Risk Aversion and Institutional Information
Disclosure on the European Carbon Market
Julien Chevallier∗, Florian Ielpo†and Ludovic Mercier‡April 4, 2008

Abstract
This article evaluates the impact of information disclosure on changes
in investors’ risk aversion on the European Carbon Market using the
newly available option prices dataset. Since the price collapse that
occurred on April 2006 due to the verification of 2005 emissions, investors are concerned by the emergence of future shocks related to
the negotiation of National Allocation Plans for Phase II. Following
the methodology existing for stock indices, we recover empirically risk
aversion adjustments on the period 2006-2007 by estimating first therisk-neutral distribution from option prices and second the actual distribution from futures. Our results show evidence of a dramatic change
in the market perception of risk around yearly compliance events thathas not been assessed yet.

JEL Codes: C14; G14; Q54
Keywords: EU ETS; Risk Aversion; Option Prices; Futures Prices∗
Corresponding author. EconomiX-CNRS, University of Paris 10, Department of Economics, Office G-307a, 200 avenue de la République, 92001 Nanterre Cedex, France. Tel:
+33 1 40 97 59 36; fax: +33 1 40 97 77 84; jchevall@u-paris10.fr†
CES-CNRS, University of Paris 1, Centre d’Economie de la Sorbonne, 106 Boulevardde l’Hopital, 75013 Paris, France. ielpo@ces.ens-cachan.fr‡
Dexia Credit Local, Paris, France. ludovic.mercier@clf-dexia.com

1

Electronic copy available at: http://ssrn.com/abstract=1117184

1Introduction

The European Union Emissions Trading Scheme (EU ETS) was created on
January 1, 2005 by the European Commission (EC) to foster early compliance with the greenhouse gases emissions reduction targets agreed in the
Kyoto Protocol. Its successful implementation is currently being evaluatedagainst its simplicity and the fairly transparency of the trading mechanisms
instored. As such, the EU ETS covers up to 46% of CO2 emissions from
European energy-intensive industries. Every year, each industrial plant isallocated EU allowances (EUA)1 corresponding to its cap and must restituteas many allowances as verified CO2 emissions. 2.2 billion of allowances wereallocated to 10,600 installations across 27 EU Member States in 2005-2007
which are tradable all around Europe on exchanges and by over-the-counter.
The next two phases of the scheme are interconnected2 and will take place
during 2008-2012 and 2013-2020.
Yet this scheme raises various design issues related to the efficiency andequity of such market-based instruments. An efficient system leads to theequalization of marginal abatement costs among participants, yielding aunique market price that acts as a medium-term signal for investors to makecost estimates of delivering different levels of energy efficiency and how much
emissions abatement to undertake. An equitable system consists in allocating allowances based on a uniform criteria that is mostly perceived as fair
and agreed upon by the various stakeholders.
During its Pilot Phase, the EU ETS has failed to provide these right incentives. First, after a price "collapse" on April 2006 due to the publicationof the 2005 verified emissions data by the EC, the EUA spot price of maturity December 2007 has been asymptotically decreasing towards zero becauseof the impossibility to transfer allowances to the next period. This provi2

Electronic copy available at: http://ssrn.com/abstract=1117184

sion may seem justified ex-ante, since nobody had a clear idea of the exact
number and the volume of traded allowances, but it prevented the schemefrom delivering its price signalling message in terms of CO2 abatement efforts needed in the EU to meet the Kyoto targets. Second, the allocationof allowances based on grandfathering and prior use rules did not achieve
its equity objective as some sectors such as power producers were far moreconstrained than other participants who received an amount of allocation
close to their business-as-usual scenario.
Thus, the EU ETS Review3 pointed out the necessity for the EC to act
more as the central authority entitled to set firmly emissions caps for Phase
II and to restore the scarcity of allowances equally among sectors, including
the sectors that will be included in the scheme in Phase III4 .
The role of coordinator, educator and enforcer played by the EC is central
to the analysis of investors’ risk aversion developed in this paper. At the startof the EU ETS, most of the information available for trading was deemedas speculative. Consequently, we attempt to characterize investors’ hedging
strategies for this new carbon commodity by asking the following central
question: can we statistically identify a shift in investors’ risk aversion aroundyearly compliance events imposed by the EC?
To our best knowledge, this analysis constitutes the first tentative assessment of risk behavior on the EU ETS since it is based on newly available
plain vanilla option prices data on the European Climate Exchange whichtransfer the risk of financial exposure between market agents. Chesney andTaschini (2008) provide an application of CO2 price dynamics modelling tooption pricing, but their study is only based on numerical simulations.
We retrieve empirically investors’ risk aversion on the EU carbon market based on the relationship that exists with the risk-neutral and histor-

3

ical probabilities as detailed by Jackwerth (2000). Yet our methodology
to recover risk aversion from option and futures prices slightly differs from
Jackwerth (2000) whose dataset with monthly frequency would yield to few
observations on this new commodity market. Rather, we base our analysis on non-parametric kernel regression (Aït-Sahalia and Lo (2000), Contand da Fonseca (2002)) to estimate the risk-neutral probability distribution
and on an asymmetric GARCH model to estimate the historical probability
distribution (Rosenberg and Engle (2002)). Such an approach proved to
be useful in documenting changes in implied risk aversion for major equity
indices.
We find some evidence that shifts in investors’ risk aversion are readily
observable on the EU ETS following the disclosure of institutional information by the EC on April 30 of each year that corresponds to complianceresults. Moreover, we observe different lower levels of volatility for EUA
price series of all maturities after the 2006 compliance period. This latter
result suggests that institutional information disclosure has a strong market
effect. Besides, our results indicate periods of increasing markets coincidewith periods of higher volatility. This inverted leverage effect reveals that,
contrary to equity markets, the risk is associated with increasing allowance
prices in a context of a low environmental constraint. Expectation building is
becoming more efficient on the EU carbon market since market agents gradually integrate accurate information published by the EC concerning the levelof CO2 emissions compared to allocated allowances, be it at the installationor aggregated levels. Thus, we highlight the role played by the regulator inchanging market participants’ expectations concerning amendments of thescheme.
The remainder of the paper is organized as follows. Section 2 discusses

