Book 2. Credit Risk

FRM Part 2

CR 20. CVA

Presented by: Sudhanshu

Module 1. Credit Valuation Adjustment

Module 2. Incremental and Marginal CVA, and CVA for a Bilateral Contract

Module 3. Wrong-Way Risk

Module 1. Credit Valuation Adjustment

Topic 1. Pricing Counterparty Risk

Topic 2. Credit Value Adjustment (CVA)

Topic 3. CVA Spread

Topic 4. Impact of Changes in Credit Spread and Recovery Rates

Topic 5. Incorporating Netting and Collateralization

Topic 1. Pricing Counterparty Risk

  • Pricing Function: Counterparty risk pricing depends on the credit exposure and default probability of the counterparty, generating reserves to absorb potential losses from default
  • Risk Mitigants: Pricing must account for risk mitigation techniques including:
    • Netting arrangements
    • Collateralization
  • Counterparty Risk Value: Represents the value of risk across all outstanding positions with a counterparty, calculated separately from and in addition to the price of the underlying financial instrument itself (e.g., swap pricing)
  • Organizational Responsibility: Best practices require clear assignment of responsibilities for calculating counterparty risk within the financial institution
  • Pricing Challenges: Greatest complexity arises with bilateral derivatives contracts (e.g., swaps with fixed and floating components) rather than one-way payment instruments such as bonds

Practice Questions: Q1

Q1. Which of the following statements is not a motivation for pricing counterparty risk?
A. Accurate pricing should only account for the cost of the trade.
B. Counterparty risk pricing should account for risk mitigants.
C. Best practices organize pricing responsibilities in the organization.
D. Pricing bilateral derivatives contracts.

Practice Questions: Q1 Answer

Explanation: A is correct.

Accurate pricing should account for not only the cost of the trade, but also the cost of counterparty risk.

Topic 2. Credit Value Adjustment (CVA)

  • CVA Definition: The expected value or price of counterparty credit risk; represents a cost to the counterparty with greater default propensity
  • Risky Value Formula: Risky value = risk-free value − CVA
    • CVA is the adjustment that accounts for counterparty credit risk
  • CVA Calculation Formula:
    •  
    •  
    • where
      • LGD (Loss Given Default): Expected loss upon counterparty default, equal to 1 minus recovery rate (1 − RR)
      • EPE (Expected Positive Exposure): Discounted expected positive exposure for future dates
      • PD (Probability of Default): Marginal default probability
  • Calculation Advantages:
    • Speed and simplicity are key features
    • Aggregates components from different risk management departments
    • Can be expressed as percentage of notional value
    • Assumes no wrong-way risk
    • Does not require simulation of default events, simplifying computation
C V A=-L G D \times \sum_{i-1}^T E P E\left(t_i\right) \times P D\left(t_{i-1}, t_i\right)

Topic 3. CVA Spread

  • CVA Spread Calculation: Divide CVA by the unit premium of a risky annuity (e.g., CDS) to produce an annual spread in basis points charged to the weaker counterparty
  • Formula:
    •  
    •  
    • where
      •                            = unit premium value of a credit default swap
      •           = CDS premium at maturity date T (can be thought of as a credit spread)
      • EPE = expected positive exposure, calculated as the average of expected exposure from present to transaction maturity
  • Key Assumptions:
    • EPE is constant over the entire profile
    • Default probability is constant over the entire profile
    • Expected exposure (EE) or default probability is symmetric over the entire profile
\frac{C V A(t, T)}{C D S_{\text {premium }}(t, T)}=-X^{C D S} \times \text { Average } E P E
C D S_{\text {premium }}(t, T)
X^{C D S}

Practice Questions: Q2

Q2. A trader wants to know the approximate CVA for a counterparty in a swap transaction. The expected potential exposure (EPE) is 7%, and its credit spread is 475 basis points. What is the CVA as a running spread?
A. ‒0.33%.
B. ‒1.48%.
C. ‒2.25%.
D. ‒9.75%.

Practice Questions: Q2 Answer

Explanation: A is correct.

