertainty can, at least in principle, lead to an increase in mitigation among PA parties, at least given that targets themselves are not moved by such uncertainty.

On the other hand, NDC target setting at later stages of the agreement (e. g., in 2025) may be impacted negatively by uncertainty. NDC targets are expected to be gradually tightened toward 2030. Greater certainty about a party’s ability to reach (or over-perform relative to) the current target, and lower costs of reaching this target, may increase the target ambition over time, and greater uncertainty may prevent such greater ambition. Laxer targets could lead to laxer mitigation activity. It is here easy to think of situations where greater uncertainty would reduce global mitigation.

This paper will discuss problems caused by uncertainty for the operation and functioning of ITMO markets: their origins, the forms the problems may take, and possible ways to overcome them. We will be less concerned with impacts on the overall climate policies of PA parties, and how NDC targets are impacted. Our concern will be more about how uncertainty affects the very functioning of ITMO markets.

There are several ways to approach ITMO markets under uncertainty. We will mention three that will play a role in the following discussion.

5
1. Financial contracts and facilities available to parties, such as option and swap contracts (including also rights of first refusal). The most commonly used contract type to date (for example under the Kyoto Protocol, KP) is simple forward contracts, where ITMOs are contracted between two parties for future delivery at a given contracted price. Put and call options contracts may both also be relevant.<sup>4</sup> Put options for future ITMO sales may serve to guarantee future ITMO market access without imposing on the selling country any obligation to offer the ITMOs, but instead to open up this possibility, and guarantee that the ITMOs need not be sold by hosts which otherwise have problems with fulfilling their NDCs. Such options may be purchased with a contracted “strike price”, _q1_ , at which they will be exercised, and expire 31 December 2030. Call options, for the purchase of ITMOs at future dates (by the PA end point), can be relevant for net ITMO buyers, most likely high- and middle-income countries. They can however also be relevant (in principle) for prospective ITMO sellers, when combined with forward sales contracts for ITMOs at fixed (pre-determined) prices, by serving as a hedge against overselling risk created by the (often lucrative) sale of forward ITMO contracts. Engaging in ITMO forward sales contracts exposes a host to increased risk of NDC noncompliance when emissions turn out to be higher than initially anticipated at or near the end point (2030). ITMOs may in such cases need to be “bought back” for NDC compliance, which could occur safely through call option contracts.<sup>5</sup> Properties of such contracts will be studied in the following, to investigate their roles for the operation of ITMO markets and NDC implementation. No option markets for ITMOs have so far been set up nor seriously contemplated. It is currently unclear whether option contract markets can be made available to PA market participants ahead of 2030; and who would in case sponsor, support, and guarantee their existence and sufficient liquidity. Institutionally, they can be set up as simple bilateral trades between two parties, or as structured markets with sufficient liquidity. We do not take a stand on this in the paper, nor do we study the implications of market structure on their efficiency and attractiveness to the parties. Note that similar market applications to emissions or offset

> 4 For standard (textbook) presentations and discussion of options markets and contracts, see Hull (2009) and Shapiro (2006). For classical work on options theory, applied to structured options markets dealing with more general cases than discussed here (and applied mainly to financial asset valuation in continuous time), see Black and Scholes (1973), and Merton (1973).

> 5 In a two-country relationship between PA parties, this could occur simply by canceling a forward-contracted delivery of ITMOs at the end point; and thus no “buying back”.

6
trading have been suggested in the literature; see in particular Ismer and Neuhoff (2006), Pizer (2011), Little et al. (2015), Environmental Defense Fund (2016), Coffman and Lockey (2017), and Lockey and Coffman (2018).

2. Other interventions, support and facilitation by donors and/or International Financial Institutions (IFIs), or by other funds and institutions supported mainly by donors. Funds or facilities can be established and created by donors to establish, enable and facilitate the existence and operation of the necessary markets, and access for hosts to these markets, to reduce or eliminate the uncertainties for countries which rely on forward and options markets for ITMOs. Few examples of such support programs exist to date. They typically require resource inputs by donors, but not necessarily very large net donor commitments. Climate finance cannot be used for direct purchase of ITMOs, but may be used to subsidize the ITMO markets (although it is ruled out by some climate finance providers such as the Green Climate Fund (GCF) and the Climate Investment Funds (CIF)). Such subsidies are however in most cases inefficient if they do not serve to correct particular inefficiencies of market operation (see Strand 2019). When support is mainly to the establishment of a viable ITMO market without (substantially) subsidizing its activities, such subsidies can be used, and could also be virtually costless at the margin for funders. Both funders and hosts may instead end up with welfare gains due to the benign impacts on market functioning.

3. Counting on host countries to come up with their own strategies for eliminating possible NDC achievement deficits, either “ex ante” (in a preparatory phase); or “ex post”, toward the end of the PA agreement (2030). Host countries could be forced into a situation of responsibility, with a need to eliminate any mitigation deficit relative to their NDC targets, and might end up with innovative ways to reduce their GHG emissions. One (expensive) way to accomplish this is to plan for sufficient over-fulfillment of the host’s NDC, to make sure that an end-point mitigation deficit does not arise. The host can, similarly, establish a “buffer” of mitigation activities and projects, that can be activated at a late stage of the PA to guard against unexpected NDC deficits. It might also be done by then activating an “emergency reserve” or “backstop” mitigation activity. These alternatives could however be expensive, and perhaps limited in scope. An advantage of the last alternative for hosts is that it may be needed only with low probability, which means that it would count little 7
in the host’s ex ante calculus. Our analysis below shows that even an expensive backstop alternative could still, in some cases, form the basis for forward ITMO sales.

A problem with such ex-post solutions executed by sovereigns is _lacking ex post incentives_ . The incentives to carry out backstop mitigation must be retained at a late stage. But a sovereign host is essentially free to implement or not implement this mitigation “fix”. This reveals a fundamental weakness of the PA: it implies no binding commitments on the parties, and is thus unenforceable versus its sovereign member countries. This problem can be reduced to some degree by establishing insurance-like solutions where hosts make payments up front to ensure that default will not occur.

This paper will focus less on other issues which can be crucial for the overall success and impact of the PA: (a) the general GHG mitigation level and policy of the respective host countries, and (b) how countries’ NDC targets are defined under the PA. As noted, NDC targets are likely to be set (and further tightened) on the basis of the estimated costs of implementing them. We will assume that NDC targets and GHG mitigation policies are both given, and that comprehensive carbon pricing is the main instrument used by hosts to reach their NDC mitigation targets.<sup>6</sup> We focus on ITMO delivery and NDC target achievement, and impacts of uncertainty on this relationship. Commitment to PA targets is also important. Since the PA relies on voluntary cooperation between all parties, trust in the willingness of the parties to seriously pursue their NDC targets is required. We will (with some qualifications) assume that host countries pursue their NDC targets vigorously. Target definition can also be important. Single- or multi-year target setting can make a difference for target attainment, measurement and recording, and for the integrity of target reaching; see Siemons and Schneider (2021), and Michaelowa et al. (2021b). In our analysis we however make explicit considerations for only one future period.

