Book 2. Credit Risk

FRM Part 2

CR 21. The Evolution of Stress Testing Counterparty Exposure

Presented by: Sudhanshu

Module 1. Counterparty Credit Risk (CCR)

Module 2. Stress Testing

Module 1. Counterparty Credit Risk (CCR)

Topic 1. CCR Exposure Measures

Topic 2. CCR Treatment

Topic 1. CCR Exposure Measures

  • Evolution of CCR:

    • CCR Development Timeline: CCR gained prominence in the 1990s and now forms a critical part of risk governance; financial institutions initially analyzed derivatives exposures by tracking current exposure and measuring regulatory capital as add-ons (calculated as percentage of gross notional values)
    • CCR Modeling Evolution: Models progressed from potential exposure models to expected positive exposure models, enabling derivatives integration into portfolio risk models alongside loans and forming the basis for Basel II regulatory capital with credit mitigants (including netting agreements)
    • Wrong-Way Risk: Risk that exposure from a counterparty grows simultaneously as the counterparty's default risk increases; does not arise with fixed-rate loans

Topic 1. CCR Exposure Measures

  • Four Key Exposure Metrics for CCR:

    • Current Exposure (Replacement Cost): The greater of zero or the market value of a transaction (or portfolio) that would be lost if the counterparty defaulted with no bankruptcy recovery
    • Peak Exposure: Distribution of exposures at a high percentile (95% or 99%) at a given future date prior to longest maturity exposure in the netting group; typically generated for multiple future dates
    • Expected Exposure: Mean (average) distribution of exposures at a given future date prior to longest maturity exposure in the netting group; also typically generated for multiple future dates
    • Expected Positive Exposure (EPE): Weighted average of expected exposures over time, where weights represent the proportion of individual expected exposures of the entire time interval
      • For minimum capital requirement purposes: measured over first year or length of longest maturing contract

Practice Questions: Q1

Q1. Which of the following exposure measures reflects the average distribution of exposures at a specific future date prior to the maturity of the longest maturity transaction within a netting set?
A. Peak exposure.
B. Current exposure.
C. Expected exposure.
D. Expected positive exposure.

Practice Questions: Q1 Answer

Explanation: C is correct.

Expected exposure measures the mean distribution of exposures at a given future date prior to the maturity of the longest maturity exposure in the netting group.

Topic 2. CCR Treatment

  • Historical Treatment via CVA: CVA represents the market value of CCR. Pre-2008 crisis, stable credit spreads kept CVAs as a small portfolio component, but the GFC caused unusual losses/gains prompting active CVA risk management
  • Dual Nature Challenge: Financial institutions may view CCR as either credit risk or market risk, but managing it in a silo exposes the institution to risks from the other perspective
  • CCR as Credit Risk:
    • Exposes institutions to changes in CVA; CVA must be included in derivatives portfolio valuation to avoid large market value swings
    • Credit risk managed at inception (typically through collateral arrangements) but not actively managed post-trade
    • Emphasis on risk mitigation and credit evaluation since all trades must be replaced in the market at default
  • ​CCR as Market Risk:
    • Allows hedging of market risk losses but leaves exposure to counterparty creditworthiness declines and default
    • CCR can be hedged by replacing contracts proportionally to counterparty's probability of default (PD) before default occurs
    • Low PD counterparties see minimal trade replacement; deteriorating credit quality counterparties have trades replaced faster and moved to other counterparties

Topic 2. CCR Treatment

  • Complexity of Dual Treatment:
    • Creates large variety of complex measurements: credit risk uses current exposure, peak exposure, and expected exposure; market risk uses CVA and CVA VaR
    • Stress testing produces extensive results: at least 2 × (number of counterparties + 1) scenarios, doubling again if instantaneous shocks are considered alongside stressed risk measures

Practice Questions: Q2

Q2. Is the following statement on the treatment of counterparty credit risk (CCR) correct?
“Treating CCR as a market risk does not allow an institution to hedge market risk losses, and it exposes the institution to declines in counterparty creditworthiness and default.”
A. The statement is correct with regard to both hedging market risk losses and counterparty creditworthiness and default.
B. The statement is incorrect with regard to both hedging market risk losses and counterparty creditworthiness and default.
C. The statement is correct with regard to hedging market risk losses only.
D. The statement is correct with regard to counterparty creditworthiness and default only.

Practice Questions: Q2 Answer

Explanation: D is correct.

Treating CCR as a market risk allows an institution to hedge market risk losses; however, it leaves the institution exposed to declines in counterparty credit worthiness and default. CCR can be hedged by the ongoing replacement of contracts with a counterparty instead of waiting for default to occur.