Calculation of the CVA as a running spread entails multiplying the counterparty’s EPE by its credit spread:

 

-7 \% \times 4.75 \%=-33 \mathrm{bps}

Topic 4. Impact of Changes in Credit Spread and Recovery Rates

  • Key Evaluation Factors: Credit spread levels, shape of the credit spread curve, recovery rate impact, and basis risk between different recovery rate assumptions
  • Credit Spread Impact:
    • CVA typically increases with rising credit spreads, but the relationship is non-linear due to the 100% default probability ceiling
    • For counterparties near default, CVA decreases slightly; at actual default, CVA falls to zero
  • Credit Spread Curve Shape:
    • Upward-sloping curve produces lower CVA compared to flat and downward-sloping curves
    • Downward-sloping curve produces higher CVA compared to flat and upward-sloping curves
  • Recovery Rate Impact:
    • Increasing the recovery rate raises implied probability of default but reduces resulting CVA
    • Settled recovery (recovery at default) vs. actual recovery (claim amount received) differences affect CVA calculations
    • Example: 10% settled recovery with 40% actual recovery produces lower CVA than 40% assumption for both settled and actual rates

Practice Questions: Q3

Q3. Regarding the impact of changes in the credit spread and recovery rate assumptions on the CVA, which of the following statements is true?
A. A decrease in the credit spread will most often increase the CVA.

B. For an upward-sloping curve, the CVA will be higher compared to a downward-sloping curve.
C. Increasing the recovery rate will reduce the CVA.
D. If the actual recovery rate is higher than the settled recovery rate, the CVA will most likely be higher compared to a situation where both recovery assumptions are the same for both rates.

Practice Questions: Q3 Answer

Explanation: C is correct.

Increasing the recovery rate will increase the implied probability of default but reduce the resulting CVA. The CVA will most often increase given an increase in the credit spread.

When considering the shape of the credit spread curve, the CVA will be lower for an upward-sloping curve compared to a downward-sloping curve.

Finally, a higher actual recovery rate will most likely lead to a lower CVA compared to a situation where the recovery assumptions are the same for both actual and settled rates.

  • Netting Effect: Netting reduces CVA by offsetting exposure when trades are settled; new trades must be sufficiently profitable to offset any CVA increase
  • CVA Change Formula (Fig reference if applicable): The incremental CVA for a new trade is calculated as:
    •  
    • where
      • V(i) = the risk-free value of new trade i
      • CVA(NS, i) = CVA including the new trade in the netting set
      • CVA(NS) = CVA of all current trades within the netting set
  • Collateralization Impact: Collateral reduces CVA by lowering the counterparty's expected exposure (EE) without affecting default probability
  • Collateral Parameters:
    • Minimum transfer amounts and thresholds increase CVA by increasing exposure linearly
    • Initial margin (negative threshold) decreases CVA
  • Margin Period of Risk (MPoR): Defines the number of calendar days over which CVA is measured; as MPoR increases, CVA approaches uncollateralized levels (at 40 days MPoR, CVA is approximately half the uncollateralized CVA)
  • CVA Scaling: CVA can be scaled using the square root of time rule; for example, 20-day MPoR CVA is approximately                          times larger than 10-day MPoR CVA

Topic 5. Incorporating Netting and Collateralization

V(i)=\Delta C V A_{N S, i}=C V A(N S, i)-C V A(N S)
\sqrt{20/10}=1.41

Practice Questions: Q4

Q4. When incorporating netting and collateralization into the CVA calculation, which of the following statements is incorrect?
I. Netting increases the CVA price because it reduces exposure when trades are settled.
II. Collateralization does not change the CVA because it only changes the counterparty’s expected exposure.
A. I only.
B. II only.
C. Both I and II.
D. Neither I nor II.

Practice Questions: Q4 Answer

Explanation: C is correct.

Both statements are incorrect. Netting reduces the CVA price as it reduces exposure when trades are settled. Collateralization also reduces the CVA, changing only the counterparty’s expected exposure (EE), but not its default probability.

