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

September 03, 2012

James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 1 / 39

Introduction Model Setup Results Extensions Conclusion

• What is Insurance?

James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 2 / 39

Introduction Model Setup Results Extensions Conclusion

• What is Insurance?
• What is a contingent financial contract?

James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 2 / 39

Introduction Model Setup Results Extensions Conclusion

What are Credit Default Swaps (CDS)?

BANK XYZ CORPORATION IFI James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 2 / 39

Introduction Model Setup Results Extensions Conclusion

What are Credit Default Swaps (CDS)?

BANK XYZ CORPORATION IFI James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 2 / 39

Introduction Model Setup Results Extensions Conclusion

What are Credit Default Swaps (CDS)?

BANK XYZ CORPORATION IFI James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 2 / 39

Introduction Model Setup Results Extensions Conclusion

What are Credit Default Swaps (CDS)?

Bank may own underlying risk

BANK XYZ CORPORATION IFI James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 2 / 39

Introduction Model Setup Results Extensions Conclusion

What are Credit Default Swaps (CDS)?

• 18th century England, insurance market was like the CDS

market today.

• Insurers wrote policies on many things for anyone.
• E.g., Merchants bought policies on someone else’s ship.
• In 1746, Parliament passed Marine Insurance act requiring

insurable interest, and no over-insurance.

James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 2 / 39

Introduction Model Setup Results Extensions Conclusion

What are Credit Default Swaps (CDS)?

Bank insures with Insurer

Underlying Debt Bank Insurer ? ?

James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 2 / 39

Introduction Model Setup Results Extensions Conclusion

What are Credit Default Swaps (CDS)?

Bank pays premium to Insurer

Underlying Debt Bank Insurer ? ?

James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 2 / 39

Introduction Model Setup Results Extensions Conclusion

Growth in Credit Derivatives

10 30 40 50 20 Mid-2003 Notional Value of Credit Derivatives (in Trillions $) Source: ISDA 2005,2007

James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 2 / 39

Introduction Model Setup Results Extensions Conclusion

Growth in Credit Derivatives

10 30 40 50 20 Mid-2003 End-2003 Notional Value of Credit Derivatives (in Trillions $) Source: ISDA 2005,2007

James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 2 / 39

Introduction Model Setup Results Extensions Conclusion

Growth in Credit Derivatives

10 30 40 50 20 Mid-2003 End-2003 Mid-2004 Notional Value of Credit Derivatives (in Trillions $) Source: ISDA 2005,2007

James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 2 / 39

Introduction Model Setup Results Extensions Conclusion

Growth in Credit Derivatives

10 30 40 50 20 Mid-2003 End-2003 Mid-2004 End-2004 Notional Value of Credit Derivatives (in Trillions $) Source: ISDA 2005,2007

James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 2 / 39

Introduction Model Setup Results Extensions Conclusion

Growth in Credit Derivatives

10 30 40 50 20 Mid-2003 End-2003 Mid-2004 End-2004 Mid-2005 Notional Value of Credit Derivatives (in Trillions $) Source: ISDA 2005,2007

James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 2 / 39

Introduction Model Setup Results Extensions Conclusion

Growth in Credit Derivatives

10 30 40 50 20 Mid-2003 End-2003 Mid-2004 End-2004 Mid-2005 Start-2007 Notional Value of Credit Derivatives (in Trillions $) Source: ISDA 2005,2007

James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 2 / 39

Introduction Model Setup Results Extensions Conclusion

Growth in Credit Derivatives

10 30 40 50 20 45.46 Mid-2003 End-2003 Mid-2004 End-2004 Mid-2005 Mid-2007 Start-2007 Notional Value of Credit Derivatives (in Trillions $) Source: ISDA 2005,2007

James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 2 / 39

Introduction Model Setup Results Extensions Conclusion

What is Counterparty Risk?

Risk that when an insured party makes a claim, the insurer is insolvent.

James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 3 / 39

Introduction Model Setup Results Extensions Conclusion

Questions

• What are the effects of counterparty risk on insurance

contracts?

• Given that an insurer can fail, how do they behave? What

are their investment objectives?

James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 4 / 39

Introduction Model Setup Results Extensions Conclusion

Questions

• What are the effects of counterparty risk on insurance

contracts?