# **2. Uncertainty: Sources and Implications**

Uncertainties facing PA hosts are key in this paper. Several types of uncertainty face potential ITMO suppliers and demanders, related to costs and efforts needed to reach their NDC targets under the PA; and what measures and market alternatives are available to meet these uncertainties.

> 6 Appendix 1 also considers the phasing-in of zero- or low-carbon technologies as the main mitigation strategy, without this altering our results noticeably.

8
Different uncertainties may interact, be mutually compounded or lessened, and be affected by donors’ and other market participants’ interventions and policies.

We distinguish between seven categories of uncertainty, of which (at least) five directly impact on hosts’ ability to fulfill their NDCs at the PA end point (2030).

_a) Lack of knowledge, or uncertainty, by a host country about the shape of its own marginal abatement cost curve (“MAC curve”), and about how the MAC curve will develop up to the PA end point (year 2030)_ . This is a potentially important type of uncertainty for host countries, in terms of predicting their potentials for GHG mitigation by 2030; it plays a key role in our formal analysis. Many country governments, in particular in low-income countries, may have poor knowledge about their own current MAC curves, and an even less secure notion about how these curves will develop over the years to come. This point interacts with and depends on points b-e below. It also depends on the broad category of uncertainty to which this belongs (in particular, Knightian “risk” versus “uncertainty”, as discussed below).

_b) The fossil fuel price, and other productive input prices, at intermediate stages and end point, are uncertain_ . A high fossil fuel price gives an automatic impetus to reduce fossil fuel consumption and carbon emissions in both the short and long run. A change in the fossil fuel price should have a similar impact on emissions as an equivalent shift in the carbon tax (at same stage). Note that the international fossil fuel price is likely to be higher when global demand for fossil fuel is higher, which is likely when global GHG mitigation activity is lower, and general economic activity is higher.

_c) Whether or not the host country is able to implement a (planned or unplanned) comprehensive mitigation policy (including carbon pricing or wider decarbonization programs) within the policy period; and at what stage and price level carbon pricing is implemented_ . The host country may have clear plans about how to set its carbon price up to 2030, but both the policy environment and implementation possibilities may be highly uncertain. Significant carbon pricing, and early carbon pricing implementation, lead to lower GHG emissions, and make it more likely that its target will be reached. The host government will however be more certain about this at an intermediate date (such as 2025), at which time the NDC target may be adjusted.

9
_d) Implemented zero- or low-carbon investments up to 2030, and impacts of these investments on mitigation._ These are highly uncertain for most PA parties today. The amount of such implementation affects the degree to which the host’s emissions level can be shifted down relative to BAU (with no such investments for given policy and activity level); or be shifted up when the BAU is based on (substantial) renewables phase-in. This factor is affected by developments for low-carbon technologies, support received for such implementation, and carbon price implementation (which incentivizes renewable-energy investments).

_e) Whether the host’ economic activity rate is high or low, and other (random) factors affecting fossil fuel demand_ . When output is higher more fossil fuels will likely be demanded, and GHG emissions will be higher.

_f) The likelihood for (current, future, and forward) ITMO markets to exist; the scope for types of ITMO trading; the liquidity of ITMO markets; and the levels the (current or future expected) ITMO demand including the future ITMO price._ A high current ITMO price, combined with readily accessible future or current ITMO markets, should imply strong incentives for GHG mitigation in a host country that expects to deliver ITMOs. A country that instead expects to be a net demander of ITMOs will also prefer a robust ITMO market, but rather one with low ITMO prices. Note that robust and liquid ITMO markets can have either high or low equilibrium prices, depending on the concrete demand and supply conditions.

_g) Uncertainty about donor involvement in carbon markets and the availability and use of external funds to stimulate global GHG mitigation and ITMO market activities_ . Donor support and guarantees may lead to more smoothly operating ITMO markets. When it is unclear whether such support may be forthcoming later in the PA implementation period, it may lead to caution and skepticism among potential hosts who are potential ITMO market participants, and perhaps less reliance on these markets.

Points a-e mainly affect uncertainty about hosts’ MAC curves, which will be the main topic of most of our discussion involving uncertainty in the following. Points a, b and e (and in part d) can largely be viewed as “random” factors from the angle of a given host. Points c and d (and in part e) are more related to policy uncertainty. In the following analysis we will mostly assume that uncertainty is purely random and that the host has little or no ability to control it. We will keep most of our attention on point a, when such focus is needed.

10
Points f-g represent uncertainty related to external conditions facing hosts. They also play a significant role in this paper, as background for much of our concern about non-existence of ITMO markets, and the need for trading alternatives including options markets. As has already been pointed out, ITMO trading holds a great potential for reducing overall costs of implementing parties’ NDCs, which could increase parties’ mitigation ambitions and overall GHG mitigation by making their NDC targets more ambitious (see Edmonds et al. 2021). On the other hand, if parties’ ambitions (and NDC targets) are given, the inability to trade ITMOs could lead to _greater_ mitigation under uncertainty. A lack of ITMO market access can induce parties to carry out more mitigation than otherwise in a preparatory phase, to ensure that their NDC targets will be fulfilled later on. But it also increases the parties’ interests in more complex contracting, by using options and other forward markets We draw this conclusion in section 4 below.

Other aspects of uncertainty can also be consequential:

- 1) _Whether uncertainty represents “Knightian risk” or “Knightian uncertainty”._ The distinction stems from Frank Knight’s (1921) seminal study where risk assumes a known probability distribution, while uncertainty does not. Knightian risk lends itself readily to mathematical modeling, while Knightian uncertainty does not; it does not yet have a firmly established and accepted analytical basis. The two risk concepts can also yield very different (and sometimes unpredictable and surprising) results (see e.g. Nishimura and Hiroyuki 2007). We will in the following take a “risk” approach, but recognize that it may be subject to limitations that will not be further deliberated.

- 2) _Whether risks are independent or correlated_ . We can identify two classes of correlated risk: correlation between the different risks faced by any given host; and correlation between (overall or more specific) risks faced by different countries. We consider both positive and negative correlations. Correlated risks across countries can have negative consequences, even for existence of ITMO markets. The reason is clear: when all countries either “overshoot” or “undershoot” their NDC targets, in either case serious market imbalances can occur, drying up the demand or supply side of the market. Global risk factors, highly correlated across countries, are development of zero-carbon technologies (d), and global business cycles (e). Such uncertainties could lead to strong positive correlations across countries, and to highly unbalanced global ITMO markets. Regarding

11
risk factors that affect a given country, there can be positive correlation between the phasing-in of zero-carbon technologies (d), carbon taxation (c), and the MAC curve (a). A positive correlation between zero-carbon technology phase-in (d) reducing emissions, and overall activity level (e), would however lead to _opposite_ impacts on carbon emissions from these two factors.

3) _Whether and to what degrees risks/uncertainties are recognized by the parties_ . We will in the following assume that probabilities experienced by a party (a “host”) are mostly subjective as they rely on (Bayesian) beliefs of the parties. They need not be “true” probabilities. For example, a host may have incomplete knowledge about the “objective” probability distribution related to the shape of its own MAC curve, but has a subjective belief about this shape. In our analysis, this host will then act based on its belief, which is not necessarily “objectively correct”.