Module 2. Incremental and Marginal CVA, and CVA for a Bilateral Contract

Topic 1. Incremental and Marginal CVA

Topic 2. Converting CVA Into a Running Spread

Topic 3. Applying CVA to Exotic Products and Path Dependency

Topic 4. CVA for a Bilateral Contract (BCVA)

Topic 5. BCVA Spread

Topic 1. Incremental and Marginal CVA

  • Standalone CVA: Provides risk managers a quick appraisal of CVA charge; limited usefulness as it accounts for risk mitigation through collateralization and netting
  • Incremental CVA: Measures the change in CVA that a new trade creates, accounting for netting effects
    • Calculated as the difference between CVA with and without the new trade
    • Uses ΔEE (incremental change in expected exposure at each point in time) caused by the new trade
    • Important for pricing new trades relative to existing positions
    • CVA with netting never exceeds CVA without netting (netting cannot increase exposure)
    • Netting benefits are inversely related to transaction size; larger transactions receive smaller netting benefits, causing incremental CVA to approach standalone CVA
  • Marginal CVA: Breaks down netted trades into trade-level contributions that sum to total CVA
    • Calculation identical to standalone CVA but substitutes marginal EE for initial EE
    • Enables rigorous analysis by identifying which trades have the greatest impact on counterparty CVA
    • Provides ex-post view of trades for better portfolio understanding

Practice Questions: Q1

Q1. With respect to the CVA calculation, which of the following statements is correct when a risk manager wishes to understand which trades have the greatest impact on a counterparty’s CVA? The manager would use:
A. incremental CVA because it accounts for the change in CVA once the new trade is priced, accounting for netting.
B. marginal CVA because he could break down netted trades into trade level contributions.
C. incremental CVA because he could break down netted trades into trade level contributions.
D. marginal CVA because it accounts for the change in CVA once the new trade is priced, accounting for netting.

Practice Questions: Q1 Answer

Explanation: B is correct.

Understanding which trades have the greatest impact on a counterparty’s credit value adjustment requires use of the marginal CVA. Incremental CVA, by contrast, is useful for pricing a new trade with respect to an existing one.

Topic 2. Converting CVA Into a Running Spread

  • CVA Spread Calculation Method: Convert upfront CVA into a running spread by dividing CVA by risky duration for the relevant maturity, adjusting the swap rate charged to the client
  • Calculation Example: For a 5-year payer interest rate swap with $100M notional, risky duration of 3.75, and standalone CVA of -$90,000:
    • Additional spread = -90,000 / (3.75 × 100,000,000) = -2.40 bps
  • Recursive Adjustment Required: Adding the spread impacts the CVA itself, requiring iterative calculation until the risky mark-to-market value reaches zero
  • Final Equilibrium Condition: Solve the equation                  ,    , where       is the contract value at adjusted rate C'
    • This ensures CVA is offset by initial value
    • Adjusted rate C' becomes the hurdle rate for profitability
\mathrm{V}_{\mathrm{C}^{\prime}}=\mathrm{CVA}_{\mathrm{C}^{\prime}}
\mathrm{V}_{\mathrm{C}^{\prime}}

Topic 3. Applying CVA to Exotic Products and Path Dependency

  • Exotic Products Valuation Challenges: Complex products requiring Monte Carlo simulation necessitate value approximations for CVA estimation due to pricing complexity
    • Swaptions may be approximated as forward swaps
    • Bermudan option payoffs may be treated as European option payoffs
  • Path Dependency Issues: Assessing future exposure at a given point requires complete path information from present to that future date, requiring probability approximations for path-dependent events in exotic derivative pricing

  • Path-Dependent Payoffs: The final value of a path-dependent option is determined not just by the final price of the underlying, but by the average price (in the case of an Asian option) or the maximum/minimum price (in the case of a lookback option) over a specified period.

  • Impact on CVA: This path dependency means that the exposure at any given time depends on the path taken to reach that time, and cannot be determined by the value of the underlying at that time alone. This significantly complicates the CVA calculation, reinforcing the need for Monte Carlo simulation to generate and evaluate a wide range of potential pa

Topic 3. Applying CVA to Exotic Products and Path Dependency

Topic 4. CVA for a Bilateral Contract (BCVA)

  • Definition: Acknowledges that both counterparties in a contract can default. BCVA is the sum of the CVA and the Debt Value Adjustment (DVA). It represents the cost of potential losses from both your counterparty defaulting on you and you defaulting on your counterparty.

  • Formula:

  • Components:

    • CVA (Credit Value Adjustment): The adjustment for the risk that your counterparty will default on you. This is calculated using your Expected Positive Exposure (EPE).

    • DVA (Debt Value Adjustment): The adjustment for the risk that you will default on your counterparty. This is calculated using your Expected Negative Exposure (ENE).