• Given that an insurer can fail, how do they behave? What

are their investment objectives?

James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 4 / 39

Introduction Model Setup Results Extensions Conclusion

Motivation

• Financial markets have very large insurance contracts

◮ Market for Credit Derivatives. ◮ Re-insurance market.

• Consider who the counterparties are:

◮ Banks ◮ Hedge Funds ◮ Insurance Companies 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

Motivation

• Financial markets have very large insurance contracts

◮ Market for Credit Derivatives. ◮ Re-insurance market.

• Consider who the counterparties are:

◮ Banks ◮ Hedge Funds ◮ Insurance Companies 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

• “Banking was as easy as 3:6:3 (money in at 3%, lend at 6%,
• n the golf course by 3 o’clock)”
• The Economist April 10, 1993
• “Credit risk, and in particular, counterparty credit risk, is

probably the single most important variable in determining whether and with what speed financial disturbances become financial shocks with potential systemic traits”

• Towards Greater Financial Stability. The report of the

Counterparty Credit Risk Management Group (CRMPG II), ISDA, 2005.

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

• “Banking was as easy as 3:6:3 (money in at 3%, lend at 6%,
• n the golf course by 3 o’clock)”
• The Economist April 10, 1993
• “Credit risk, and in particular, counterparty credit risk, is

probably the single most important variable in determining whether and with what speed financial disturbances become financial shocks with potential systemic traits”

• Towards Greater Financial Stability. The report of the

Counterparty Credit Risk Management Group (CRMPG II), ISDA, 2005.

James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 4 / 39

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

• n 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

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

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

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

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

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

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

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 RB with probability:

◮ Safe: ps ◮ Risky: pr

• 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

BANK

• Return RB with probability:

◮ Safe: ps ◮ Risky: pr

• 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)

Rf θf (θ)dθ +

Rf (θ − G)f (θ)dθ

• 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

Model Setup - Insurer (IFI)

• Portfolio (realized at t = 2)

Rf θf (θ)dθ +

Rf (θ − G)f (θ)dθ

• 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 RI > 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

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 RI > 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

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 RI > 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

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 RI > 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

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 RI > 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

t = 0 Bank endowed with (S)afe

• r (R)isky loan

Bank insures proportion γ of loan for premium Pγ IFI choses liquid (β) and illiquid (1 − β) investment

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

t = 1 t = 2 If needed, IFI pays contract or goes bankrupt IFI and Bank receive payoffs IFI learns portfolio valuation (˜ θ) and State of insurance contract realized ( ˜ ψ)

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 Invests γP β 1 − β Liquid 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

ΠNI

IFI =

Rf θf (θ)dθ

• IFI succeeds

+

Rf

(θ − G)f (θ)dθ

• 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

max

β

ΠI

IFI

= Pγ(β + (1 − β)RI) +(1 − b) [ Rf

−Pγ(β+(1−β)RI )

θf (θ)dθ + −Pγ(β+(1−β)RI )

Rf

(θ − G)f (θ)dθ] + (b) [ Rf

C(γ−βPγ)

(θ − C(γ − βPγ) − βPγ) f (θ)dθ + C(γ−βPγ)

Rf

(θ − G) f (θ)dθ]

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

max

β

ΠI

IFI

= Pγ(β + (1 − β)RI)

• 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

max

β

ΠI

IFI

= + (1 − b)

• Prob. of No Claim

[ Rf

−Pγ(β+(1−β)RI )

θf (θ)dθ

• IFI succeeds

+ −Pγ(β+(1−β)RI )

Rf

(θ − G)f (θ)dθ]

• 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

max

β

ΠI

IFI

= + b

• Prob. of Claim

[ Rf

C(γ−βPγ)

(θ − C(γ − βPγ) − βPγ) f (θ)dθ

• IFI succeeds

+ C(γ−βPγ)

Rf

(θ − G) f (θ)dθ]

• 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

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

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

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]. Intuition. The IFI will chose more illiquid investment thereby raising 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

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]. Intuition. The IFI will chose more illiquid investment thereby raising 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) ⇒

(1 + Z) (1 − pR)) C(γ−β∗

S P∗ S γ)

C(γ−β∗

R P∗ R γ)

dF(θ)