# **3. ITMO Trading in the Absence of Option Markets**

# **3.1 Initial Setting: Spot Market**

We start with a very basic case, setting up our general model structure. We consider a spot market for ITMOs which is active at the end point of the PA (in 2030). The host is assumed to be able to adjust its mitigation activity immediately and optimally to the ITMO price at the end point.<sup>7</sup> The ITMO seller (host country; or project host) is assumed to face either a competitive ITMO market, or unlimited trade with other PA hosts, where an unlimited number of ITMOs can be sold by all private entities in the host economy at a market price _q_ , considered exogenous by the host. We assume that the host has implemented an economy-wide carbon price, _t_ , the only mitigation alternative used. Carbon emissions from the host’s energy use is proportional to its fossil-fuel consumption (today, and/or at the time when any future contract can be signed). Call the “businessas-usual” (BAU) carbon emissions _R0_ ; carbon emissions at the end point _RB_ , and the country’s NDC target _R* < R0_ . _R*_ and _R0_ are both exogenous, and the host only uses fossil-fuel energies in the BAU state. The host is allowed to sell all its emissions reduction beyond its NDC target, _R* – RB_ , in the ITMO market. We here assume no uncertainty, and no discounting.

> 7 This is unrealistic in view of the current rules under which Article 6 operates; in particular, that there is no ITMO market, and no banking of ITMOs, beyond 2030. We may however think of, and here represent, a spot carbon market which could be allowed to evolve over time, also beyond 2030 with a continual sequence of spot market outcomes to which the host in question here adjusts.

12
The host’s net return from its economic activity in 2030 is given by: In equation (3.1), _p_ is the fossil fuel price, and _T_ the government carbon tax revenue (= _t RB_ ). ITMO sales at the end point are here assumed to be non-negative ( _R* – RB_ ≥ 0) for low-income country hosts (on which we focus). Equation (3.1) implies a stylized, linear-quadratic production structure for the ITMO seller, where γ is a scaling constant in the host’s macro production function; see Doda and Taschini (2017), Strand (2020a, b), Mundaca and Strand (2021) for recent similar modeling approaches.<sup>8</sup> The private sector’s behavior is assumed to be captured by maximizing (3.1) with respect to _RB_ (taking _T_ as given): Assume that the host’s baseline emissions rate is given by This baseline is simply given by a zero ITMO price, and zero carbon tax, in (3.2). The country’s NDC emissions target is defined by _s_ (> 0) represents the comprehensive carbon price (or tax) required by the host country to (effectively and efficiently) implement its unconditional NDC target _R*_ . Higher _s_ means that _R*_ is smaller, and the country’s NDC is “more ambitious” (required mitigation to reach the NDC equals _s/γ_ > 0). _s/γ_ is then simply the additional mitigation beyond BAU required for NDC fulfillment. ( _s_ is not an actual carbon tax, but represents the _level of a carbon tax required_ to reach the NDC, given no ITMO trading possibilities and no uncertainty.) A more ambitious NDC target

> 8 Our production structure represents a simple second-order Taylor approximation to the “true” structure, so that the marginal effects of policy instruments, here the carbon tax _t_ , are constant. This model is a precise representation only for relatively small changes in policy variables.

13
(lower _R*_ , and higher _s_ ) makes it more demanding for the host to fulfill its NDC, and deliver ITMOs at the final stage. We do not specify what is behind this target.

The host’s MAC curve is here linear in _t_ and _q_ ; it is represented simply by the first-order condition (3.2). This is an over-simplification, but has the advantage of making the analysis highly transparent, and easy to interpret.<sup>9</sup> The amount of net forward ITMO contracts sold by the host under certainty is defined as _RI_ : (3.5) follows from the host’s NDC target being accurately met, and is found setting _RB = R*_ . _v_ can be interpreted as a “net excess carbon price”: how much higher must the host’s total carbon price, _q + t_ , be relative to the carbon price which exactly implements the country’s NDC, for the host to be able to sell ITMOs in the amount _RI_ ? When _s > q + t_ (the host has an “ambitious” NDC target), this host is a net ITMO buyer, typical for high-income countries with ambitious NDCs.

# **3.2 Forward ITMO Contracting When Host NDC Fulfillment Is Uncertain**

We will now consider impacts of uncertainty for a host which potentially supplies ITMOs, for the host’s mitigation behavior. We represent uncertainty about the host’s GHG emissions at the end point in a very simple way, and by a single stochastic variable. We also consider impacts of uncertainty on the host’s ability and willingness to engage in forward and options contracting for ITMOs. We introduce two “points of time”: “ex ante”, when policy is implemented under uncertainty; and “ex post”, when the uncertain variable is revealed. For analytical simplicity we assume no discounting between these two time points. We now also assume that the host’s GHG mitigations policy must be determined at the ex-ante stage; and that it has no or very small possibilities to adjust its emissions ex post.

We focus on a comprehensive and uniform carbon tax _t_ as the only mitigation policy for the host to reach (or attempt to reach) its NDC target under uncertainty.<sup>10</sup> Define the GHG emissions rate

> 9 Note that the MAC curve from (2.2) is linear in the country’s policy instrument _t_ .

> 10 In Appendix 1 we consider a different alternative where mitigation is implemented by phasing in zero-carbon technology in parts of the economy, and carbon taxation not applied. Our main conclusions are similar in both cases.

14
of the host country at the end point (2030), _RB_ , as viewed from the “ex ante” starting point, by the following relation which replaces (3.2): Here _z_ is a random variable (from the point of view of the host) affecting final GHG emissions. Assume that _Ez_ = 0, and that _z_ has a uniform distribution on its support [- _z0, z0_ ]. The probability density of _z_ on its support is then constant and equals 1/(2 _z0_ ). A larger _z0_ means greater uncertainty about the host’s emissions level at the end point.

The uniform distribution has both advantages and disadvantages relative to other alternatives such as the normal distribution. The uniform distribution is the simplest to handle analytically, and to interpret. Another advantage in our context is that no outcomes can occur outside of a given range. The stochastic variable _z_ has well-defined lower and upper bounds, making it possible for the host to choose a “safe” range for its mitigation which ensures that its NDC will be fulfilled. This is not possible with the normal distribution, where no such bounds exist. A disadvantage of the uniform (rectangular) distribution could be that a bell-shaped distribution often represents a more realistic description of uncertainty in the real world.

Assume that the host cannot guarantee compliance by being able to purchase ITMOs or reduce its own GHG emissions ex post. We first seek to derive the condition under which ITMOs can be sold forward, which is _RB < R*_ in the most unfavorable state for the host, namely _z = z0_ . This gives the following condition for positive ITMO delivery by the host: Here _z1_ is defined as the value of _z_ which makes the host “just” in compliance. Assume _q + t – s_ > 0. The condition (3.7) then implies that a positive ITMO supply can be contracted and delivered by the host without compromising its NDC target under certainty (with _Ez_ = 0 and _z0_ = 0); as well as when z0 < _q + t - s_ .