4the expected investors’ risk perception with respect to institutional design
features of the EU ETS. Section 3 details the estimation methodology torecover the risk-neutral and historical probabilities from option and futures
prices. Section 4 discusses the empirical results. Section 5 concludes.

2

Risk Behavior on the EU Carbon Market

The characterization of risk behavior and risk management strategies on theemerging EU carbon market constitutes an important field of research forseveral reasons.
First, the rents distributed to existing incumbents on a "first-come, firstserved" basis represents a market value of =C40 billion that was created at thesame time as CO2 emissions were capped. This allocation methodology, also
known as grandfathering, is the most frequently observed since the market
determines the size and nature of property rights and there are less politicalpressures to instore such as scheme. Its main benefits lie in the fact thatit recognizes incumbents and specific non-deployable investments, rewards
first-movers and economizes transaction costs. Since January 1, 2005 carbon allowances therefore form another asset in commodities against which
industrials and brokers need to hedge. As the volume of transaction on
the EU ETS has been increasing steadily from 262 million tons in 2005 to
1,443 million tons in 2007, this trading activity reflects market participants’progressive learning of this new financial market. Thus, we are interested
in examining closely the formation of investors’ risk appetite related to the
diffusion of institutional information.
Second, during Phase I of the EU ETS (2005-2007), spot prices experienced a high level of volatility around each compliance event. Since industrial
installations have the obligation to surrender to the EC the exact number
5

of allowances that matches their verified emissions each year around end of
March, this institutional compliance event may be used as the cornerstone ofeach major change in investors’ risk aversion. The official report by the European Commission is disclosed by mid-May5 , but installation operators havealready a fair amount of information between the publication of their own
report and the compilation of verified emissions by the EC to approximate
the global level of emissions relative to allowances allocated and to adjust
their anticipations. By the end of April 2006, a spot price correction of 54%
within four days followed the announcement by the EC that CO2 emissions
were approximately 3% lower than the allocated allowances during the 2005
compliance period (Ellerman and Buchner (2008)). This particular kind of
institutional event led to a shift in investors’ risk aversion that we aim at
capturing in this paper.
Third, carbon allowances exhibit strong characteristics of being a nonstandard commodity (Paolella and Taschini (2008)), since installations do
not need to physically hold allowances to produce but only to match themwith verified emissions for their yearly compliance report to the EC. Consequently, the probability of a potential illiquidity trap exists if market participants face a market squeeze during the compliance event. This specificity
of EU allowances adds another line of argument to justify our specific interest in the formation of risk aversion and purchasing strategies by market
participants around compliance events.
On October 2006, following multiple EC announcements6 to tighten allocation caps for Phase II, we observe a divorce between the EUA spot and futures price series. While the EUA spot price pattern was decreasing towards
zero until December 2007, the EUA futures price series stabilized around=C20 per ton. This price signal is currently sustained on the medium-term

6

by the decision of the European Council to maintain the European carbon
market at least until 2020. Thus, the futures price series seems to reflect
better the dynamics behind investors’ anticipations and hedging strategies,
which explains why we have decided to work with futures instead of spot
prices.
It appears interesting to highlight for the purpose of this study that,around each yearly publication of verified emissions results by the EC, investors’ anticipations with respect to risk are changing. Indeed, despite its
recent creation, Seifert et al.

(2007) emphasize that most market agents,

and not only large market players such as power producers, are attempting
to estimate accurately CO2 emissions levels and abatement efforts on the
EU ETS. In what follows, we test the hypothesis that strong reversals ininvestors’ anticipations occur during the 2006 compliance event7 . Moreover,
we expect the level of volatility to decrease after the diffusion of informationby the EC which tends to dissipate previously misleading trading informationon this new market.
In this section, the discussion on EU allowance characteristics in terms of
trading patterns and price developments leads us to argue that institutional
information disclosure by the EC has a clear effect on adjustments in risk
behaviors since it provides reliable market updates on agents’ positions interms of actual CO2 emissions with respect to allocated allowances. In thenext section, our estimation strategy is detailed to identify statistically thosechanges in investors’ risk aversion that are expected to occur around yearlycompliance events.

7

3

Estimation Methodology

As presented in Bertholon et al. (2007), there are several ways to deal withthe risk aversion estimation problem. Absolute risk aversion can be expressedin terms of the historical and risk-neutral probability distributions (AïtSahalia and Lo (2000), Jackwerth (2000), Rosenberg and Engle (2002)):

RA(x) =

f 0 (x) q 0 (x)
−
f (x)
q(x)

(1)

where q(x) is the risk neutral density and f (x) is the historical density acrossstates. It is easy to see that once two of them are known, the third one isreadily available as a by-product. Here, we have at hand enough data toestimate both the risk neutral and historical distributions without making
assumption about the shape of investors’ risk appetite. Thus, risk aversion
will be deduced from our estimation of the risk neutral and historical probability measures. Following the terminology established in Bertholon et al.
(2007), this approach fits the "Risk-Neutral Constrained Direct Modelling"strategy, i.e. we make limited assumption on the risk neutral and historical
distributions and no assumption on the pricing kernel.
Following Aït-Sahalia and Lo (2000), we estimate the risk neutral distribution non-parametrically, while the historical distribution is recovered froma semi-parametric GARCH procedure (Barone-Adesi et al. (2007), Rosenberg and Engle (2002)). As explained above, from these estimates we will
deduce an empirical estimate of risk aversion. This methodology will thenallow us to investigate the empirical characteristics of investors’ risk aversion
on the European carbon market, along with its potential shifts around yearlycompliance events.
Let us first detail how to recover both the risk-neutral and historical8

probability distributions.