• expected saving in counterparty risk

≥ P∗

R − P∗ S

• amount extra to be paid in insurance premia

“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) ⇒

(1 + Z) (1 − ps) C(γ−β∗

S P∗ S γ)

C(γ−β∗

R P∗ R γ)

dF(θ)

• expected cost of the additional counterparty risk

≤ P∗

R − P∗ S

• amount to be saved in insurance premia

“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 Pooling Pooling and Separating Pooling and Separating Separating 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

• 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

• 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. Intuition. The bank prefers the IFI to invest in liquid asset. 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

Contract Inefficiency - The Moral Hazard

Proposition

Any equilibrium in which β∗ ∈ [0, 1) is inefficient. Intuition. The bank prefers the IFI to invest in liquid asset. 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

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: Ψ(x) =    if x ≤ 0

x M

if x ∈ (0, 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

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: Ψ(x) =    if x ≤ 0

x M

if x ∈ (0, 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

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: Ψ(x) =    if x ≤ 0

x M

if x ∈ (0, 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

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: Ψ(x) =    if x ≤ 0

x M

if x ∈ (0, 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 Type (Probability of Default) M 1

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:

pA = r with probability 1

2

s with probability 1

2

• Let pi = pA + Xi

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

• All banks receive a private aggregate shock:

pA = r with probability 1

2

s with probability 1

2

• Let pi = pA + Xi

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 Type (Probability of Default) 1 s + M s r r + M

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
• Size of contracts insured by IFI:

M

0 γdΦ(x) = Mγ

• The conditional distribution of pi|s FOSD pi|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

• Each bank insures γ
• Size of contracts insured by IFI:

M

0 γdΦ(x) = Mγ

• The conditional distribution of pi|s FOSD pi|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

• Each bank insures γ
• Size of contracts insured by IFI:

M

0 γdΦ(x) = Mγ

• The conditional distribution of pi|s FOSD pi|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

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

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 Intuition. There is no uncertainty in IFIs beliefs as to aggregate quality. A single bank cannot effect IFIs beliefs. All wish to be revealed as receiving Xi = 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

Equilibrium

Consider No Aggregate shock.

Lemma

There can be no separating equilibrium in the idiosyncratic shock Intuition. There is no uncertainty in IFIs beliefs as to aggregate quality. A single bank cannot effect IFIs beliefs. All wish to be revealed as receiving Xi = 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 Type (Probability of Default) M 1

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

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 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

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, λM + (1 − λ)M′) ≤ λh(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

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, λM + (1 − λ)M′) ≤ λh(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

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, λM + (1 − λ)M′) ≤ λh(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

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, λM + (1 − λ)M′) ≤ λh(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

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, λM + (1 − λ)M′) ≤ λh(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

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, λM + (1 − λ)M′) ≤ λh(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

Introduction Model Setup Results Extensions Conclusion

• cost of monitoring: c(M), with c′ > 0, c′′ > 0
• For simplicity, rule out corner solutions with Inada conditions:

c′(0) = 0, c′(M) = +∞.

• Consider no insurance available

S,R

1

ψdH(ψ; M) + (1 − γ) 1 dH(ψ; M)ψ + γ 1 (ψ − Z)dH(ψ; M) − c(M) ≥ S,R

1

ψdH(ψ; M′) + (1 − γ) 1 dH(ψ; M′) + γ 1 (ψ − Z)dH(ψ; M′) − c(M′) ∀ M′ = M

James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 35 / 39

Introduction Model Setup Results Extensions Conclusion

• cost of monitoring: c(M), with c′ > 0, c′′ > 0
• For simplicity, rule out corner solutions with Inada conditions:

c′(0) = 0, c′(M) = +∞.

• Consider no insurance available

S,R

1

ψdH(ψ; M) + (1 − γ) 1 dH(ψ; M)ψ + γ 1 (ψ − Z)dH(ψ; M) − c(M) ≥ S,R

1

ψdH(ψ; M′) + (1 − γ) 1 dH(ψ; M′) + γ 1 (ψ − Z)dH(ψ; M′) − c(M′) ∀ M′ = M

James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 35 / 39

Introduction Model Setup Results Extensions Conclusion

• cost of monitoring: c(M), with c′ > 0, c′′ > 0
• For simplicity, rule out corner solutions with Inada conditions:

c′(0) = 0, c′(M) = +∞.