When uncertainty is greater so that _z0 ≥ q + t - s_ , ITMOs cannot be contracted forward by the host without the host being in non-compliance in some possible future states. The probability that the host will not be in compliance ex post, when not buying ITMOs back, is _P(0)_ given by 15
How the host country will respond to a situation where _P(0)_ > 0 depends on additional factors. First, how important is it for the host to _always_ “stay in compliance” (be able to honor its NDC)? If this is extremely important, the host may (when feasible) select its own policies and strategies so that this holds in all future states.<sup>11</sup> Secondly, how difficult is it to use a higher carbon tax, _t_ , to increase GHG mitigation at later times? Note that reducing _s_ is not allowed under the PA; the NDC target can be tightened over time, but not relaxed.<sup>12</sup> Thirdly, can the host access an ex-post (late-stage) spot marked for ITMOs where NDC deficits can be eliminated by purchasing offsets? Such a spot market may not become available under current trading rules for Article 6; see section 1.

Fourthly, can or will the host fail to honor a contract for forward ITMO delivery, if necessary to stay in compliance ex post? We do not explicitly model the behavior of parties that issue (and guarantee for) forward ITMO contracts, but (briefly, in the appendix) consider problems caused by breach for parties buying forward ITMO contracts.

# **4. Alternatives for Improving the Conditions for ITMO Markets and Meeting ITMO Deficits**

# **4.1 Discussion of Alternatives**

We will now consider other alternatives for facilitating ITMO trading, combined with meeting potential ITMO deficits by host countries, including those arising from forward ITMO sales, and options contracting. Much of this discussion will deal with how problems for ITMO markets due to risks and uncertainty can be mitigated by the PA parties themselves, and by outside participants such as donors or IFIs. We identify and discuss 9 alternatives:

> 11 Such strategies are feasible under our assumption of a uniform distribution of uncertain outcomes for the host. With other distributions, such as normality, this is technically not the case. The host must then always accept some final uncertainty about compliance (with no other ex post remedies). 12 We can however still think of indirect ways to slacken the NDC target. Assume that a host had anticipated a tightening of its NDC target by 2025. A “real slackening” could mean to not go forward with such tightening.

16
1) _Planning for NDC over-achievement_ . Under uncertainty, the host could simply increase its mitigation action and thereby reduce its expected emissions below its NDC level. In our model, the carbon tax _t_ represents the only explicit mitigation action by the host country. This tax could be raised to a level that makes compliance certain, possibly even with some ITMO forward sales. A necessary condition for this is: _t + q_ can here be interpreted as the host’s total carbon price, where we consider _q_ as exogenous for the individual host country. Greater uncertainty means a higher _z0_ . This increases the carbon tax _t_ necessary to stay in compliance for certain (with no other mitigation or ITMO purchases). With moderate value of _s_ (reasonable for a low-income country with “low” mitigation ambition in its NDC), a limited value of _z0_ , and a considerable value of _q_ , the value of _t_ fulfilling (4.1) could be small or even negative. Incentives would then be provided for this host to sell ITMOs forward. More generally, greater uncertainty (higher _z0_ ) has a positive impact on mitigation by forcing hosts to “over-shoot” their NDC mitigation target (as the carbon tax fulfilling (4.1) is higher when _z0_ is greater).

2) _“Backstop” mitigation_ . The host could have available other (“reserve” or “backstop”) mitigation alternatives near 2030. In real-world piloting alternatives, a common practice has been to try to identify “reserve” mitigation alternatives that could be less responsive to carbon taxation. “Backstops” may be expensive to execute but may be helpful if the mitigation gap is limited.

3) _Access to (inexpensive) future offset markets_ . A host country which fails to be in NDC compliance in 2030 (due to excessive emissions and forward ITMO sales), can then be compliant through ex-post ITMO purchases. With such markets available there should be no fundamental bar to selling ITMOs forward. Existence of a future spot market for ITMOs (with reasonable ITMO price) is however highly uncertain, even unlikely, today. Most hosts will likely be hesitant to enter into forward ITMO sales contracts if they need to rely on this market alternative.

4) _Access to expensive future offset markets_ . The quantity of offsets available could be limited in such markets. A cost-benefit analysis may be required to determine whether contracting for future ITMO deliveries is optimal. Also here, there is high uncertainty whether such a market will exist.

17
5) _Put options for ITMO sellers_ . The host may purchase put options to sell ITMOs near 2030, at a given (contracted) ITMO price. The options are executed when the host’s GHG emissions rate is below its NDC target. The World Bank has created a Pilot Auction Facility (PAF) for auctioning of options to sell verified climate assets (emissions reductions certificates) at a later date, at an auctioned price where the party offering the lowest sales price wins the auction. The winner is provided a guarantee that the climate asset can be delivered at a future date and price, but has no obligation to sell. See Vivid Economics (2018), World Bank (2017a). In our context, hosts would be given the option to supply ITMOs near 2030 at a fixed price, without obliging the host to sell. Such options purchases can be useful not only for net ITMO sellers, but possibly also for net ITMO buyers. For the latter group, put options could be combined with forward ITMO purchases, which could be excessive and potentially “undone” later by exercising acquired put options. Such transactions however appear as less attractive to low-income countries by imposing early costs (when put options are purchased, and investments made for later GHG abatement), while revenues (from ITMO sales when exercising the put options) come later. Another transaction structure with similar impacts for low-income countries (likely net ITMO suppliers) involves climate finance. An ITMO buyer country can finance mitigation in the low-income country via climate finance, and have the climate finance payment reimbursed when the ITMO transaction takes place ex post (as put options are exercised).

6) _Call options for ITMO sellers_ , combining fixed-price forward ITMO sales with state-contingent buyback of ITMOs using call options. This is a somewhat more complex mechanism than put option contracts considered above; no such trades have so far been proposed. Consider a host which has engaged in fixed-price forward ITMO sales but may feel insecure about fulfilling its NDC requirement when uncertainty is unfavorable ( _z_ takes high values). This host can then contract a sufficient number of call options, for ITMO purchase near 2030, to stay in NDC compliance and also deliver its ITMOs contracted forward. The relevance of this instrument requires that forward ITMO sales, combined with call options for ITMO buyback, are available to the host at an acceptable ex-post contract price.

7) _Call options for late ITMO purchases by net ITMO buyers_ . Forward ITMO contracting is not the only possible forward trading mechanism for net ITMO buyers. Having the option to buy 18
ITMOs later may be more convenient for hosts whose GHG mitigation cost are particularly uncertain.<sup>13</sup> These hosts are typically high-income countries with ambitious NDC targets.

8) _Use of climate finance and/or donor support_ . Climate finance cannot be used for direct purchase of ITMOs, but can be used to support the operation of ITMO markets, when considered as attractive or necessary. The ITMO trading markets, and their use by the parties, may appear (much) less risky when the markets and their transactions are strongly backed by donor financing.

9) _Opening up for Article 6 rules changes_ . Several rules today seem relevant for amendment. They include the allowance of banking; the opening up of ex-post markets; and the possibility of opening up to and/or stimulating the formation of carbon clubs under the PA.