3.1

Risk Neutral Probability Distribution

Under no arbitrage restrictions, the price of an European call is:Z +∞C(τ, K) = B(τ )(ST − K) q(ST ) dST = B(τ ) EQ [(Sτ − K)+ ]

(2)

−∞

where C(τ, K) is the premium for a call option of time to maturity τ andstrike price K, S is the underlying asset price and r is the risk-free interest
rate. B(τ ) is the price of a zero coupon bond with maturity τ and represents
the corresponding discount factor, i.e. B(τ ) = e−rτ . EQ [.] denotes the
expectation computed using the risk-neutral distribution. Following Breeden
and Litzenberger (1978), we have:∂ 2 C(τ, K)= B(τ ) q(ST |ST = K).
∂K 2

(3)

Equation (3) describes the formal relationship between the second derivativeof the call price with respect to the strike price and the risk-neutral density.
Since we are mostly interested in recovering the "average" pricing kernelin the option market, we propose to use Aït-Sahalia and Lo (2000) non
parametric estimator to the risk neutral density. This estimator uses thelink between implied volatility and the risk-neutral distribution: since both
implied volatility and risk neutral distribution depend on the moneyness,
it is possible to infer the risk neutral distribution from implied volatilities
series. When σ(K) is a function of the strike that is twice differentiable, using
the Black-Scholes model and eq.(3) result, Andersen and Wagener (2002)

9

showed that:
∂2C
(4)
∂K 2



2
√ 
√ ∂2σ
1
2d1
∂σ
d1 d2 K τ
∂σ
√ +
.
=
+
+K τ
σ(K) ∂Kσ∂K∂K 2
σ(K)K τq(Sτ |Sτ = K) = erτ(5)For σ(τ, K) to be expressed as a function of the strike price, it may be
estimated either parametrically with a polynomial8 or non-parametrically.
Aït-Sahalia and Lo (2000) recommend the use of a non parametric estimator of the volatility surface (see also Cont and da Fonseca (2002)). Thisestimator is particularly adapted to situations where we do not need a dayby-day estimator of this probability density function, but an estimator of theaverage risk neutral distribution over a large time period. This approach is
close to what may be found in Jackwerth (2000). We propose to use thenon-parametric approach that also offers the advantage to be more robust to
market anomalies which are very likely to occur on such a new commodity
market. Thus, we introduce a non-parametric Nadaraya-Watson estimatorwith k = K
S defined as the moneyness and τ fixed as in Cont and da Fonseca(2002):
k − kjτ − τi
K
K
σ(τi , kj )
h1
h2
i j


σ(k, τ ) =X  τ − τi k − kj
K
K
h1
h2

(6)

1 2
1
K(x) = √e− 2 x
2π

(7)

X



i j

with

the Gaussian kernel. {h1 , h2 } are bandwidth parameters that determine
the degree of smoothing. As pointed out by Cont and da Fonseca (2002),
too small values will lead to a bumpy surface while too large ones will smooth10

away important details. On the optimal choice of these parameters, we follow
the methodology used in the latter paper. Once we have this non parametric estimator of implied volatility, we are able to derive it with respect tothe strike price and then use it in eq. (5) to finally recover the risk neutral distribution for a given horizon τ . It is noteworthy to remark that thismethodology imposes martingality restrictions as a by-product. These restrictions are essential to recover the risk neutral distribution (Jurczenko etal. (2001)).
Finally, we recall how to obtain implied volatility series from option
prices. Building on the previous notation, C(τ, K)obs is the observed call option price and C(τ, K, σ)BS is the Black-Scholes (BS) price computed using
the implied volatility σ. By definition, we have C(τ, K)obs = C(τ, K, σ)BS .
The implied volatility of the strike price is obtained by numerically inverting
the BS formula, which can be done by solving:min (C(τ, K)obs − C(τ, K, σ)BS )2σ(8)Then, allowing σ to be a function of the strike price, we may use eq.(3)to recover the risk-neutral distribution.

Next, we present our methodology to recover the historical distribution.