• Consider no insurance available

S,R

1

ψdH(ψ; M) + (1 − γ) 1 dH(ψ; M)ψ + γ 1 (ψ − Z)dH(ψ; M) − c(M) ≥ S,R

1

ψdH(ψ; M′) + (1 − γ) 1 dH(ψ; M′) + γ 1 (ψ − Z)dH(ψ; M′) − c(M′) ∀ M′ = M

James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 35 / 39

Introduction Model Setup Results Extensions Conclusion

• cost of monitoring: c(M), with c′ > 0, c′′ > 0
• For simplicity, rule out corner solutions with Inada conditions:

c′(0) = 0, c′(M) = +∞.

• Consider no insurance available

S,R

1

ψdH(ψ; M) + (1 − γ) 1 dH(ψ; M)ψ + γ 1 (ψ − Z)dH(ψ; M) − c(M) ≥ S,R

1

ψdH(ψ; M′) + (1 − γ) 1 dH(ψ; M′) + γ 1 (ψ − Z)dH(ψ; M′) − c(M′) ∀ M′ = M

James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 35 / 39

Introduction Model Setup Results Extensions Conclusion

• cost of monitoring: c(M), with c′ > 0, c′′ > 0
• For simplicity, rule out corner solutions with Inada conditions:

c′(0) = 0, c′(M) = +∞.

• Consider no insurance available

S,R

1

ψdH(ψ; M) + (1 − γ) 1 dH(ψ; M)ψ + γ 1 (ψ − Z)dH(ψ; M) − c(M) ≥ S,R

1

ψdH(ψ; M′) + (1 − γ) 1 dH(ψ; M′) + γ 1 (ψ − Z)dH(ψ; M′) − c(M′) ∀ M′ = M

James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 35 / 39

Introduction Model Setup Results Extensions Conclusion

• cost of monitoring: c(M), with c′ > 0, c′′ > 0
• For simplicity, rule out corner solutions with Inada conditions:

c′(0) = 0, c′(M) = +∞.

• Consider no insurance available

S,R

1

ψdH(ψ; M) + (1 − γ) 1 dH(ψ; M)ψ + γ 1 (ψ − Z)dH(ψ; M) − c(M) ≥ S,R

1

ψdH(ψ; M′) + (1 − γ) 1 dH(ψ; M′) + γ 1 (ψ − Z)dH(ψ; M′) − c(M′) ∀ M′ = M

James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 35 / 39

Introduction Model Setup Results Extensions Conclusion

• Given CDIC, this can be re-written as:

c′(M)

Marginal Cost of Monitoring

= S,R ψdHM(ψ; M) + γ 1 ZdHM(ψ; M)

• Marginal Benefit of Monitoring

James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 36 / 39

Introduction Model Setup Results Extensions Conclusion

Insurance, No Counterparty Risk

c′(M) + γ 1 dHM(ψ; M)

• Marginal Cost of Monitoring

= S,R ψdHM(ψ; M) + γPM

• Marginal Benefit of Monitoring
• Desire to monitor decreases

James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 37 / 39

Introduction Model Setup Results Extensions Conclusion

Insurance, No Counterparty Risk

c′(M) + γ 1 dHM(ψ; M)

• Marginal Cost of Monitoring

= S,R ψdHM(ψ; M) + γPM

• Marginal Benefit of Monitoring
• Desire to monitor decreases

James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 37 / 39

Introduction Model Setup Results Extensions Conclusion

Insurance with Counterparty Risk

Double Moral Hazard problem

c′(M) + γ 1 dHM(ψ; M) Rf

C(γ−β∗P∗γ)

dF(θ)

• Marginal Cost of Monitoring

= S,R ψdHM(ψ; M) + Zγ 1 dHM(ψ; M) C(γ−β∗P∗γ)

Rf

dF(θ) + γP1

M

• Marginal Benefit of Monitoring
• β∗ solved for from IFI’s problem
• RESULT: Can show that desire to monitor can increase from no

counterparty risk case

• RESULT: Adding this moral hazard problem doesn’t change

qualitative results

James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 38 / 39

Introduction Model Setup Results Extensions Conclusion

Insurance with Counterparty Risk

Double Moral Hazard problem

c′(M) + γ 1 dHM(ψ; M) Rf

C(γ−β∗P∗γ)

dF(θ)