We will in the following discuss in more depth, and explicitly analyze, four cases: the options cases 5-7, plus case 2 (ex-post backstop mitigation). These solutions will indicate how they, under our assumptions, can optimally be used by the parties, how trading volumes will depend on relevant parameters, and their welfare impacts, compared to when such alternatives are lacking.

We will also remark that opening up for banking of ITMOs beyond 2030 could have quite different implications given overall over-compliance of parties’ NDCs, versus a situation with overall under-compliance. With general over-compliance and perfectly functioning ITMO markets, total ITMOs produced will be excessive and parties will gain from banking their excessive ITMO amounts for use in following trading periods.<sup>14</sup> General, overall, under-compliance will lead to a fundamentally different situation. The ITMO market price in 2030 will then tend to be (very) high, giving parties with surplus ITMOs high incentives to sell these in the market to under-complying parties, instead of banking them. Some or many parties will then not be able to fulfill their NDC commitments, leading to default with possible withdrawal from the PA. Banking will be of little or no value. Intervention of donors in the ITMO market will neither be helpful, except that such interventions can reduce the degree of under-compliance by spurring increased late-stage

> 13 A pilot case, where this type of call options are being implemented, relates to an agreement on crediting of GHG emissions reductions from Peru’s solid waste sector, between the Peruvian government and the Nordic Partnership Initiative representing Nordic country governments. See Climate Focus (2018). 14 This has been the situation in the aftermath of the KP: Many parties are still sitting with bankable surpluses that, presumably, can be applied for compliance under the PA.

19
mitigation (for example, via late scale-up of investments in renewable technologies which are already available).

# **4.2 Put Options for ITMO Sellers**

We first consider put options for ex-post ITMO sales. This is a particularly relevant case for hosts that expect to be net ITMO sellers but may still not sell ITMOs early. We focus on a simple case, where the host is exactly in compliance with its NDC target given no ITMO trade, and has no net forward ITMOs sales, which implies _q + t_ is the effective carbon price facing the host’s private sector. From (4.2), the host is exactly in NDC compliance when its emissions are at a maximum ( _z = z0_ ), and the host has no net forward ITMO sales nor purchases.

Put options for future conditional ITMO sales cannot by themselves help the host to stay in NDC compliance. But they can increase the host’s expected revenues by making ITMO sales available for hosts in ex-post states with low _z_ .

The analytical derivation of the optimal strategy of a host which purchases such options is found in Appendix 2. We there show that the optimal number of put options purchased by the host is _q1_ is here the price paid per ITMO supplied ex post, and _q2_ the cost per put option purchased. From (4.2), when _z_ < _z0_ , the host’s ex post emissions are lower, and the host is more in over-compliance versus its NDC, and has more ITMOs to sell ex post. The optimal strategy of the host is to choose a cutoff level for _z_ , called _z1_ , above which the host covers its entire surplus supply of ITMOs ex post by put options, and below which the number of put options corresponds to the optimal level for _z = z1._ (4.3) provides the solution for the cutoff level _z1_ . When _z1_ is set higher, the number of put options purchased by the host, _(z0 – z1)/γ_ , is reduced. By reducing the number of put options, the host forsakes the most excessive amounts of possible ITMO sales, related to the lowest realizations of _z_ . Highly excessive ITMO levels occur with a small probability; purchasing extra put options to cover these events is not optimal. _z1_ is sensitive to the put option cost, _q2_ .

20
Note also that in the extreme case of _q2 ≥ q1_ (the cost of the option to sell ITMOs is at least as high as the ITMO price), no put options are purchased, since there are no net gains from ITMO sales.

Whenever _q2 < q1_ , some put options are purchased. Typically, _q2_ is only a fraction of _q1_ , implying that a host’s optimal options purchases could be large relative to the maximal number.<sup>15</sup> Optimized welfare for the host from having access to put options ex post (given no other access to ex-post ITMO sales) is: _A1_ is a constant representing welfare without put option access. _EW(p)_ implies a non-trivial value of put options access, easily (much) larger than the standard deadweight cost of imposing a moderate carbon tax _t_ (which is _t_<sup>_2_</sup> _/2γ_ ).<sup>16</sup> Inefficiency of this solution occurs as the number of ITMOs sold in the most favorable ex post states, with values of _z_ below _z1_ , is capped by the number of put options purchased, from (4.3).

Arguably, put options for future ITMO delivery will be demanded mainly by higher-income or emerging countries and not by low-income hosts. A cost to cover the option price must be incurred early; the same must any investments required to harness the later mitigation benefits; while the payments for exercising the put options come at the end point. This skew cost-benefit profile might however be alleviated by climate finance payments when such financing is required to make the market operative and available to lower-income hosts.

Finding countries willing to supply such put options may be challenging. They must expect to be future ITMO buyers, thus typically higher-income countries. Expected ITMO buyers also face uncertainty, which may make them unwilling to take ITMOs when these countries happen to be in actual compliance, as ITMOs are not bankable beyond 2030 under current Article 6 rules.

Several questions arise with this analysis, one is whether such an options market will necessarily exist; and if they can be purchased, whether they will always be honored ex post.

> 15 For example, in PAF pilot auctions carried out so far, the transacted put options costs have been between 15% and 40% of the transacted strike price for certified emissions reduction sales.

> 16 In particular, note that 2z0 represents the range of values of the uncertain variable (with same dimension as t).

21
Another question is whether an ITMO markets with ITMO market price of at least _q1_ will be open near the PA end point. If so, these put options will be worthless. Appendix 2 discusses such cases where put options are honored by the issuer, or are relevant to the host country, with probability _θ_ < 1. We show that the number of put options purchased by the host, _v(p)_ , will then equal The number of put options purchased will be reduced. Such purchases become less attractive for the host, as some (good) states will not require put options to be exercised. Welfare for the host will however increase due to the occurrence of the future good states.

# **4.3 Call Options for Net ITMO Sellers**

In this alternative, the host sells ITMOs forward early, and guards against future NDC noncompliance by purchasing ITMOs near 2030, by exercising call options.

The host’s NDC target is still given by (3.4), and its emissions in 2030 given by (3.6).

A detailed analysis of this case is found in Appendix 3. A main result is that the host will sell an amount of ITMOs forward equal to _v/γ_ , given by Here _q4_ is the call option price, while _q3_ is the cost of ITMO buybacks in 2030. We assume that _q3 > q_ (the contracted price of ex-post ITMO buybacks is higher than the ITMO forward price). The number of call options purchased by the host is: Regardless of the cost of ITMO buybacks, the host will choose to purchase at least some call options for such buybacks. The reason is that when only a few ITMOs are sold (and a few call options purchased), the probability that the host will need to purchase ITMOs ex post to stay in compliance is very small; while the forward sale of the corresponding ITMOs occurs for certain. The host must here be assumed to have the incentives to incur the buyback cost _q3_ ex post.

