Counterparty Risk in Financial Contracts: Should the Insured Worry - PowerPoint PPT Presentation

Introduction Model Setup Results Extensions Conclusion “Over the weekend, ACA, a small bond insurer, has been in frantic talks to avoid insolvency... ACA sold banks a kind of insurance against losses on risky debt. If it collapses, this insurance will be rendered worthless, and every other bank that had dealt with it will suffer losses.” - Counterparty risk fears re-enter mainstream. Financial Times, Mon., Jan. 21, 2008. James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 5 / 39

Introduction Model Setup Results Extensions Conclusion Moral Hazard • What are the incentives of the insurers in the market? Potential Moral hazard • Myself: insurer invest too “illiquily” • Acharya and Bisin (2011): insurers trades in opaque markets (e.g., OTC) and sells too much other protection. Each new contract poses and “externality” on every other one. • Biais, Heider and Hoerva (2012): debt overhang - CDS buyer is like a debt holder! If the contract gets riskier, the insurer may start to misbehave. • All three feature endogenous counterparty risk James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 6 / 39

Introduction Model Setup Results Extensions Conclusion Main Results • I uncover a new moral hazard problem on insurer side. • Compare to Akerlof (1970): Moral hazard problem can alleviate adverse selection problem! • Applicable to correlated aggregate risk (e.g. the credit crises!) James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 7 / 39

Introduction Model Setup Results Extensions Conclusion Players • Insured Party (Bank) ◮ Endowed with Risky or Safe loan (equal prob.) ◮ Insure a fixed amount of its loan with insurer • Insurer (IFI) ◮ Endowed with a portfolio that can be sold off (costly) at interim stage ◮ Investment decision regarding insurance contract James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 8 / 39

Introduction Model Setup Results Extensions Conclusion BANK • Return R B with probability: ◮ Safe: p s ◮ Risky: p r • Insures proportion ( γ ) of loan. Suffer cost Z if no protection. James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 9 / 39

Introduction Model Setup Results Extensions Conclusion Model Setup - Insurer (IFI) • Portfolio (realized at t = 2) � 0 � R f θ f ( θ ) d θ + R f ( θ − G ) f ( θ ) d θ 0 • Portfolio can be accessed at t = 1, however, cost of liquidation C ( · ) with C ′ > 0, C ′′ ≥ 0. James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 10 / 39

Introduction Model Setup Results Extensions Conclusion Information and Beliefs • Only Bank knows loan quality • Define b as IFIs expectation of the probability of claim. • IFI investment choice for premia: liquid (storage - return 1), illiquid (return R I > 1) • If claim made, only liquid asset available • P is price per unit of protection. James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 11 / 39

Introduction Model Setup Results Extensions Conclusion Timing Bank endowed with (S)afe IFI choses liquid ( β ) and illiquid or (R)isky loan (1 − β ) investment Bank insures proportion γ of loan for premium Pγ t = 0 James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 12 / 39

Introduction Model Setup Results Extensions Conclusion Timing IFI learns portfolio valuation (˜ θ ) and State of insurance contract realized ( ˜ IFI and Bank receive payoffs ψ ) If needed, IFI pays contract or goes bankrupt t = 1 t = 2 James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 12 / 39

Introduction Model Setup Results Extensions Conclusion Liquid β IFI Invests γP 1 − β Illiquid James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 12 / 39

Introduction Model Setup Results Extensions Conclusion IFI’s payoff - No Insurance � R f � 0 Π NI IFI = θ f ( θ ) d θ + ( θ − G ) f ( θ ) d θ 0 R f � �� IFI succeeds IFI fails James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 12 / 39

Introduction Model Setup Results Extensions Conclusion IFI’s payoff - With insurance contract • IFI maximizes (expected) profit for a fixed b and P choosing β . James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 12 / 39

Introduction Model Setup Results Extensions Conclusion IFI’s payoff - With insurance contract Π I max = P γ ( β + (1 − β ) R I ) IFI β � R f +(1 − b ) [ θ f ( θ ) d θ − P γ ( β +(1 − β ) R I ) � − P γ ( β +(1 − β ) R I ) + ( θ − G ) f ( θ ) d θ ] R f � R f + ( b ) [ ( θ − C ( γ − β P γ ) − β P γ ) f ( θ ) d θ C ( γ − β P γ ) � C ( γ − β P γ ) + ( θ − G ) f ( θ ) d θ ] R f James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 12 / 39

