Financial Risk Manager Part 2
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The Chief Risk Officer (CRO) at an investment bank has tasked the risk department with assessing the bank’s derivative exposure to a counterparty over a three-year period. The risk department assumes a constant hazard rate process for the counterparty’s default probability. The table below provides trade and forecast data on the CDS spread, expected exposure, and recovery rate for the counterparty:
Year 1 Year 2 Year 3 Expected positive exposure (AUD million) 14 14 14 CDS spread (bps) 200 300 400 Recovery rate (%) 80 70 60
The CRO has also provided the following assumptions for the analysis:
- A credit support annex is in place, requiring the counterparty to post AUD 11 million in collateral to mitigate the exposure.
- The risk-free interest rate is 3%, with a flat term structure over the three-year period.
- Both the collateral and expected positive exposure remain constant as projected over the three-year contract duration.
- The same discount factors are applied to both the expected positive exposure and the collateral.
- The bank’s annual default probability is 0%.
Using the provided data and assumptions, calculate the unilateral Credit Valuation Adjustment (CVA) for this derivative position.
The Chief Risk Officer (CRO) at an investment bank has tasked the risk department with assessing the bank’s derivative exposure to a counterparty over a three-year period. The risk department assumes a constant hazard rate process for the counterparty’s default probability. The table below provides trade and forecast data on the CDS spread, expected exposure, and recovery rate for the counterparty:
| Year 1 | Year 2 | Year 3 | |
|---|---|---|---|
| Expected positive exposure (AUD million) | 14 | 14 | 14 |
| CDS spread (bps) | 200 | 300 | 400 |
| Recovery rate (%) | 80 | 70 | 60 |
The CRO has also provided the following assumptions for the analysis:
- A credit support annex is in place, requiring the counterparty to post AUD 11 million in collateral to mitigate the exposure.
- The risk-free interest rate is 3%, with a flat term structure over the three-year period.
- Both the collateral and expected positive exposure remain constant as projected over the three-year contract duration.
- The same discount factors are applied to both the expected positive exposure and the collateral.
- The bank’s annual default probability is 0%.
Using the provided data and assumptions, calculate the unilateral Credit Valuation Adjustment (CVA) for this derivative position.
Explanation:
The calculation of Credit Valuation Adjustment (CVA) in the provided file content is based on the following steps:
-
Marginal Probability of Default (PD) Calculation: The marginal probabilities of default for each year are calculated using the formula , where is the time in years. This results in:
- Year 1: 9.52%
- Year 2: 18.13% (with a marginal increase of 8.61% from Year 1)
- Year 3: 25.92% (with a marginal increase of 7.79% from Year 2)
-
Discount Factor (DF): The discount factors for each year are given as:
- Year 0: Not applicable (as it's the base year)
- Year 1: 0.9704
- Year 2: 0.9418
- Year 3: 0.9139
-
Recovery Rate (RR): The recovery rates for each year are:
- Year 1: 80%
- Year 2: 70%
- Year 3: 60%
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Expected Exposure (EE): The expected exposure is constant at AUD 14 million for each year.
-
Collateral (C): The collateral amount is AUD 11 million for each year.
-
Net Exposure (EE'): After netting the collateral, the net exposure is:
- Year 1: AUD 3 million
- Year 2: AUD 3 million
- Year 3: AUD 3 million
-
CVA Calculation: The CVA for each year is calculated using the formula , which results in:
- Year 1: AUD 0.0554 million
- Year 2: AUD 0.0730 million
- Year 3: AUD 0.0854 million
-
Total CVA: The total CVA is the sum of the annual CVAs, which equals AUD 0.2138 million.
The incorrect options provided are:
- Option B: Incorrectly uses a hazard rate of 10% as the marginal default probability.
- Option C: Incorrectly uses the recovery rate instead of the loss given default (LGD) in the calculation.
- Option D: Incorrectly assumes no collateral is considered in the calculation.
The correct approach to calculate the CVA is demonstrated in the file content, taking into account the marginal probabilities of default, discount factors, recovery rates, expected exposures, and collateral amounts. The total CVA, as calculated, is AUD 0.2138 million.