22
When (4.2) holds (the host is exactly in NDC compliance in its worst state given no call option access), the first main term in (4.6) drops, and the number of ITMOs sold forward equals the number of call options purchased. This number depends on the ITMO forward sales price, _q_ , minus the call option price _q4_ , incurred for all ITMOs sold, as all ITMOs may (in the worst case) need to be bought back for the host to stay in compliance for certain. The volume of ITMOs sold forward is reduced proportionately by the cost per ITMO purchased ex post, _q3_ ; and increased proportionately by _z0_ which indicates the uncertainty facing the host ex post.

Under certainty about the host’s emissions ( _z0_ = 0), the host buys no call options, and sells no ITMOs forward. Any forward ITMO sales would need to be matched by ITMOs purchased ex post for certain, which is here more expensive.<sup>17</sup> All ITMOs must be purchased back, at a higher cost _q3_ per ITMO, and _q4_ must be paid for availability of each option.

Given that (4.2) holds, the host’s GHG emissions are (using (3.6)) Emissions are lower than the NDC target given by (3.4). The host country is still in non-compliance for values of _z_ close to (not much below) _z0_ , due to the host’s forward sale of ITMOs from (3.4). The host is exactly in compliance, purchasing no ITMOs back, when _z = z1_ .

Optimized net welfare for the host from access to call options is found as: where _A2_ is a constant.

This sub-section has not discussed features of the supply side of this type of options contracting. Reasonably, such call options will typically be offered and issued by net ITMO sellers. A question is then whether the option issuer will honor its contractual duty to supply the required ITMOs if the call options are exercised by the option buyer in 2030. This is not problematic with more developed contingent or spot ITMO markets available at a late stage of the PA. Note however that

> 17 It can here not be advantageous for the host to sell additional ITMOs forward, and buy them back later under certainty.

23
it is exactly the possibility of not having such markets available, that raises the need for option contracting in the first place. A further question arising is then whether it may be necessary to provide availability of such options for hosts, using climate finance or other donor or IFI support.

On the other hand, if spot markets for ITMOs with low ITMO prices are available in 2030, the purchased call options will turn out to be unnecessary and not exercised.

Appendix 3 discusses both these cases. It is shown that uncertainty about the ability to exercise call options leads to a lower demand for such options. When ex-post ITMO spot markets with low ITMO prices are available, the number of call options purchased _increases_ . This is because forward contracted ITMO sales then becomes more attractive for hosts. Each forward sale needs to be covered by one call option for the host to still guarantee to stay in compliance in all possible states.

Consider finally how _q3_ (the contractual ITMO buyback price) and _q4_ (the call option price) are set. The call option issuer can keep its value of offering the call option contract at a given level by reducing _q3_ and increasing _q4_ . It should then be possible for the seller to push the ex-post price, _q3_ , down to a manageable level by increasing _q4. q3_ can then be set to ensure that the option will actually be exercised when needed. We assume as noted that _q3 ≥ q_ , but may still be limited so that the ex-post incentives to buy back ITMOs are preserved.<sup>18</sup>

# **4.4 Call Options for ITMO Buyers**

We will now consider the use of call options for contingent future ITMO purchases by parties which expect to be net ITMO buyers. These parties will more typically be high-income (or emerging) but not low-income countries. We will assume that these parties have access to a call options market; call option contracts are honored ex post; and hosts do not have access to an expost spot market for ITMOs. We still focus on a case where the party (net ITMO buyer) is exactly in compliance (but not in over-compliance) in its ex-ante state with highest GHG emissions (when _z_ = _z0_ ). Assume that these parties can sell and buy ITMOs in the forward market, but have zero net purchases of ITMOs. These countries are assumed to have “ambitious” NDC targets, implying that

> 18 This is different from the case, studied in sub-section 4.5 below, where an expensive “backstop” technology needs to be used for NDC compliance, which may not be ex-post incentive compatible for the host.

24
_s_ in (3.4) is “high”. Such countries have incentives to use call options so as to reduce their carbon tax, _t_ , required for NDC compliance.<sup>19</sup> In this case, _t = s + z0 – q – v_ , which means that when the number of call options, v/γ, is increased, the party’s carbon tax can be reduced equivalently. This reduces the party’s deadweight loss related to the carbon tax. The total carbon price for this host is in this case still _t + q_ . The party’s GHG mitigation is implemented by reducing its carbon tax to _t-v_ , where _v/γ_ is the number of call options acquired by the party for later possible ITMO purchases.

The party’s optimal call option purchase level is (see Appendix 4): (4.11) resembles (4.7) in sub-section 3.3, but differs somewhat. Call options are here purchased for two reasons: because it allows the party to relax its carbon tax, which is beneficial (as the party’s economic deadweight loss is reduced); and for holding call options which is an efficient way for the host to meet possible NDC under-compliance under uncertainty, when an ITMO spot market near the end point (with low ITMO prices) may not exist.

With certainty about the host’s emissions ( _z0_ = 0), from (4.11) no call options are purchased. The country then uses only the carbon tax, _t_ , to stay in NDC compliance. Under uncertainty ( _z0_ > 0), the country always purchases some call options regardless of their costs, represented by the two cost variables, _q3_ (the contracted cost of acquiring ITMOs at a late stage), and _q4_ (the cost per option).<sup>20</sup> Th number of call options purchased increases with the level of uncertainty ( _z0_ ), and when _q3_ and _q4_ are lower. Greater uncertainty leads to a need for more forceful mechanisms to avoid being in non-compliance. _v(c)/γ_ drops when either cost element, _q3_ (the contracted ITMO

> 19 A simplification in this case is to assume that these parties do not purchase ITMOs forward to reduce their statutory carbon tax by even more than what is accomplished by (4.10). The carbon tax is reduced only to the extent that call options for future ITMO purchases are acquired. See Appendix 4 for further discussion of this case. 20 A condition is here _z0 + s – q4_ > 0, which we assume holds.

25
price) or _q4_ (the cost per call option) increases. _v(c)/γ_ can be higher or lower in (4.11) compared to (4.7). It is lower (higher) when the ITMO forward trading price, _q_ 3, is high (low).

Also here, as in sub-section 4.3, we assume that no ex-post spot market for ITMOs with “moderate” ITMO prices (lower than _q3_ ) is available during late stages of the PA (near 2030). With a positive ex-ante probability that such markets are available, it becomes more attractive to utilize late-stage alternatives for ITMO purchases, since purchasing offsets through the late ITMO market is then cheaper. This also stimulates the net ITMO forward sale, which must be matched with acquiring more call options (to ensure NDC compliance when the ITMO spot market is not available). The solution is further discussed in Appendix 4.

# **4.5 Forward Contracting of ITMO Sales with Unlimited (Expensive) Backstop Mitigation**

We now consider a case where option contracts are not available, the host can sell ITMOs forward, and a “backstop” exists which enables the host to supply extra mitigation at a cost _r_ per ton of CO2 abated ex post. We assume that the cost _r_ is “high” relative to the forward ITMO price, _q_ .

There are (at least) three approaches to this problem. With the first, the host has no limits on ex post mitigation at unit cost _r_ .<sup>21</sup> The second approach implies a limit, _R0_ , on ex post mitigation at this cost. Both these approaches assume that the host country is willing to implement this expensive mitigation ex post. A third alternative is that the host’s lacks the willingness to comply with its NDC commitment ex post when _r_ is above a certain level.

