
Explanation:
CVA (Credit Value Adjustment) is calculated as the sum of discounted expected losses: CVA = Sum over t of [ LGD(t) * PD(t) * EE(t) * DF(t) ]
First, determine Loss Given Default (LGD): LGD(t) = 1 - Recovery Rate Year 1: LGD = 1 - 0.80 = 20% Year 2: LGD = 1 - 0.70 = 30% Year 3: LGD = 1 - 0.60 = 40%
Next, calculate the hazard rate (lambda) for each year: lambda = CDS Spread / LGD Year 1: lambda = 200 bps / 0.20 = 1000 bps = 10% Year 2: lambda = 300 bps / 0.30 = 1000 bps = 10% Year 3: lambda = 400 bps / 0.40 = 1000 bps = 10% Since the hazard rate is constant at 10%, we can find the marginal Probability of Default (PD) for each year using PD(t) = exp(-lambda * (t-1)) - exp(-lambda * t). Year 1 PD = 1 - exp(-0.1) = 0.0952 Year 2 PD = exp(-0.1) - exp(-0.2) = 0.0861 Year 3 PD = exp(-0.2) - exp(-0.3) = 0.0779
Next, define Expected Exposure (EE): Since Expected Positive Exposure (EPE) is AUD 14 million and collateral is AUD 11 million, uncollateralized EE = 14 - 11 = AUD 3 million for all years.
Then, calculate Discount Factors (DF) at r = 3%: Year 1 DF = exp(-0.03 * 1) = 0.9704 Year 2 DF = exp(-0.03 * 2) = 0.9418 Year 3 DF = exp(-0.03 * 3) = 0.9139
Finally, calculate the CVA components: Year 1: 0.20 * 0.0952 * 3 * 0.9704 = 0.0554 Year 2: 0.30 * 0.0861 * 3 * 0.9418 = 0.0730 Year 3: 0.40 * 0.0779 * 3 * 0.9139 = 0.0854
Total CVA = 0.0554 + 0.0730 + 0.0854 = AUD 0.2138 million, which rounds to AUD 0.214 million.
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| 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 |
Additionally, the CRO has presented the risk team with the following set of assumptions to use in conducting the analysis:
Given the information and the assumptions above, what is the correct estimate of the unilateral CVA for this position?
A
AUD 0.214 million
B
AUD 0.253 million
C
AUD 0.520 million
D
AUD 0.998 million