  • Relationship to DVA and BCVA:
    •           is the Loss Given Default of your institution, and         is the probability of default for your institution.
    • BCVA, therefore, considers the value of all future expected losses and gains due to default by both parties. It is a more comprehensive measure of counterparty risk than CVA alone.
BCVA=CVA+DVA
D V A=-L G D_I \times \sum_{i-1}^m \operatorname{ENE}\left(t_i\right) \times P D_I\left(t_{i-1}, t_i\right)
P D_I
LGD_I

Topic 5. BCVA Spread

  • BCVA Spread Formula: BCVA can be expressed as a basis point charge to the weaker counterparty using the ratio of BCVA to CDS premium:
    •  
    •  
    • where
      •          : the institution's own CDS spread
      • EPE: expected positive exposure
      • ENE: expected negative exposure (opposite of EPE)
  • Running Spread Representation: The formula represents BCVA as a running spread that accounts for the institution's own default risk through reduction of unilateral CVA charge by its own credit spreadmultiplied by the ENE.
  • Distinction from Unilateral CVA: The calculation is identical to unilateral CVA except for an additional subtractive calculation that reflects the financial institution's own BCVA component
\frac{B C V A(t, T)}{C D S_{\text {premium }}(t, T)}=-X_C^{C D S} \times \text { average EPE }-X_I^{C D S} \times \text { average ENE }
X_I^{C D S}

Topic 5. BCVA Spread

  • Example: A risk manager needs a quick calculation of the BCVA on a swap. Assume inputs are as follows: EPE = 5%, ENE = 3%, counterparty credit spread = 300 bps, and financial institution credit spread = 200 bps. Calculate the BCVA from the perspective of the financial institution.
  • Answer: From the perspective of the financial institution:
    • ​
    •  

    • This is what the financial institution may charge the counterparty for overall counterparty risk.

\begin{aligned} \text{BCVA} &= -EPE × \text{counterparty credit spread}-ENE \times \text{institution credit spread} \\ \text{BCVA} &=(-5 \% \times 300) \times-(-3 \% \times 200)=-9 \mathrm{bps} \end{aligned}

Module 3. Wrong-Way Risk

Topic 1. Wrong-Way Risk (WWR) and Right-Way Risk (RWR)

Topic 2. Examples of WWR and RWR

Topic 3. WWR Modeling

Topic 4. Impact of Collateral on WWR

Topic 5. Impact of CCPs on WWR

Topic 1. Wrong-Way Risk (WWR) and Right-Way Risk (RWR)

  • Wrong-Way Risk (WWR) Definition: Any association, dependence, or linkage between exposure and counterparty creditworthiness that increases overall counterparty risk, resulting in higher credit value adjustment (CVA) and lower debt value adjustment (DVA)
  • WWR Challenges: Difficult to determine due to complexities in assessing variable relationships and lack of relevant historical data
  • Right-Way Risk (RWR) Definition: Any dependence or linkage between exposure and counterparty default probability that decreases overall counterparty risk, reducing CVA and increasing DVA
  • Historical Focus Imbalance: WWR has received significant attention historically while RWR has been relatively neglected, though both risks are important; financial institutions should increase RWR and decrease WWR
  • RWR as Market Normality: Derivatives markets functioning normally exemplify RWR; hedges in normal markets automatically generate RWR by reducing counterparty risk
    • Example: Coffee producer shorts forward contracts to protect against falling prices
    • Example: Textile manufacturer longs cotton derivatives anticipating price increases

Topic 1. Wrong-Way Risk (WWR) and Right-Way Risk (RWR)

  • WWR in Market Disruptions: Markets do not always produce normal behavior (evidenced by the global financial crisis); protection buyers against debt defaults (e.g., CDOs) became WWR victims when unfavorable interaction between exposures and insurers' default probabilities intensified counterparty credit risk
  • Counterparty Risk Calculation: Counterparty risk equals the product of exposure and counterparty's default probability at a specified loss given default rate; similar to loan loss reserves but with fluctuating exposure in OTC derivatives markets
  • WWR/RWR Examples: Changes in exposure and counterparty credit quality produce unfavorable (WWR) or favorable (RWR) dependencies, influenced by external factors including interest rates, inflation, exchange rates, and global events
  • Credit Quality Paradox: Higher counterparty credit quality actually increases WWR because high-quality counterparty defaults are less expected than low-quality counterparty defaults