3.2

Historical Probability Distribution

There exists an emerging body of literature on the spot-forward parity in the
EU ETS. Seifert et al. (2007) reveal a very steep spot price volatility increase
when coming toward the end of the trading period. Borak et al. (2006) also
pointed out that the term structure for allowance prices changed from initial

11

backwardation to contago and is subject to abrupt changes of expectations.
This situation provides a first element of justification to use futures instead ofspot prices series in our dataset. Besides, as explained in Section 2, futures
exhibit a more coherent price pattern since the April 2006 price collapsethat occurred for all maturities. This approach is also in line with Paolella
and Taschini (2008) who argue that the study of spot price dynamics isinadequate due to early political uncertainties on the allowance market. That
is why we prefer to consider futures contract prices of maturity December
2008 and December 20099 . As for the estimation methodology, Benz andTruck (2006) and Paolella and Taschini (2008) strongly support the useof GARCH specifications to model the returns of CO2 emission allowances
which is also developed below.
Following the literature dedicated to the stock market, we choose tomodel the historical distribution using a semi-parametric asymmetric GARCH(p,q) model as in Barone-Adesi et al. (2007). We discuss the goodness of fitof the chosen model compared to other specifications for the CO2 returnseries in the next section. Note the methodology adopted by Jackwerth(2000) is not applicable because the monthly frequency used would lead to
few observations. Besides, it is worth underlining that unlike Rosenberg andEngle (2002) and Jackwerth (2000) we use longer term option prices witha 16-month investor horizon10 to display our results.
The estimated model is:
rt =µ + t
(9)2
σt2 =ω0 + ω1 2t−1 + ω2 σt−1
+ δ max(0, −t−1 )2

22 ) < 0 towith t ∼ N (0, 1). If δ > 0, we have Cov(rt − rt−1 , σt−1
− σt−2take into account the asymmetry also known as the skewness effect in stock
12

price dynamics and the leverage effect in financial economics. The model isestimated in a Pseudo Maximum Likelihood (PML) framework by assuming returns are Gaussian. As Gourieroux et al.

(1984) put it, estimatingby PML will lead to unbiased estimates even if the probability distributionfunction does not necessarily contain the true distribution. Barone-Adesi etal. (2007) and Rosenberg and Engle (2002) proved the robustness of thisapproach. The estimates covariance matrix is estimated using the BHHH
matrix (see Berndt at al. (1974)). We then recover the estimated residuals
and bootstrap them to simulate sampled paths for any maturity of interest. Using these simulated returns, we estimate the conditional historical
distribution density using the following Gaussian kernel:Sj − SSKhj .
f (S) = X 
Sj − S
K
h
X



(10)

j

As in Jackwerth (2000), we select the following bandwidth parameters:
1.8σ
h= √
5
n

(11)

where S is a point of the future value of the asset price support, h is thekernel bandwidth, σ is the standard deviation of the sample returns and n is
the number of observations. Using this methodology, we intend to cope with
the non normality of future returns as diagnosed in the next section. Thus,
our results will not be tainted by any ill-chosen distribution assumption.
The next section presents the results of our estimation strategy.

13

4

Estimation Results and Discussion

This section briefly summarizes the data used, and then discusses the results.

4.1

Data

The data used include plain vanilla option closing prices in =C of maturity
December 2008 and December 2009 traded from October 1, 2006 to November 23, 2007 on the European Climate Exchange (ECX), the most liquid
trading platform for carbon derivatives with approximately 86.5% of the total exchange-based trades of allowances. Tables 1 and 2 display the numberof available observations for each contract and the average volume for eachstrike of option prices in the dataset. Descriptive statistics regarding eachcontract may be found in Tables 3 and 4 (see the Appendix). For both contracts, the negative skewness indicates a distribution with an asymmetrictail extending towards more negative values. The positive excess kurtosis
suggest a fat tailed empirical distribution and the presence of extreme observations. Thus, as stated by the Jarque Berra test statistics, residuals are
not Gaussian which is characteristic of financial time-series. The Box Pierce
statistic reveals residuals are not autocorrelated. We only consider optionsof moneyness included between 0.5 and 1.5 to remove unreliable observations
characterized by a low volume and a low sensitivity to volatility.
We also use futures prices drawn from ECX for the same period11 . Figures 1 and 2 show strong reversals of the futures price series depending on
the time period, i.e. before and after the yearly compliance event. The underlying asset of the contracts are first and second period spot prices. As
underlined in the previous section, due to infrequent trading of spot prices,
we prefer using future prices which reflect more accurately agents’ trading
anticipations and hedging allowance strategies12 . The risk free rate is the14one year swap rate in =C commonly used by market agents.
Over the period going from October 1, 2006 to November 23, 2007, wechoose to split our dataset before and after the yearly compliance event imposed by the EC to evaluate investors’ changes in anticipations. Installations
need to report by the end of March their verified emissions that occurred during the preceding year. For instance, CO2 emissions at the installation level
for the calendar year 2006 were reported on March 30, 2007. Then, theinformation becomes publicly available when the EC officially publishes its
report between the end of April and mid-May. Thus, to reflect these institutional events and to capture the state of information available to all market
participants with most accuracy, Samples #1 and #2 have been split on
April 30, 2007, i.e. at the time where the EC issued its official report for the2006 compliance result13 . For each contract of maturity December 2008 andDecember 2009, we therefore identify our two subsamples as being "October
1, 2006 - April 30, 2007" and "May 1, 2007 - November 23, 2007".
During both periods, we assume the risk-neutral and historical distributions to be sufficiently stationary to use market prices and recover both ofthem. This methodology only provides us with estimates of average riskaversion on the time periods under consideration14 . As a final assumption,
we choose to work with an average time to maturity of τ = 1.3 on annual
basis in our dataset15 .