# **a) No constraints on backstop mitigation**

We first assume no constraints on the host’s ability and willingness to implement extra mitigation ex post, at constant marginal cost _r_ . This cost must be compared to the benefit of the ITMO sales at price _q_ , in amount _v/γ_ . When the host is exactly in NDC compliance in the worst possible state when not selling nor buying ITMOs forward ( _q + t – z0 – s_ = 0; (4.2) holds), optimal forward ITMO sale equals ex-post backstop mitigation, _v(b)/γ_ (see Appendix 5):

> 21 More reasonably in this case, the marginal cost of additional mitigation would not be constant but instead increasing. This can be treated relatively simply by assuming that the relevant marginal cost, r, is what will be realized at the equilibrium point.

26
(4.12) takes virtually the same form as (4.7) for purchase of call options to stay in compliance ex post. A difference is that (4.12) has no deduction for purchase of call options (represented by _q4_ in (4.7)), but on the other hand a (much) higher cost of ex post mitigation, _r_ , relative to the ex-post ITMO price, _q3_ , in (4.7).

_r_ could be large relative to _q_ . For example, if _r = 2q_ , the number of ITMOs sold forward is _v/γ = z0/γ_ . In this special case, ITMO forward sales comprise half the difference in emissions across the entire ex post emissions distribution facing the host. Whenever the mitigation distribution has a positive spread ( _z0_ > 0), ITMO forward sales will be positive regardless of the backstop cost (any large _r_ leaves _v/γ_ > 0). Higher _r_ reduces forward ITMO sales proportionately.<sup>22</sup> As in cases with options, ITMO sales also increase with greater uncertainty (higher _z0_ ). Greater uncertainty provides more scope for gains by selling ITMOs forward, and cover deficits ex post with backstop mitigation. Put otherwise, while ITMO forward sales have probability one, the ex-post backstop mitigation costs have lower probability and have less weight in the calculous of the host.

Optimized net welfare of having access to the backstop alternative is (see Appendix 5) Where _A4_ is a constant. The host’s GHG emissions rate is here determined in the same way as in Appendix 3.

Our assumption of a constant marginal cost of additional backstop mitigation, _r_ , is unrealistic. More likely, _r_ increases in the amount of backstop mitigation applied. If so, formulas (4.12) and (4.13) are imprecise, as _r_ would need to be replaced by the marginal mitigation cost at the equilibrium point, _r’_ . Typically, _r’ > r_ ; _v(b)_ would be reduced, and _RES*_ could be higher or lower.

# **b) Constraints on amount of backstop available ex post**

Consider a limit _R0_ on the amount of ex post mitigation available to the host. This translates to a maximum ex ante ITMO sale given by _v0/γ = R0_ . This constraint will have an impact if and only if _R0 < v/γ_ from (4.12). The host country’s ITMO forward sales will then equal _R0_ .

> 22 In our model _r_ is assumed constant. It is much more realistic for _r_ to increase in the amount of backstop mitigation. _r_ should then be replaced by its marginal value in (4.12), which provides an approximation.

27
# **c) Lack of willingness to stay in NDC compliance ex post**

When _r_ is (very) high, backstop mitigation may not be executed even when available. Consider _z_ close to _z0_ ex post, so that the host would be NDC non-compliant in the absence of backstop mitigation given forward ITMO sales, and has no other mechanism for achieving compliance, and no further ex-ante arrangements to ensure compliance. Assume that the available amount of backstop mitigation exceeds _v(b)/γ_ from (4.12). It is then _ex ante_ optimal for the host to resort to backstop mitigation to stay in compliance. But _this may not be optimal ex post_ . When the host is not able to commit to later mitigation ex ante, it may not be willing to execute it ex post. When _z_ turns out to be close to _z0_ , the host country may instead choose to default on its NDC commitment if that is viewed as a “cheaper” alternative, including reputational or other losses following from an NDC default.

This outcome may have several backgrounds. The host country may have a different government in 2030 which may not wish to carry out the required (perhaps, painful) ex post mitigation imposed by another government. Similar cases were observed under the Kyoto Protocol (KP), even for wealthy countries. Canada opted out of the KP when it discovered, near the end of the implementation period, that compliance was not achievable with current mitigation instruments. Australia dropped out when changing to a more conservative government.

When the host country’s primary target is to stay in NDC compliance ex post, and does not have access to offset markets ex ante nor ex post, greater uncertainty about the emissions level at the end point will tend to increase its early GHG mitigation activity. In one sense this is “helpful” as it serves to increase a country’s overall mitigation level. On the other hand, it increases the host’s mitigation costs; and makes it less attractive to the host to later tighten its NDC target. It also provides for an inefficient solution as the countries with the greatest relative uncertainty are those most in need to overshoot their mitigation levels.

We finally remark that a very similar “backstop” alternative can be developed also for net ITMO buyers, in similar fashion to the analysis in sub-section 4.4. Instead of using the backstop alternative to expand its forward sales of ITMOs, such a host will rather reduce its GHG mitigation, by lowering its carbon tax _t_ , as a more economical alternative for such a host.

28
# **4.6 Use of Climate Finance and Other Donor Support**

In the alternatives we have discussed it is far from clear that the required markets can be enabled. The option market solutions require a credible and liquid option supply side to satisfy option demand; and these markets must be sufficiently liquid to always satisfy desired supply. Existence of such markets in 2030 cannot be guaranteed under current Article 6 rules. A key problem is that banking of ITMOs beyond 2030 is not allowed under current rules. Trading of put or call options at or near the end point could be problematic when the issuing party is in over-compliance and at the same time is required to purchase ITMOs when put options are executed; or is in undercompliance when required to sell ITMOs when call options are executed. Positive correlations of mitigation across hosts can exacerbate these problems.

A question is whether donor funding can overcome such problems. Note then first that climate finance is not allowed for direct purchase of ITMOs. Subsidizing ITMOs through providing climate finance to underlying mitigation activities is not prohibited by Article 6 rules but typically inefficient (Strand 2019). But when the alternative is possible lack of market existence, external finance which enables these markets could have substantial positive efficiency impacts.

There exist technical ways in which donor funding can be deployed for ITMO market support in these situations. One donor (or donor group) could set up two technically separate modes of ITMO market and ITMO financing: one climate finance fund, and one “ITMO fund”.

This donor could then support mitigation activities in low-income countries with its climate finance, and at the same time purchase “conditional call options” for ITMOs corresponding to the emission reductions achieved with the supported mitigation activity. The host would then be obliged to transfer ITMOs only if it achieves over-compliance relative to its NDC target (and the ITMO transfer would be ex-post to target achievement).

If the call option alternative is exercised by the host, the donor would need to use its ITMO funding to repay its ex-ante provided climate finance.

More generally, all providers of climate finance could consider allowing for similar ITMO transfers, provided that the climate finance is being reimbursed by ITMO funds.