  • General Concepts:

    • Loan Guarantee Scenario:
      • WWR: Borrower Company XYZ and guarantor Company ABC share ownership or operate in same industry; market/economic factors cause both to default simultaneously
      • RWR: Guarantor and borrower in different industries without shared ownership; XYZ's loan guarantee remains valid even if XYZ defaults
    • Protection Seller Concentration:
      • WWR: ABC sells protection exceeding its capital in concentrated area; macro factors increase exposure while deteriorating ABC's credit quality, making XYZ's protection worthless
      • RWR: Increase in exposure sufficiently offset by improvement in creditworthiness
    • CVA Estimation: CVA (product of exposure and default probability) assumes independence; unfavorable (favorable) association between default probability and exposure produces WWR (RWR), increasing (decreasing) overall CVA
    • Quantification Approach: WWR/RWR involves estimating CVA based on expected exposure conditional on counterparty default (realistic interconnected markets scenario) versus unconditional default probability under independence assumption

Topic 2. Examples of WWR and RWR

  • OTC Put Options

    • ​WWR Example: Macroeconomic events deteriorate counterparty creditworthiness (increasing default probability) while simultaneously triggering underlying asset price fall (increasing payoffs for long); positive correlation between exposure and default probability increases overall counterparty risk despite increasing payoffs

    • RWR Example: Counterparty able to fulfill obligation despite increase in position obligation; normalcy of transaction maintained
    • Note: Out-of-the-money put options have more WWR than in-the-money put options

  • OTC Call Options

    • ​RWR Example (Normalcy): Macroeconomic factors cause counterparty default probability to decline while underlying asset price increases; counterparty in strong position to fulfill obligation despite higher payoffs for call buyer

    • WWR Example: Counterparty unable to fulfill obligation due to increased position obligation (higher underlying value for long equals higher obligation for short), increasing counterparty risk exposure

Topic 2. Examples of WWR and RWR

  • Credit Default Swaps (CDSs)

    • ​WWR Example - 2007-2009 Crisis: Protection buyers on CDOs/MBS-backed bonds experienced classic WWR when

      • Real estate bubble burst caused MBS values to freefall
      • Monoline insurers (AMBAC, MBIA) with concentrated protection positions flooded with claims
      • Both default probability and risk exposure of insurers rose simultaneously
      • Despite huge CDS gains, nothing materialized due to deteriorating insurer creditworthiness
    • RWR Example: Insurance company with nonconcentrated exposure experiences fewer claims, maintains creditworthiness, and fulfills obligations despite increasing CDS risk exposure

  • Commodities

    • ​WWR Example - Oil Hedging: Airline long oil forward contract at fixed price with dealer holding concentrated positions

      • Rising oil prices increase airline gains (buy cheap oil below spot) and dealer risk exposure
      • Flood of claims from multiple airlines pressures dealer's credit quality
      • Simultaneous increase in risk exposure and default probability increases overall counterparty risk
    • RWR Example: Dealer with nonconcentrated position maintains sound creditworthiness despite rising exposure, able to fulfill obligations, lowering expected risk exposure for airline

Topic 2. Examples of WWR and RWR

  • Foreign Currency Transactions

    • ​WWR Example: US commercial bank enters cross-currency agreement with emerging market bank (Uzbekistan)

      • Sovereign debt crisis creates credit stress for local bank
      • Local currency depreciates significantly
      • Transaction value increases substantially for US bank while counterparty risk exposure increases
      • Positive association between default probability (credit stress) and risk exposure (declining currency) increases overall counterparty risk
    • RWR Example: Risk exposure increases but default probability declines due to creditworthiness improvement, reducing overall counterparty risk​

Topic 2. Examples of WWR and RWR

  • Foreign Currency Swaps

    • WWR Example - Japanese Banks Pre-2007 Crisis:
      • Japanese banks entered swap agreements to obtain dollar funding using yen
      • Post-Lehman default, yen appreciated significantly against dollar
      • Japanese banks gained (pledged yen buys more dollars) while counterparty risk exposure increased
      • Deteriorating US macro conditions increased default probabilities of US financial institutions
      • Positive association between exposure and default probability generated overall counterparty risk increase for Japanese banks
    • RWR Example: Risk exposure and default probabilities not positively associated; macro factors improve creditworthiness balancing increased exposure; counterparty meets obligation despite appreciating yen​

