Can cross-border financial markets
create good collateral in a crisis?
Makoto Saito, Shiba Suzuki, and Tomoaki Yamada

Future of Central Banking under Globalization

2010/5/26

Questions raised here Theoretical question

Can cross-border markets create high-quality collateral whencollateral is urgently needed?
 Does collateral creation emerge endogenously in equilibrium?
 Toward policy implications

Is public collateral provision during financial crises justifiable,
given a theoretical case of collateral creation as an equilibrium
phenomenon?
 Which kinds of economic functions are carried out by public
collateral provision?
Future of Central Banking under Globalization

2010/5/26

Public collateral provision during a financialcrisis Public collateral provision during a financial crisis often

consists of:1.

Public institutions (including central banks) provide private agentswith high-quality collateral (safe bonds).

2.

Private agents utilize safe bonds as collateral to issue risky bonds.

3.

Public institutions quite positively evaluate private risky bonds(‘Reasonable’ prices may be even above fundamental prices).

4.

Both public institutions and private agents expand financial balance
sheets to maintain such financial operations.

Future of Central Banking under Globalization

2010/5/26

Public safe bonds as collateralCentral Bank

Private Agents

Private risky bonds as financing instruments

Future of Central Banking under Globalization

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Two-country setup with country-specificcatastrophic shocks and solvency constraints
 Country-specific catastrophic shocks:

Level shocks (not growth shocks)
 Maybe persistent Cross-border financial markets:

Complete markets
 To trade Lucas trees and contingent bonds between twocountries Solvency (collateral) constraints:
In any financial portfolio, gross repayments on debts need to beup to gross receipts from investments for every possible futurestate.
Future of Central Banking under Globalization

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How to compute the constrained competitiveequilibrium We first compute the constrained social optimal bysolving a social planner’s problem.
We do not solve directly market problems.

 Then, we translate the constrained social optimal to theconstrained competitive equilibrium.

The corresponding market problem is not dynamicallycomplete markets, but time-0 complete markets.
 A difference between the two versions of complete markets is
no longer trivial in the presence of solvency constraints.
Future of Central Banking under Globalization

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Future of Central Banking under Globalization

Market problem
1. Each country’s optimization problem:∞ ∑∑max{ci },{θ i },{ai }itt[ i t ]β π(s |s0 )u c (s ) ,tt

t=0 st ∈S t

its.t. c (s )+p(z )θ (s )+∑s′ ∈Sq(st , s′ )ai (st , s′ ) ≤ wi (st ),[ t+1] i tp(z ) + d(zt+1 ) θ (s ) ≥ −ai (st , s′ ), ∀s′ ∈ S.

Future of Central Banking under Globalization

2. Market clearings:
θ1 (st ) + θ2 (st )=1,a1 (st , s′ ) + a2 (st , s′ )=0, for all s′ ∈ S.

3. Resource constraints:e(zt ) = e1 (yt ) + e2 (yt ) + d(zt ).
4. Availability of Lucas trees:d(zt ).
α=e(zt )Future of Central Banking under Globalization

Collateral (solvency) constraints[ t+1] i tp(z ) + d(zt+1 ) θ (s ) ≥ −ai (st , s′ ), ∀s′ ∈ S.
1. Contingent claims as insurance: For state s′ ,i t ′i′ t ′a (s , s ) > 0 (insuree), and a (s , s ) < 0 (insurer).
2. Contingent claims as bonds: For all states s′ (∀′i t ′i′ t ′s ), a (s , s ) > 0 (creditor), and a (s , s ) < 0(debtor).
3. Without any physical delivery, it is possible tohave θ(st ) < 0. A short position in Lucas trees
without delivery can be regarded as risky bonds.

Future of Central Banking under Globalization

Computing social optimal by a representative agentmax{c1 ,c2 }∞∑∑[ 1[ 1][ 2]]

β π(s |s0 ) ζ (s )u c (s ) + ζ (s )u c (s )
tttt

2tt

t=0 st ∈S t

1. Negishi weights (ζ i (st )) are time-varying!
2. A constrained state implies that a state where
resources cannot be transferred from a constrained
state to another state (or today).
3. Thus, in a constrained state, consumption becomes
too much.
4. Consequently, Negishi weight is revised upward at
a state where a solvency constraint is binding.

.

Future of Central Banking under Globalization

5. It is possible to compute stochastic discountfactors from a representative agent framework.
6. With a solvency constraint binding,∑ ∑( j) ∑ ∑t j iQ(st , sj )ei (yj )Q(s , s )c s =j≥t sj ≽stj≥t sj ≽ststill holds from a constrained state onward.
7. That is, it is assumed that a consumer can ﬁnancecurrent consumption against far future endowment
in time-0 complete markets, much more ﬂexible
than dynamically complete markets.