• Marginal Cost of Monitoring

= S,R ψdHM(ψ; M) + Zγ 1 dHM(ψ; M) C(γ−β∗P∗γ)

Rf

dF(θ) + γP1

M

• Marginal Benefit of Monitoring
• β∗ solved for from IFI’s problem
• RESULT: Can show that desire to monitor can increase from no

counterparty risk case

• RESULT: Adding this moral hazard problem doesn’t change

qualitative results

James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 38 / 39

Introduction Model Setup Results Extensions Conclusion

Insurance with Counterparty Risk

Double Moral Hazard problem

c′(M) + γ 1 dHM(ψ; M) Rf

C(γ−β∗P∗γ)

dF(θ)

• Marginal Cost of Monitoring

= S,R ψdHM(ψ; M) + Zγ 1 dHM(ψ; M) C(γ−β∗P∗γ)

Rf

dF(θ) + γP1

M

• Marginal Benefit of Monitoring
• β∗ solved for from IFI’s problem
• RESULT: Can show that desire to monitor can increase from no

counterparty risk case

• RESULT: Adding this moral hazard problem doesn’t change

qualitative results

James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 38 / 39

Introduction Model Setup Results Extensions Conclusion

Conclusion

• Modelled the incentive and informational effects of

counterparty risk

• A moral hazard problem can be present on the insurer side of

market

• The new moral hazard can alleviate the adverse selection

problem

• Contract size needn’t be large
• FUTURE: Regulatory implications: different counterparties

are regulated differently. What if anything should we do about it??

James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 39 / 39

Introduction Model Setup Results Extensions Conclusion

Conclusion

• Modelled the incentive and informational effects of

counterparty risk

• A moral hazard problem can be present on the insurer side of

market

• The new moral hazard can alleviate the adverse selection

problem

• Contract size needn’t be large
• FUTURE: Regulatory implications: different counterparties

are regulated differently. What if anything should we do about it??

James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 39 / 39

Introduction Model Setup Results Extensions Conclusion

Conclusion

• Modelled the incentive and informational effects of

counterparty risk

• A moral hazard problem can be present on the insurer side of

market

• The new moral hazard can alleviate the adverse selection

problem

• Contract size needn’t be large
• FUTURE: Regulatory implications: different counterparties

are regulated differently. What if anything should we do about it??

James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 39 / 39

Introduction Model Setup Results Extensions Conclusion

Conclusion

• Modelled the incentive and informational effects of

counterparty risk

• A moral hazard problem can be present on the insurer side of

market

• The new moral hazard can alleviate the adverse selection

problem

• Contract size needn’t be large
• FUTURE: Regulatory implications: different counterparties

are regulated differently. What if anything should we do about it??

James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 39 / 39

Introduction Model Setup Results Extensions Conclusion

Conclusion

• Modelled the incentive and informational effects of

counterparty risk

• A moral hazard problem can be present on the insurer side of

market

• The new moral hazard can alleviate the adverse selection

problem

• Contract size needn’t be large
• FUTURE: Regulatory implications: different counterparties

are regulated differently. What if anything should we do about it??

James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 39 / 39

Introduction Model Setup Results Extensions Conclusion

What if there are more than two types of banks?

Consider 3 types: 1 Probability of Default Highest risk type are sufficiently risky so that they are most con- cerned about counterparty risk

James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 39 / 39

Introduction Model Setup Results Extensions Conclusion

What if there are more than two types of banks?

Consider 3 types: 1 Probability of Default Middle risk type are sufficiently risky so that they do not want to report safe, but not risky enough to report highest risk level

James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 39 / 39

Introduction Model Setup Results Extensions Conclusion

What if there are more than two types of banks?

Consider 3 types: 1 Probability of Default Safest risk type are sufficiently safe so that they do not wish to report any more risk

James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 39 / 39

Introduction Model Setup Results Extensions Conclusion

Extending to N types

• Range for complete separation shrinks as N grows
• If chosen parameters does not support complete separation,

then will get interval separation. i.e. agents will report that there probability of default is within a range

James R. Thompson The University of Waterloo Counterparty Risk in Financial Contracts: Should the Insured Worry about the Insurer? 39 / 39