29
A question is whether donors would be willing to put up funds for such purposes, in adequate amounts to assure market actors that ITMO markets will be operative during the final stages of the PA. As of today, resources allocated globally to dedicated climate finance are small (of the order $3 billion per year) and could currently not play such a role.<sup>23</sup> On the other hand, presuming that donors have serious concerns for mitigation at a global level, one could easily envisage a big increase in such funding if necessary to make the ITMO markets operative and credible, when this is fully recognized by donors and effectively communicated to the relevant PA parties. Excess funds would then be used for purchasing and stimulating global mitigation in excess of NDC targets (also beyond the targets of these donors). The key issue for donors should then be the cost imposed on them per ton CO2 mitigated, which could be moderate, or even potentially negative if ITMO market efficiency (or even market existence) would otherwise be in peril.

# **4.7 Opening Up for Article 6 Rule Changes**

A main Article 6 rule change, that could improve on the possibilities of market existence and functioning, would be to allow for banking of ITMOs beyond 2030, and to the next implementation period of the PA. Revisions of Article 6 rules are however not planned to happen until 2028, which would be too late to have impact for the current implementation period which ends in 2030. Thus, unfortunately, the possibility for such rules changes to have impacts on execution of the PA agreement at the moment (May 2022) seems remote.

# **5. Conclusions and Final Comments**

We have in this paper discussed issues raised by uncertainty about NDC compliance among parties to the Paris Agreement (PA), and how these problems can be alleviated by alternative market modes of ITMO transactions. The traditional market form, used widely for the two trading mechanisms, the Clean Development Mechanism (CDM) and Joint Implementation (JI), under the KP, was (early-stage) forward contracting with later verified emissions reduction (VER) delivery (corresponding here to ITMO delivery). With high uncertainty about mitigation outcomes (and parties’ abilities to fulfill their NDC responsibilities based on own policies only), such forward contracting may under the PA however jeopardize NDC fulfillment. Parties may then need to have available additional strategies and market mechanisms to ensure NDC compliance. This paper

> 23 See World Bank 2020.

30
emphasizes four alternatives for handling such uncertainties. Three of them imply using option markets: 1) Put option contracts for ITMO sellers, for late ITMO sales when sellers are in NDC over-compliance. These are relevant for parties which aim to be net sellers in the ITMO market and do not (necessarily) expect a future spot market for ITMOs with high ITMO prices. 2) Forward ITMO contracting combined with call options for (late) buyback of ITMOs, for ITMO sellers. 3) Call options for late ITMO buybacks to be used by ITMO net buyers. Alternatives 2 and 3 are relevant for the parties when future ITMO spot markets with “reasonable” (low) ITMO prices cannot necessarily be expected. The fourth alternative relies on establishing precautionary strategies for mobilizing extra (“backstop”) mitigation options. The paper provides explicit and highly intuitive solutions for optimal option purchases and precautionary strategies, which rely on specific assumptions about production structure (linear-quadratic production functions) and uncertainty regarding hosts’ ex post GHG emissions (uniform probability distributions).

Among the four alternatives analyzed, 1 and 2 both serve to reduce or eliminate the risk of noncompliance under uncertainty for ITMO sellers; while at the same time making sure that these hosts can engage in forward ITMO transactions when desirable. Alternative 2 embeds a more advantageous revenue profile for low-income hosts than alternative 1, as alternative 2 permits hosts to sell ITMOs forward at a possibly high value, thus obtaining net mitigation-related funds early. Alternative 1 instead implies early costs (for purchasing put options), while revenues (from ITMO sales) come later. Alternative 3 is most relevant for higher-income countries which are uncertain and worried about their final NDC compliance.

We have also calculated the welfare gains for a party from having access to each of the four alternatives, under our model assumptions. These welfare gains can be substantial. One might here think of a net welfare gain relative to the “backstop” alternative which does not depend on options markets. Note that we have not considered welfare gains for “the other party” to each type of options market transaction (e. g., the ITMO buyer in cases where ITMO seller welfare change in calculated), which may also be substantial.

For all the three options alternatives we have studied, market non-existence and failure are clear possibilities as “the other side” of the market may in all cases be thin or even absent. Market support by donor or IFI funding may be required for assuring that these markets function adequately. We have argued that donors may be willing to (and ought to) put up the required funds 31
to ensure smooth ITMO and options market functioning. Our “backstop” alternative can be considered a “reserve” (or “last resort”) alternative relevant only when no other alternatives are available for relevant hosts. We show that even when expensive “last resort” mitigation may in some cases be necessary for a host to stay in ex-post compliance, (potential) ITMO-selling hosts may still be willing to sell ITMOs forward and use the “backstop” alternative for ex-post compliance at least to some degree. But high cost of the “backstop” can be problematic as ex-post incentives to implement it may fail; if so, this alternative will no longer be incentive compatible and thus not viable.

We have throughout assumed that all parties are highly committed to fulfilling their NDCs, and that uncertainty for individual hosts takes a very simple form and is limited to a given range of outcomes, determined by a uniform distribution. We assume that all hosts make sure, through sufficient levels of GHG mitigation, that their NDC targets will be reached for certain. In our analysis we have also, for the most part, taken each party’s basic GHG mitigation level, as well as its NDC target setting, as exogenous. A complete analysis of these topics is beyond the range of what this paper can cover.

A main result from our analysis is that uncertainty about mitigation outcomes makes hosts more cautious in their mitigation policies, which means more mitigation and lower emissions than otherwise. In this sense, uncertainty can be considered as helpful to global mitigation. But such an unambiguous conclusion might ignore important dynamics related to PA implementation. NDC mitigation targets are flexible, and are expected to be updated and made more ambitious as the PA implementation period progresses. As we have shown, the parties’ welfare is increased substantially by access to forward and option markets. Getting access to these markets can then give “room for” selecting higher NDC ambition levels and more ambitious mitigation targets. Edmonds et al. (2021) indicates that use of the Article 6 trading mechanisms could lead to a drastic increase in mitigation implemented by the PA, and is based on exactly this argument. A key point here is that the process of updating to more ambitious NDCs over time can be curtailed when uncertainty is greater. The overall impact of uncertainty on global GHG mitigation under the PA is then unclear.

This paper represents the first formal analysis of the implications of options market trading for the operation and likely outcomes for global GHG mitigation under the PA. Several loose ends are 32
however left. We have focused on the demand side of the forward ITMO markets and not, in similar formal ways, analyzed these markets’ supply sides. We have neither discussed, to any depth, all relevant issues related to the overall functioning of the ITMO markets. We need to further study key differences that are likely to arise with general over-compliance (when parties typically wish to bank excessive ITMOs), versus general under-compliance (when defaults will occur, with some, perhaps many, parties withdrawing from the PA). Another weakness is that only two points of time, “ex ante” and “ex post”, are explicitly considered in the analytical modeling. Instead, several intermediate time points could be relevant at which stock taking and NDC updating will take place. The paper specifies no mechanism for possible updating of NDCs, nor for updating of uncertain variables and states and the optimal climate policy responses to these. Such topics must be left for future research, hopefully soon as the need for well-functioning markets for implementing the PA targets, and a full understanding of how such markets work, is already urgent, and will soon become even more urgent.

33