Introduction Model Setup Results Extensions Conclusion IFI’s payoff - With insurance contract Π I max = P γ ( β + (1 − β ) R I ) IFI β � �� Premium James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 13 / 39

Introduction Model Setup Results Extensions Conclusion IFI’s payoff - With insurance contract Π I max = IFI β � R f + (1 − b ) [ θ f ( θ ) d θ � �� − P γ ( β +(1 − β ) R I ) Prob. of No Claim � �� IFI succeeds � − P γ ( β +(1 − β ) R I ) + ( θ − G ) f ( θ ) d θ ] R f � �� IFI fails James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 13 / 39

Introduction Model Setup Results Extensions Conclusion IFI’s payoff - With insurance contract Π I max = IFI β � R f + [ ( θ − C ( γ − β P γ ) − β P γ ) f ( θ ) d θ b �� C ( γ − β P γ ) Prob. of Claim � �� IFI succeeds � C ( γ − β P γ ) + ( θ − G ) f ( θ ) d θ ] R f � �� IFI fails James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 13 / 39

Introduction Model Setup Results Extensions Conclusion Result Proposition The amount put in the liquid asset ( β ) is increasing in the belief of the probability of a claim ( b ) James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 14 / 39

Introduction Model Setup Results Extensions Conclusion Market Clearing Price Lemma The riskier the loan is perceived to be, the higher the insurance premium that must be paid. Intuition. If claim more likely to be made, IFI needs to be compensated for extra loses to break even. James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 15 / 39

Introduction Model Setup Results Extensions Conclusion Bank Incentives • Define β ∗ S ≡ β ∗ b = S , β ∗ R , P ∗ S , P ∗ R . • Message M ∈ { S , R } • Bank Payoff: Π( i , M ) where i ∈ { S , R } James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 16 / 39

Introduction Model Setup Results Extensions Conclusion Equilibrium Definition An Equilibrium is defined as a β , P , b such that: 1. b is consistent with Bayes’ rule where possible. 2. Choosing P, the IFI earns zero profit with β derived according to the IFI’s problem. 3. The bank chooses its message optimally James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 17 / 39

Introduction Model Setup Results Extensions Conclusion Beliefs Proposition If the IFI believes a claim is less likely to be made than it actually is, the banks counterparty risk rises whenever β ∈ (0 , 1]. The IFI will chose more illiquid investment thereby raising Intuition. the probability they fail if a claim is made. • Use beliefs that correspond to separating equilibrium. ◮ i.e. IFI always believes the bank’s reported type. James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 18 / 39

Introduction Model Setup Results Extensions Conclusion Risky prefers to report Risky Π( R , R ) ≥ Π( R , S ) ⇒ � C ( γ − β ∗ S P ∗ S γ ) P ∗ R − P ∗ (1 + Z ) (1 − p R )) dF ( θ ) ≥ S � �� C ( γ − β ∗ R P ∗ R γ ) amount extra to be paid in insurance premia � �� expected saving in counterparty risk “Counterparty Risk Effect Dominates” James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 19 / 39

Introduction Model Setup Results Extensions Conclusion Safe prefers to report Safe Π( S , S ) ≥ Π( S , R ) ⇒ � C ( γ − β ∗ S P ∗ S γ ) P ∗ R − P ∗ (1 + Z ) (1 − p s ) dF ( θ ) ≤ S C ( γ − β ∗ R P ∗ R γ ) � �� amount to be saved in insurance premia � �� expected cost of the additional counterparty risk “Premium Effect Dominates” James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 20 / 39

Introduction Model Setup Results Extensions Conclusion Overview of Equilibria Pooling and Separating Pooling and Separating Pooling Separating Pooling Increasing Z ( Z = how much bank is averse to counterparty risk) James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 21 / 39

Introduction Model Setup Results Extensions Conclusion Contract Inefficiency - The Moral Hazard • Contracting imperfection: Bank cannot control investment of IFI • Fix IFI at any belief and maintain zero profit condition on the IFI • social planners problem forces more liquid, but bank has to pay more for this James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 22 / 39