Module 2. Stress Testing

Topic 1. Stress Testing Current Exposure

Topic 2. Stress Testing Expected Loss

Topic 3. Stress Testing CVA

Topic 4. Stress Testing DVA

Topic 5. Shortcomings of Stress Testing CCR

Topic 1. Stress Testing Current Exposure

  • Common Approach: Financial institutions apply current exposure stresses by repricing portfolios under risk-factor change scenarios, with counterparties showing largest current and stressed exposures reported to senior management
  • Example: Equity crash scenario (e.g., 25% market decline) generates reports showing:
    • Top counterparties with largest stressed current exposure
    • Credit ratings, mark-to-market values, collateral values, and current exposures
    • Identification of counterparties most vulnerable to specific market events
    • Multiple scenario tables (equity crashes, credit events, interest-rate shocks) potentially highlighting different counterparties
  • Shortcoming 1 - Aggregation Challenges: Aggregating stress results is difficult and requires additional information:
    • Simply summing all exposures assumes simultaneous default of all counterparties (unlikely scenario)
    • Stressed current exposures ignore counterparty credit quality
    • Results focus on trade values, not counterparty's capacity or willingness to repay
    • Particularly problematic when comparing high-risk early-stage companies versus highly-rated mature companies
    • Incorporating counterparty credit quality into each stress scenario is operationally challenging
  • Shortcoming 2 - WWR: Stress results of current exposure do not provide information on wrong-way risk, as they omit counterparty credit quality from the analysis

Practice Questions: Q1

Q1. An analyst notes that stress testing current exposure is problematic because aggregating results is typically not meaningful, although it is easy to account for the credit quality of the counterparty.
Are the analyst’s statements correct?
A. The analyst is correct with regard to both aggregating results and credit quality.
B. The analyst is correct with regard to aggregating results only.
C. The analyst is correct with regard to credit quality only.
D. The analyst is incorrect with regard to both aggregating results and credit quality.

Practice Questions: Q1 Answer

Explanation: B is correct.

The analyst is correct to state that aggregating stress results is not meaningful. Simply taking the sum of all exposures only considers the loss that would occur if all counterparties were to simultaneously default. This is an unlikely scenario. The analyst’s statement on credit quality of the counterparty is incorrect since stresses do not factor in the credit quality of the counterparty.

Topic 2. Stress Testing Expected Loss

  • Loan Portfolio Expected Loss:
    • ​EL Formula: Expected loss is a function of probability of default (       ), exposure at default (          ), and loss given default (         ):
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    • Stressed Expected Loss (        ): Conditional on impact of macroeconomic variables (unemployment rate, exchange rates) on PD:
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    • Stress Loss Calculation: Difference between         and EL; scenarios created by stressing PDs or macroeconomic/balance sheet variables
E L=\sum_{i=1}^N P D_i \times E A D_i \times L G D_i
E L_S=\sum_{i-1}^N P D_i^S \times E A D_i \times L G D_i
PD_i
EAD_i
LGD_i
EL_S
EL_S

Topic 2. Stress Testing Expected Loss

  • Derivatives Portfolio Expected Loss
    • Key Difference: Replaces stochastic exposure at default (EAD) with expected positive exposure (          ) multiplied by alpha factor (α):
    • Formulas for EL and         are given by:
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    • Stress Testing Approach: Scenarios created by stressing PDs, macroeconomic variables, balance sheet values, or market variables (swap rates, equity prices)
      • Impact may increase or decrease EL depending on portfolio directional bias, margining status, and excess margin
    • EPE Stress Characteristics: Market variable shocks are typically instantaneous; common approach shocks current exposure only rather than over time
      • Impact depends on degree of collateralization and portfolio moneyness
E L=\sum_{i-1}^N P D_i \times\left(E P E_i \times \alpha\right) \times L G D_i
E L_S=\sum_{i-1}^N P D_i^S \times\left(E P E_i^S \times \alpha\right) \times L G D_i
EL_S
EPE_i

Topic 2. Stress Testing Expected Loss

  • Joint Stresses and Wrong Way Risk
    • Joint Credit-Market Stresses: Conceptually simple but challenging in practice due to weak connections between credit quality and market variables
      • Equity-based approaches closest to modeling joint stresses, but link between exposure shock and equity-based PD remains unclear
    • Wrong-Way Risk: Current best practice is to stress current exposure and identify most vulnerable counterparties rather than modeling PD-exposure connection
  • CCR Treatment Approaches
    • ​CCR as Credit Risk: Improves loan portfolio management; enables aggregating losses with loan portfolios and considering counterparty credit quality
    • CCR as Market Risk: Facilitates joint stresses of credit quality and exposure; allows deriving PD from market variables

Practice Questions: Q2

Q2. Which of the following statements best reflects the reason why a financial institution does not need to consider aggregating stresses to the expected positive exposure (EPE) with its loan portfolio?
A. Loans are not sensitive to market variables.
B. Stresses to EPE are not sensitive to market variables.
C. The EPE and the loan portfolio are negatively correlated.
D. The EPE and the loan portfolio are positively correlated.

Practice Questions: Q2 Answer

Explanation: A is correct.