Calibration setup: A purely transitory case
 A country-specific catastrophic shock reduces laborendowment by 20% with probability 1.8% per year.
The labor endowment share of the damaged country declines from50% to 44.4% (by 5.6%)

 The availability of Lucas trees is extremely limited

α = 0.1%
 The solvency of an insurer country, which is backed by investments
in Lucas trees, is lowered substantially.
 A calibrated case:Country 1 faces a catastrophic event in time 0. But, there is not any
more catastrophic event in either country.
Future of Central Banking under Globalization

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Future of Central Banking under Globalization

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Almost perfect insurance as the social
optimal: Country 2 (damaged country)
 The loss borne by Country 2 reduces from 5.6% to 0.2%

in time 0.

Direct loss Insurance benefit from Country 1
 Gross return from Lucas trees
 Ex-post borrowing must be

-5.6%
+0.7%
+0.7%
4.0%

 Country 2 bears 0.1% long-run losses (from time 2onward).

Future of Central Banking under Globalization

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Almost perfect insurance as the social
optimal: Country 1 (nondamaged country)
 The gain obtained by Country 1 reduces from 5.6% to0.2% in time 0.

Direct gain Insurance payment to Country 2
 Gross return from Lucas trees
 Ex post lending must be

+5.6%
-0.7%
+0.7%
5.4%

 Country 1 receives 0.1% long-run benefits (from time 2onward).

Future of Central Banking under Globalization

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How is the almost perfect insurance outcome (socialoptimal) achieved by market transactions?
 It is impossible to support the social optimal by financialtransactions even when markets are dynamically complete.
A big difference emerges between economies with and without
solvency constraints!

 It requires time-0 complete markets.
To achieve the social optimal, not only one-period contingent bonds,
but also multi-period contingent bonds are necessary.
Given severe solvency constraints, one-period installment is too short forthe damaged country to cover catastrophic losses.

However, time-0 complete markets may not be realistic.
They require a fairly wide variety of financial instruments, and involve
extremely complicated financial transactions.
Future of Central Banking under Globalization

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Can the social optimal be sustained by dynamicallycomplete markets with minor interventions? (1/2)
 Yes, if asset pricing slightly deviates from arbitrage pricing.
In particular, the price of Lucas trees is slightly above
fundamentals:

 Deviation from arbitrage pricing may be justifiable in aneconomy with solvency constraints.

 Richness in Lucas trees would give Country 2 (damaged)

an opportunity to finance by making short in Lucas trees.
Future of Central Banking under Globalization

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Can the social optimal be sustained by dynamicallycomplete markets with minor interventions? (2/2)
 Richness in Lucas trees and Cheapness incontingent bonds result in: Country 2 can finance resources by making long incontingent bonds and short in Lucas trees.

 Country 1 can construct long-run investment

opportunities by making long in Lucas trees and shortin contingent bonds.

Future of Central Banking under Globalization

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Large-scale bilateral financial transactions
in time 0 Country 2 (damaged):Long positions in contingent bonds:
 Short positions in risky bonds (Lucas trees): Ex-post borrowing:
3.6%
-7.5%
4.0%

 Country 1 (nondamaged):Long positions in risky bonds (Lucas trees):
 Short positions in contingent bonds:
 Ex-post lending:Future of Central Banking under Globalization

8.8%
-3.6%
5.4%

2010/5/26

Payoff structure of contingent bonds
 Country 2’s receipts and repayments in time 1:
Cat. shocks on

Receipts fromsafe bonds

Repayments on
risky bonds(Lucas trees)

Solvency
constraints

Neither country

11.8%

11.8%

Binding

Country 2 only

9.5%

8.0%

Not binding thanks
to insurance fromCountry 1Country 1 only

8.0%

8.0%

Binding

Both countries

5.1%

5.1%

Binding Utilizing safe bonds issued by Country 1 as good collateral,

Country 2 can finance effectively uncovered losses.
Future of Central Banking under Globalization

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Large-scale bilateral transactions emerges
only in the aftermath.

Future of Central Banking under Globalization

2010/5/26

Summary of calibration exercises
 Even when markets are only dynamically complete (a set ofcontingent claims is fairly limited), slight richness in Lucas trees
allows for restoring the social optimal as follows.
Country 1 issues safe bonds on large scale.
 Country 2 exploits such safe bonds as collateral, and issues risky
bonds (short positions in Lucas trees without delivery).
 Both countries close such large-scale bilateral transactions
immediately after a catastrophic shock goes away.
 The above implications survive with high degree persistence

and consecutive occurrence.
Future of Central Banking under Globalization

2010/5/26

Policy implications from the calibration
exercises
 How we should interpret central banks’ behavior during afinancial crisis, including:aggressively positive evaluation of private risky bonds (even above
fundamental prices), large-scale public collateral provision, and expanding hugely financial balance sheets.
 It is justifiable.

With slight richness in private risky bonds initiated by public
interventions, financially-damaged agents can finance effectively
uncovered losses in a situation where the availability of financial
instruments is rather limited.
 Large-scale interventions need to be closed immediately after afinancial crisis goes away.
Future of Central Banking under Globalization

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