Introduction Model Setup Results Extensions Conclusion Contract Inefficiency - The Moral Hazard Proposition Any equilibrium in which β ∗ ∈ [0 , 1) is inefficient. The bank prefers the IFI to invest in liquid asset. Intuition. This is sub-optimal from IFIs perspective, therefore, must have higher premium. Raise β until the marginal cost (increased premium) equals marginal benefit (decreased counterparty risk). James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 23 / 39

Introduction Model Setup Results Extensions Conclusion What we’ve covered so far... • We showed how a moral hazard problem can be present on the insurer side of market • We showed how this moral hazard can alleviate the adverse selection problem James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 24 / 39

Introduction Model Setup Results Extensions Conclusion Extensions 1. Multiple Insured Parties (Banks) 2. Moral Hazard in Bank-Borrower Relationship James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 25 / 39

Introduction Model Setup Results Extensions Conclusion Extension 1: Multiple Banks • Consider one insurer and many banks • Each bank is insignificant to the insurer’s decision. • Let there be a measure M < 1 banks • Each bank is given a type (probability of default - X) according to a uniform draw with CDF:  0 if x ≤ 0  x Ψ( x ) = if x ∈ (0 , M ) M  1 if x ≥ M James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 26 / 39

Introduction Model Setup Results Extensions Conclusion Probability of Type 1 0 M Type (Probability of Default) James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 27 / 39

Introduction Model Setup Results Extensions Conclusion • All banks receive a private aggregate shock: � r with probability 1 2 p A = with probability 1 s 2 • Let p i = p A + X i James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 28 / 39

Introduction Model Setup Results Extensions Conclusion Probability of Type 0 s r r + M 1 s + M Type (Probability of Default) James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 28 / 39

Introduction Model Setup Results Extensions Conclusion • Each bank insures γ � M • Size of contracts insured by IFI: 0 γ d Φ( x ) = M γ • The conditional distribution of p i | s FOSD p i | r James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 29 / 39

Introduction Model Setup Results Extensions Conclusion Beliefs Lemma There is less counterparty risk when beliefs are that the aggregate shock is risky over it being safe Intuition. Similar to previous Lemma James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 30 / 39

Introduction Model Setup Results Extensions Conclusion Equilibrium Consider No Aggregate shock. Lemma There can be no separating equilibrium in the idiosyncratic shock There is no uncertainty in IFIs beliefs as to Intuition. aggregate quality. A single bank cannot effect IFIs beliefs. All wish to be revealed as receiving X i = 0. James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 31 / 39

Introduction Model Setup Results Extensions Conclusion Probability of Type 0 1 M Type (Probability of Default) James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 31 / 39

Introduction Model Setup Results Extensions Conclusion Equilibrium Both aggregate and idiosyncratic shock. Proposition There exists a parameter range such that there is a unique separating equilibrium Intuition. If one bank can reveal its aggregate shock, it is revealed for all. An individual bank can effect IFIs investment. Result now similar to previous proposition. James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 32 / 39

Introduction Model Setup Results Extensions Conclusion Probability of Type 0 1 S S + M R R + M Type (Probability of Default) James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 32 / 39

Introduction Model Setup Results Extensions Conclusion Extension 2: Classical Moral Hazard Problem • Bank typically assumed to have a proprietary monitoring technology. ◮ Auto insurance analogue: I can (some what) control my probability of a car crash. • What happens to incentive to monitor under insurance with and without counterparty risk? James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 33 / 39

Introduction Model Setup Results Extensions Conclusion • Drop adverse selection problem for simplicity • Can define a continuous monitoring space on compact interval [0 , M ]. • Bank loan return distribution: h ( ψ ; M ), ˜ ψ ∈ [0 , 1] implies default • Assume Monotone likelihood ratio property (MLRP) - more monitoring increases the probability of a higher return. • Assume convexity-of-distribution function. For any λ ∈ [0 , 1], for any M,M’: h ( ψ, λ M + (1 − λ ) M ′ ) ≤ λ h ( ψ ; M ) + (1 − λ ) h ( ψ ; M ′ ) • CDFC + MLPR - increasing the monitoring, increases, at a decreasing rate the probability that the return will be above some level ψ . James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 34 / 39

Counterparty Risk in Financial Contracts: Should the Insured Worry - PowerPoint PPT Presentation

Introduction Model Setup Results Extensions Conclusion Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? James R. Thompson School of Accounting and Finance: The University of Waterloo CES, Munich

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