Topic 2. Examples of WWR and RWR

  • Interest Rate Transactions

    • WWR Example - European Sovereign Debt Crisis:
      • Economic downturn led to policy interest rate cuts
      • Fixed-rate receivers against Italian financial institutions gained as euro swap rate declined
      • Declining swap rate increased counterparty risk exposure
      • Deteriorating economic conditions increased Italian financial institutions' default probability
      • Simultaneous increase in risk exposure and default probability generated WWR for fixed-rate receiver holders
    • RWR Example: Without positive association between risk exposure and default probability, Italian financial institutions fulfill obligations comfortably despite increased exposure​

Topic 2. Examples of WWR and RWR

Practice Questions: Q1

Q1. How many of the following statements regarding wrong-way risk (WWR) and right-way risk (RWR) are correct?

  • Co-movement in risk exposure and default probability producing a decline in overall risk is an example of wrong-way risk.
  • Co-movement in risk exposure and default probability producing an increase in overall counterparty risk is an example of right-way risk.
  • Co-movement in risk exposure and default probability producing neither a decline nor an increase in the overall counterparty risk is an example of wrong-way risk.
  • Co-movement in risk exposure and default probability producing a decline in risk exposure but an increase in counterparty default probability is an example of right-way risk.

A. None.
B. All.
C. Two.
D. Three.

Practice Questions: Q1 Answer

Explanation: A is correct.

A decline in overall counterparty risk is an example of right-way risk. An increase in overall counterparty risk is an example of wrong-way risk. An increase in overall counterparty risk is a condition for the emergence of wrong-way risk. A decline in risk exposure but increase in counterparty default probability may or may not lower overall counterparty risk.

Practice Questions: Q2

Q2. Which of the following events would likely lead to an increase in WWR?
I. The borrower and the guarantor are business partners.
II. A monoline insurer sold protection concentrated in a business or industry.
A. I only.
B. II only.
C. Both I and II.
D. Neither I nor II.

Practice Questions: Q2 Answer

Explanation: C is correct.

WWR will increase if the borrower and guarantor are business partners. The guarantees offered by a monoline insurer may turn out to be worthless if the risk exposure increases and the guarantor is hit by a flood of claims due to a concentrated position in an industry or business.

Practice Questions: Q3

Q3. Which of the following statements regarding WWR and RWR is correct?
A. A long put option is subject to WWR if both risk exposure and counterparty default probability decrease.
B. A long call option experiences RWR if the interaction between risk exposure and counterparty default probability produces an overall decline in counterparty risk.
C. Declining local currency can decrease the position gain in a foreign currency transaction, while increasing risk exposure of the counterparty.
D. The 2007–2009 credit crisis provides an example of WWR from the perspective of a long who had sold credit default swaps (CDSs) as protection against bond issuers’ default.

Practice Questions: Q3Answer

Explanation: B is correct.

A long call option experiences RWR if risk exposure and counterparty default probability results in decreased counterparty risk. A long put option is subject to WWR if both risk exposure and counterparty default probability increase. Declining local currency can increase the position gain in a foreign currency transaction, while increasing counterparty risk exposure. The 2007–2009 credit
crisis provides an example of WWR from the perspective of a long who had bought CDSs as protection against bond issuers’ default.

Practice Questions: Q4

Q4. How many of the following statements regarding counterparty risk are correct?

  • Speculation in normal-functioning derivatives markets automatically produces RWR.
  • RWR has been the center of attention in historical context, whereas WWR has not been paid much relative attention.
  • The counterparty default probability does not enter into the equation for estimating the overall counterparty risk.
  • Unlike exposure to OTC derivatives, which is normally assumed to be a fixed amount for a specified time period, exposure to bank loans fluctuates depending on market conditions.

A. None.
B. All.

C. Two.
D. Three.

Practice Questions: Q4 Answer

Explanation: A is correct.

Hedging, and not speculation, in normal functioning markets automatically produces RWR. Historically, RWR was relatively neglected by institutions for planning purposes. The counterparty default probability is one of the key elements in estimating overall counterparty risk. OTC exposures fluctuate based on market conditions.