4.2

Estimation Results

Let us briefly summarize the estimation methodology developed in this paper. First, the risk neutral distribution is recovered from ECX option prices.
Second, the historical distribution is approximated by the historical return
distribution of futures allowance prices. Thus, over the entire dataset from15

October 1, 2006 to November 23, 2007 we estimate the historical and risk
neutral distributions. Third, as detailed in eq. (1), we infer from these probability distributions the absolute risk aversion functions for a representative
investor with a 16-month investor horizon16 .
As for the historical probability distribution, Tables 5 and 6 indicate
the best model is the asymmetric GARCH(1,1)-GJR to accommodate theleverage effect (see the Appendix). The result of the likelihood ratio test
confirms the GARCH GJR is the best fit for the historical distribution. The
chosen model is the GJR-GARCH model of Glosten et al. (1993) that we
re-state below for the ease of the presentation:

rt = µ + σt t2
σt2 = ω0 + ω1 It + α(rt−1 − µ)2 + βσt−1+ δ max(0, −(rt−1 − µ))2

t ∼ N (0, 1),with rt the one-day logarithmic return at time t and It = 1 if t is in
Sample #2 (after the compliance result) and 0 for Sample #1 (before thecompliance result). We are especially interested in the fact that ω1 is statistically different from zero and negative: the European carbon market ischaracterized by more volatility before the compliance event on April, 2007
than after the compliance event. This finding is consistent with what we
expected in Section 2, i.e. that information disclosure is due to reduce uncertainty and thus volatility on financial markets.
Compared to previous literature, our estimates strongly depart from theusual equity-based results. First, while ω0 and α are higher than the values
found in Rosenberg and Engle (2002) and Barone-Adesi et al. (2007), β issystematically lower. However, the degree of persistency of the conditional

16

variance as measured by (α + β) is close to the values in the previously cited
papers. Second, and most interestingly, λ is negative: periods of increasing
market coincide with periods of higher volatility. This increasing feature is
the exact opposite of the usual leverage effect found on equity markets17 .
In a context of a low environmental constraint on the carbon market, therisk associated to the option contract consists in increasing allowance prices
which is the opposite of a standard commodity market18 . Thus, beyond theinformation disclosure effects that led to a lower average volatility in the
globally increasing Sample #2, the volatility during increasing periods has
been higher than during decreasing periods. Thus, we are able to disentangle
two different asymmetric volatility effects, the first being dependent on information disclosure and the second being an uncovered feature on this newmarket. However, as explained below when investigating implied volatility,
the first effect usually dominates the other.
The rationale behind the second effect may be stated as follows. As shownin Figures 5 and 6 (see the Appendix), the implied volatilities exhibit smiles
with a dramatically different slope depending on the sample considered. For
both contracts December 2008 and December 2009, the smile observed in
Sample #1 (displayed in blue) is skewed to the right which suggests operators
anticipated a decrease of the carbon price before the release of 2006 verified
emissions. For Sample #2 (displayed in red), the smile displays a leftward
asymmetry which suggests operators anticipated an increase of the carbon
price after the confirmation that the number of allocated allowances washigher than verified emissions at the aggregated level19 . Between the twocontracts, our analysis finds a level of implied volatility in the range of 0.8-0.9
for the second contract of maturity December 2009, which is higher than thevalues obtained for the first contract of maturity December 2008 comprised

17

between 0.6-0.8. This result may be explained by the fact that the averagetime to maturity for option prices in the dataset is higher for the second
contract compared to the first contract.
The logic at stake to comment the level of implied volatilities obtained isthe following. When investors anticipate a sharp price decline, the rationale
behind option pricing consists in buying puts with strikes lower than theunderlying asset spot value and selling calls with higher strikes. Given the
one-to-one relation between option prices and implied volatility, this results
in a low implied volatility for low levels of moneyness compared to higher
ones. Thus, the implied volatility is lower for levels of moneyness strictlysuperior to one indicating these declining trends. At every point of the support, the lower the implied volatility, the higher the probability of occurrenceof the event. This relationship also explains the changes in the skewness of
the risk neutral distribution.
Therefore, we uncover a dramatic shift in investors’ anticipation aroundthe 2006 compliance event. We expect this result to be of lower magnitude
than during the 2005 compliance event20 . On April 2007, the EC revealed
that verified emissions were about 30 million tons or 1.45% lower than the2006 allocation21 . Two distinct messages are embedded in this diffusion of
institutional information. First, the EC confirmed that allocated allowanceswere higher than the actual level of CO2 emissions. This first element may
explain why market agents were expecting a drop in the carbon price before
the 2006 compliance event. Second, the EC revealed that verified emissions
were lower than allocated allowances by only 1.45% for the 2006 complianceresult, which corresponds to a thinner margin than for the 2005 complianceresult22 . Thus, market agents have adapted the financial risk of being exposed to a situation of allowance shortage, which may explain why they were18

expecting an increase in the carbon price after the 2006 compliance event.
As developed in Section 2, this futures dynamics is sustained by further EC
announcements to restrict allocation and to rely on auctioning during Phase
II which have a positive effect on the expected allowance scarcity. As a final
line of argument, the decision to maintain the EU ETS at least until 2020
may also contribute to this increasing price pattern.
The results obtained for the objective and risk neutral distributions confirm our intuitions. For the risk neutral distribution, in Figures 5 and 6, theblue line which denotes the risk neutral density for Sample #1 has a steeper
curve than the red line for Sample #2, which induces more volatility. These
results are therefore consistent with what we what we expected, i.e. to obtain lower levels of implied volatility after the EC annoucement. The results
for the historical density yield the same asymmetries as for the risk neutral
density of contracts December 2008 and December 2009.
Turning our attention to risk aversion, the empirical pricing kernels
present noticeable shapes that underline the dramatic change in the market risk aversion. We recall that the empirical pricing kernel is defined asq̂(x)for each point of the support of the asset price. Figures 5 and 6 clearlyfˆ(x)illustrate this point: before the yearly compliance result (# Sample 1), market agents expect a drop in the spot price whereas after the yearly complianceresult (# Sample 2) a sharp price increase is expected. From Figures 5 and
6, we may assert that the pricing kernel is countercyclical, i.e. it is inversely
related to the current market trend. The pricing kernel is decreasing in thecontext of increasing markets and conversely, as pointed out by Rosenberg
and Engle (2002).
These results should be compared to results obtained on equity markets,
using comparable ranges of maturities and moneynesses. We use options