A financial institution does not need to consider aggregating stresses to the EPE with its loan portfolio, because loans are not sensitive to market variables and, therefore, will not have any exposure changes from changes in market variables.

Topic 3. Stress Testing CVA

  • Stress Testing CCR: Stress testing CCR for market risk examines losses in market value of counterparty exposure due to market risk events or credit spread changes
  • CVA Considerations:
    • Financial institutions typically stress test only unilateral CVA (counterparty's default to the institution)
    • Should also consider bilateral CVA (BCVA) to account for institution's potential default to counterparties
  • CVA Calculation: Simplified CVA formula (excluding wrong-way risk):
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    • All components depend on market variables (credit spreads, market spreads, derivatives values)
  • ​Stressed CVA: Apply instantaneous shock to market variables affecting discounted expected exposure or risk-neutral marginal default probability
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\text C V A=-\sum_{n-1}^N L G D_n^* \times \sum_{j-1}^T E P E_n^*\left(t_j\right) \times P D_n^*\left(t_{j-1}, t_j\right)
C V A_S=-\sum_{n-1}^N L G D_n^* \times \sum_{j-1}^T E P E_n^S\left(t_j\right) \times P D_n^S\left(t_{j-1}, t_j\right)
\text{Stress Loss}=CVA_S - CVA

Topic 3. Stress Testing CVA

  • Credit-Risk vs. Market-Risk Framework Differences:
    • Both rely on EL as function of LGD, exposure, and PD, but values differ by perspective
    • CVA uses risk-neutral values (vs. physical values for ELs)
    • CVA uses ELs over transaction's life (vs. specific time horizon for ELs)
  • Correlation and Market-Based Modeling: CVA uses market-based PD model that incorporates correlation between exposure and PD, significantly influencing CVA; institutions should stress test correlation assumptions due to uncertainty

Topic 4. Stress Testing DVA

  • DVA Component: Financial institutions must include liability effects in stress calculations through bilateral CVA to properly calculate CVA profit and loss; this incorporates the debt value adjustment (DVA), which represents the institution's option to default to a counterparty
  • BCVA Formula Differences: BCVA differs from standard CVA in two key ways:
    • Incorporates ENE calculated from the counterparty's perspective
    • Includes the counterparty's probability of survival (denoted as    ) since the institution's default option depends on counterparty survival first
  • BCVA Formula:
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  • CDS Spread Dependence: Survival probability depends on CDS spreads, and losses depend on the institution's own credit spread, which may produce counterintuitive results (e.g., losses occurring from credit quality improvement)
  • Stress Testing Application:
    • Calculate stress losses by subtracting current BCVA from stressed BCVA
    • BCVA allows CCR to be treated as market risk, enabling consistent inclusion in market risk stress testing
    • Gains or losses from BCVA stress can be added to market risk stress test results
\begin{aligned} B C V A & =-\sum_{n=1}^N \operatorname{LGD}_n^* \times \sum_{j=1}^T \operatorname{EPE}_n^*\left(t_j\right) \times \operatorname{PD}_n^*\left(t_{j-1}, t_j\right) \times S_I^*\left(t_{j-1}\right) \\ & -\sum_{n=1}^N \operatorname{LGD}_I^* \times \sum_{j=1}^T \operatorname{ENE}_n^*\left(t_j\right) \times \operatorname{PD}_I^*\left(t_{j-1}, t_j\right) \times S_n^*\left(t_{j-1}\right) \end{aligned}
S_I

Practice Questions: Q3

Q3. Is the following statement on bilateral credit valuation adjustment (BCVA) correct?

“The formula for BCVA is similar to the formula for CVA, except that the BCVA formula uses expected positive exposure (EPE) and it incorporates the probability of the counterparty’s survival.”
A. The statement is correct with regard to both EPE and probability of survival.
B. The statement is correct with regard to EPE only.
C. The statement is correct with regard to probability of survival only.
D. The statement is incorrect with regard to both EPE and probability of survival.

Practice Questions: Q3 Answer

Explanation: C is correct.

The BCVA formula differs from the CVA formula in that BCVA incorporates expected negative exposure (ENE), and the probability of the counterparty’s survival must be included in the BCVA formula.

Topic 5. Shortcomings of Stress Testing CCR

  • Limited Integration: CCR stress testing is relatively new, and institutions typically do not aggregate CCR with loan portfolio or trading position stress tests
  • Incorrect Exposure Measure: Institutions commonly stress test current exposure when incorporating losses with loan or trading positions, but should instead use expected exposure or expected positive exposure to avoid significant errors
  • At-the-Money Exposure Errors: Using current exposure can lead to particularly significant errors when measuring derivatives market values for at-the-money exposures
  • Delta Sensitivity Limitations: Calculating exposure changes using delta sensitivities is challenging for CCR due to delta's nonlinear nature
    • Linearization of delta sensitivities in models can produce significant errors