Practice Questions: Q5

Q5. Which of the following statements is correct?
I. Depreciation of the yen after the default of Lehman Brothers gave a substantial gain to Japanese bank foreign currency swaps positions to obtain dollar funding in interest rate swaps.
II. Fixed-rate receivers experience a value gain to the extent that the swap rate increases.
A. I only.
B. II only.
C. Both I and II.
D. Neither I nor II.

Practice Questions: Q5 Answer

Explanation: D is correct.

Appreciation, and not depreciation, of the yen generated a substantial gain for Japanese banks with foreign currency swaps positions. A fixed-rate receiver experiences a value gain to the extent that the swap rate declines.

Topic 3. WWR Modeling

  • Hazard Rate Approach (Intensity Approach): Easiest method to implement; generates stochastic simulation for credit spreads and computes conditional expected positive exposure for default paths (typically with wider spreads)
    • Limitation: Does not generally indicate strong dependence between default and exposure, potentially underestimating WWR
  • Structural Approach: Maps default distribution and exposure distribution onto a bivariate distribution; WWR identified through combination of early default time and higher exposure
    • Positive correlation between default time and exposure indicates higher CVA
    • Advantage: Uses pre-existing exposure distribution
    • Disadvantage: Information may not be relevant to current conditions
  • Parametric Approach: Direct method examining historical link between portfolio exposure and credit spreads; high portfolio values linked to above-average credit spreads suggest WWR presence
    • Higher dependency parameter indicates higher CVA
    • Reliability depends on historical data reflecting current scenarios
  • Jump Approach: Most applicable to WWR as it implies a jump at default (e.g., FX rates jump when counterparty defaults due to currency devaluation)
    • Jump factor referred to as residual value (RV) factor; FX rate depreciates by (1 – RV)
    • Historical evidence shows larger jumps for large firms and highly rated sovereigns due to more significant market shocks

Topic 4. Impact of Collateral on WWR

  • Collateral as Exposure Reduction: Collateral effectiveness in reducing WWR depends on the pattern of exposure increase
  • Gradual Exposure Increase: When exposure increases gradually before default, collateral is typically taken to minimize WWR impact
    • Benefits from collateral increase as WWR increases
    • Additional collateral is relatively easy to request and receive
  • Jump-to-Default Exposure: When exposure jumps suddenly at a specific point in time, collateral benefits are very limited
    • Example: Currency devaluation associated with sovereign default makes timely collateral receipt difficult
  • WWR Collateral Examples:
    • Payer interest rate swap collateralized with high-quality government bond (swap value increases when rates rise, causing margin to decrease)
    • Cross-currency swap collateralized by either currency in the transaction (FX rate moves increase exposure while reducing collateral value when margin is held in the currency being paid)
    • Firm posting its own bonds as collateral (more direct but weaker example of WWR)

Topic 5. Impact of CCPs on WWR

  • CCP Role in Systemic Risk Mitigation: Central counterparties provide central clearing services for financial transactions between member firms, standing in the middle of previously bilateral OTC transactions and operating as the buyer for every seller and vice versa, eliminating direct counterparty risk
  • Market-Neutral Operations: CCPs remain market-neutral by netting all buy-side transactions with offsetting sell-side transactions through multilateral netting, requiring counterparties to post collateral via margin accounts with daily or intra-day MtM processes
  • Default Resolution Process (Novation): In the event of default, CCPs close out non-performing bilateral contracts and replace them with new counterparties capable of meeting obligations; losses are mutualized among all member firms through default funds held on reserve and fed by member contributions
  • CCP Vulnerability to WWR: CCPs are particularly susceptible to wrong-way risk due to dependence on collateral and default fund contributions
    • If defaulting member's posted margin and default fund contributions fail to cover losses, CCPs must use own equity capital and/or non-defaulting members' default funds
    • Loss waterfall structure may be insufficient if initial margins and default fund contributions fail to incorporate WWR
  • WWR Mitigation Strategies:
    • CCPs should demand higher margins and default fund contributions from higher credit quality members (since WWR increases with credit quality)
    • Impose higher haircuts on risky and illiquid assets posted as collateral to address members posting such assets that create higher WWR levels