19

with a longer time to maturity than Jackwerth (2000) or Rosenberg andEngle (2002) and our moneyness ranges are consequently wider than theirs.
Only Barone-Adesi et al. (2007) present empirical results for a comparable
range of strikes and maturities. Their estimates are ranging from 2 to 5. As
shown in Figures 5 and 6, our estimates range from nearly 0 to 10. These
considerably wider estimates suggest that the slope of the pricing kernel issteeper in our paper. This result applies especially for low moneynesses in
Sample #2. Similar comments arise for the graphs of risk aversion wherea steep slope for the pricing kernel is associated with a high level of risk
aversion.
Thus, one may conclude that risk aversion on the European carbon market is higher than the values typically found on equity markets. It appears
consistent with the risk premium associated to the financial exposure on sucha new carbon commodity market and the necessity to adopt accurate risk
management strategies.

5

Summary and Concluding Remarks

To our best knowledge, this paper constitutes the first attempt to characterize investors’ risk aversion on the European carbon market based on the
newly available plain vanilla option prices dataset taken from the European
Climate Exchange. On the EU ETS, investors update their subjective beliefs
about the distribution of allowance returns based on institutional constraints.
Since the revelation of lower verified emissions than allocated allowances by
3% led to a price correction of 54% on April 2006, we test the empirical relationship between information disclosure by the European Commission andshifts in investors’ risk aversion.
Based on the theoretical link that exists between the risk neutral and20historical probabilities distribution on the one hand, and the risk aversion
function on the other hand, we construct our estimation strategy by adapting to longer term options the existing methodology developed by Jackwerth(2000), Aït-Sahalia and Lo (2000) and Rosenberg and Engle (2002). Following Aït-Sahalia and Lo (2000), we estimate the risk neutral distribution
non parametrically from option prices while the historical distribution isrecovered semi parametrically from futures using an asymmetric GARCH
procedure, as presented in Barone-Adesi et al. (2007) and Rosenberg andEngle (2002). Our study ranges from October 1, 2006 to November 23,
2007. Since the shifts in risk aversion are more likely to occur around yearlycompliance events, we split our dataset on April 30, 2007.
Our findings may be summarized as follows. First, we find a lower level of
implied volatility after the EC communication of the 2006 compliance results
for contracts of maturities December 2008 and 2009. Second, we uncover theexact opposite of the usual leverage effect found on equity markets whereby
periods of increasing markets coincide with periods of higher volatility. The
former result emphasizes the critical role of information disclosure that was
expected. The latter result reveals that the risk is associated with increasing
allowance prices in a context of a low environmental constraint. Third, thepricing kernel reacts counter-cyclically. Fourth, based on a comparison for acomparable range of maturities and moneynesses, we show that risk aversion
is higher on the European carbon market than on equity markets.
The increasing futures dynamics observed after the 2006 compliance result may be interpreted as an increasing awareness in terms of future tightened caps. As the EU ETS is confirmed to operate at least until 2020,
investors are taking into account a medium-term carbon price signal. This
trend will most likely be strenghtened by the recent EU ETS review which

21

involves more sectors and an increasing reliance on auction mechanisms toallocate allowances as part of the global fight against climate change.

22Notes1

One EU allowance is equal to one ton of CO2 emitted in the atmosphere.

2i.e. the transfer of banked or borrowed allowances is allowed between Phase II andIII.
3

Available at http : //ec.europa.eu/environment/climat/emission/reviewen.htm. Cited

February, 2008.
4

More particularly, the aviation and petro-chemicals sectors as of 2013.

5

Indeed, the EC is bound by law to publish the compliance result on May 15 of eachyear at the latest (see Directive 2003/87/CE).
6

See for instance EC SPEECH/06/624 available at

http://europa.eu/rapid/pressReleasesAction.do?reference=SPEECH/06/624&format=HTML&aged=1&language=EN&guiLanguage=en. Cited January 2008.
7

Note that it is not possible to test for shifts in investors’ risk aversion during the 2005

compliance event due to data limitation on the availability of option prices, but we expect
lower effects on April 2007 compared to the magnitude of EUA price changes on April
2006.
8

See Andersen and Wagener (2002) and Briere (2006).

9

Note we rule out contracts that are not liquid such as the contract of maturity De-

cember 2007.
10

As explained in Cont and da Fonseca (2002), this investor horizon has been identified

as the best fit in our dataset. Note that this choice does not affect the robustness of theresults.
11

We do not include futures prices of maturity December 2007 in our sample since thiscontract has less observations and is less liquid.
12

See Ielpo and Guegan (2008) for more details.

13

Note the choice of the sample splitting date between end of March and end of April

does not affect the stability of the results.
14

See Rosenberg and Engle (2002) on this specific point.

15

The choice of τ does not affect the stability of the results.

16

The choice of this investment horizon has been discussed in the previous section.

17

Recall that the leverage effect implies a higher level of volatility associated to decreas-ing prices.
18This logic is conform to the disconnection between first and second period allowance23

prices described earlier, i.e. investors expect increasing allowance prices in a context ofincreasing allowance scarcity overtime.
19

On April 2007 the second compliance disclosed that verified emissions were about 30

million tons or 1.45% lower than the 2006 allocation. See the EU Environment DG at
http://ec.europa.eu/environment/press/index.htm. Cited February 2008.
20

As stated earlier, option prices are not available to capture the magnitude of thiseffect.
21

See the EU Environment DG at http://ec.europa.eu/environment/press/index.htm.

Cited February 2008.
22

Recall that verified emissions were lower than allocated allowances by 3% during the2005 compliance period (Ellerman and Buchner (2008)).

24

References
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Risk Aversion. Journal of Econometrics 2000; 94, 9–51.
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by Fitting Implied Volatility Smiles: Some Methodological Points andan Application to the 3M Euribor Futures Options Prices. ECB Working
Paper Series 2002.
Barone-Adesi, G.,Engle, R.F., Mancini, L. A GARCH Option Pricing Modelin Incomplete Markets. Swiss Finance Institute Research Paper Series
2007.
Benz, E., Truck, S. Modeling the Price Dynamics of CO2 Emission Allowances. Working Paper 2006; Bonn Graduate School of Economics.
Berndt, E.K., Robert, E.,Hall, B.H., Hausman, J.A. Estimation and Inference in Nonlinear Structural Models. Annals of Economic and Social Measurement 1974; 3; 653–665.
Bertholon, H., Monfort, A., Pegoraro, F. Econometric Asset Pricing Modelling. CREST Working Paper 2007.
Borak, S., Hardle, W.,Truck, S., Weron, R. Convenience Yields for CO2 Emission Allowance Futures Contracts. SFB 649 Discussion Paper 2006; 076;
Humboldt Universitat; Berlin.
Briere, M. Market Reactions to Central Bank Communication Policies:
Reading Interest Rate Options Smiles. Working Papers CEB 2006; 06-009.
Bunn, D., Fezzi, C. Interaction of European Carbon Trading and Energy
Prices. Fondazione Eni Enrico Mattei Working Paper 2007; 123.
25

Breeden, D.T., Litzenberger, R.H. Prices of State-Contingent Claims Implicit
in Option Prices. The Journal of Business 1978; 51(4); 621–651.
Chesney, M., Taschini, L. The Endogenous Price Dynamics of the Emission
Allowances: an Application to CO2 Option Pricing. Swiss Finance Institute Research Paper Series 2008; 08-02.
Cont, R., da Fonseca, J. Dynamics of Implied Volatility Surfaces. Quantitative Finance 2002; 2; 45–60.
Ellerman, A.D., Buchner, B.K. Over-Allocation or Abatement? A Preliminary Analysis of the EU ETS Based on the 2005-06 Emissions Data. Environmental and Resource Economics 2008; doi:10.1007/s10640-008-9191-2.
Glosten, L.R., Jagannathan, R., Runkle, D.E. On the Relation between
the Expected Value and the Volatility of the Nominal Excess Return on
Stocks. Journal of Finance 1993; 48; 1779–1801.
Gourieroux, C., Monfort, A., Trognon, A. Pseudo Maximum Likelihood
Methods : Theory. Econometrica 1984; 52; 680–700.
Ielpo, F., Guégan, D. Flexible Time Series Models for Subjective Distribution Estimation with Monetary Policy in View. Brussel Economic Review
2008; forthcoming.
Jackwerth, J.C. Recovering Risk Aversion from Option Prices and Realized
Returns. The Review of Financial Studies 2000; 13(2); 433–451.
Jurczenko, E., Maillet, B., Negrea, B. A Note on Skewness and Kurtosis
Adjusted Option Pricing Models under the Martingale Restriction. Quantitative Finance 2001; 21; 479–499.

26

Paolella,

M.S.,

sion

Trading

Taschini,

L.

Allowances.

An

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Economics 2002; 64; 341–372.
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Acknowledgements
The authors are grateful to Dexia for the use of their Bloomberg database.
The usual disclaimer applies.

6

Appendix27

28

Strikes in =C
Call prices
Put prices
Total
Strikes in =C
Call prices
Put prices
Total
15
285
285
570
16
247
247
494

Table 1: Number of available option prices
Source: European Climate Exchange

December 2009

December 2008

16
285
285
570
17
247
247
494

17
285
285
570
18
247
247
494

18
285
285
570
19
247
247
494

19
285
285
570
20
247
247
494

20
285
285
570
21
247
247
494

21
285
285
570
22
247
247
494

22
285
285
570
23
247
247
494

23
285
285
570
24
247
247
494

24
285
285
570
25
247
247
494

25
285
285
570
26
247
247
494

26
285
285
570
27
247
247
494

27
285
285
570
28
247
247
494

28
285
285
570
29
247
247
494

29
285
285
570
30
247
247
494

30
285
285
570
31
156
156
312

31
156
156
312
32
156
156
312

32
156
156
312
33
156
156
312

29

Strikes in =C
Call prices
Put prices
Total
Strikes in =C
Call prices
Put prices
Total
15
N.A.
185
185
16
N.A.
N.A.
N.A.

16
N.A.
80
80
17
N.A.
N.A.
N.A.

Table 2: Average volume contract for each strike
Source: European Climate Exchange

December 2009

December 2008

17
50
118
168
18
N.A.
N.A.
N.A.

18
50
172
222
19
N.A.
15
15

19
142
103
246
20
135
200
335

20
143
58
200
21
N.A.
N.A.
N.A.

21
73
58
132
22
50
N.A.
50

22
159
200
359
23
N.A.
N.A.
N.A.

23
213
N.A.
213
24
N.A.
N.A.
N.A.

24
58
N.A.
58
25
366
N.A.
366

25
185
N.A.
185
26
N.A.
N.A.
N.A.

26
317
N.A.
317
27
N.A.
N.A.
N.A.

27
96
N.A.
96
28
N.A.
N.A.
N.A.

28
500
N.A.
500
29
N.A.
N.A.
N.A.

29
222
N.A.
222
30
217
N.A.
217

30
158
N.A.
158
31
N.A.
N.A.
N.A.

31
N.A.
N.A.
N.A.
32
N.A.
N.A.
N.A.

32
100
N.A.
100
33
N.A.
N.A.
N.A.

30

Min
-0,092-2,644-2,618-2,644

Max
0,094
2,027
1,963
2,027

Average
0,001-0,002-0,026
0,017

Std. Dev.
0,026
0,91
0,872
0,939

Table 3: Descriptive statistics for December 2008 contract

Returns
Residual
Residual sample #1
Residual sample #2

Skewness-0,404-0,345-0,452-0,262

Excess Kurtosis
1,667-0,1040,355-0,347Jarque Berra test
0
0,056
0,091
0,306

Box pierce test
0,202
0,265
0,236
0,865

31

Min
-0,088-2,619-2,373-2,619

Max
0,101
2,076
2,086
1,985

Average
0,001-0,005-0,0340,018

Std. Dev.
0,025
0,908
0,871
0,936

Table 4: Descriptive statistics for December 2009 contract

Returns
Residual
Residual sample #1
Residual sample #2

Skewness-0,259-0,306-0,337-0,272

Excess Kurtosis
1,685-0,1490,172-0,31Jarque Berra test
0
0,097
0,292
0,307

Box pierce test
0,332
0,377
0,467
0,837

0

5

10

Price

15

20

25

Dec. 2008 ECX Future

2007
Time

Figure 1: Historical price of the ECX future for December 2008 contract

0

5

10

Price

15

20

25

Dec. 2009 ECX Future

2007
Time

Figure 2: Historical price of the ECX future for December 2009 contract

32

33

Estimatet-Stat.
Estimatet-Stat.
Estimatet-Stat.

ω0
0,079
6,074
0,010
3,552
0,009
3,799

ω1
-0,033-2,261-0,006-5,336-0,006-5,859α
0,088
12,054
0,102
54,7980,128
39,471

β
0,812
152,358
0,823
164,938δ
-0,061-18,046

The estimated model is:

µ
0,129
6,036
0,150
8,159
0,181
9,416

t ∼ N (0, 1)2
σt2 = ω0 + ω1 It + α(rt−1 − µ)2 + βσt−1+ δ max(0, −(rt−1 − µ))2

rt = µ + σt tTable 5: Estimation of the time series models for the December 2008 contracts.

GJR-GARCH(1,1)

GARCH(1,1)

ARCH(1)

Log-likelihood-666,097
0,000-659,105
0,000-658,519
0,000

34

Estimatet-Stat.
Estimatet-Stat.
Estimatet-Stat.

ω0
0,081
5,800
0,009
3,832
0,009
4,238

ω1
-0,037-2,378-0,006-5,544-0,006-6,250α
0,078
12,2920,105
54,8690,132
38,876

β0,808
155,761
0,820
170,801δ
-0,064-18,370

The estimated model is:

µ
0,136
6,625
0,150
8,709
0,181
10,022t ∼ N (0, 1)2
σt2 = ω0 + ω1 It + α(rt−1 − µ)2 + βσt−1+ δ max(0, −(rt−1 − µ))2

rt = µ + σt tTable 6: Estimation of the time series models for the December 2009 contracts.

GJR-GARCH(1,1)

GARCH(1,1)

ARCH(1)

Log-likelihood-659,259
0,000-652,274
0,000-651,645
0,000

0.02
0.00

0.01

Volatility

0.03

0.04

Historical volatility

2007
Time

Figure 3: Historical volatility estimated from asymmetric GARCH(1,1)
model for December 2008 contract

0.03
0.02
0.00

0.01

Volatility

0.04

0.05

Historical volatility

2007
Time

Figure 4: Historical volatility estimated from asymmetric GARCH(1,1)
model for December 2009 contract

35

Risk Neutral Distribution

0.8

1.0

1.2

0.6

0.8

1.0

1.2

Absolute Risk Aversion

0.8

1.0

1.2

−0.02

0.06

Implied volatility
Risk Aversion

Moneyness

1.4

0.6

0.8

Moneyness

1.0

1.2

Moneyness

2

6

10

Empirical pricing kernel

EPK

1.4

Moneyness

0.72

0.6

1.0

1.4

0.68

Volatility

0.6

0.8

Density

0.8
0.2

Density

1.4

Objective Distribution

0.6

0.8

1.0

1.2

Moneyness

Figure 5: Estimation results for December 2008 contract with τ = 1.3
36

1.4

1.4

Risk Neutral Distribution

0.8

1.0

1.2

1.4

0.6

0.8

1.0

1.2

1.4

1.6

Implied volatility

Absolute Risk Aversion

0.8

1.0

1.2

1.4

0.00

0.10

Moneyness

Risk Aversion

Moneyness

0.88

0.6

1.0

1.6

0.84

Volatility

0.6

0.8

Density

0.8
0.2

Density

1.4

1.2

Objective Distribution

1.6

0.6

0.8

Moneyness

1.0

1.2

1.4

1.6

Moneyness

6
4
2

EPK

8

Empirical pricing kernel

0.6

0.8

1.0

1.2

1.4

Moneyness

Figure 6: Estimation results for December 2009 contract with τ = 1.3
37

1.6