Answer: To derive the credit valuation adjustment (CVA), we use the standard formula: CVA = Er=o(1 - RRt)(EEt)(PDt)(DFt), where (at any time t): The discount factor (DFt) is determined from the risk-free rate of 3%. For year 1, 2, and 3, they are exp(-0.03)=0.9704, exp(-0.03*2)=0.9418, and exp(-0.03*3)=0.9139, respectively. The hazard rate is constant over the 3 years, and = spread/(1 - RR) = 10%. Therefore: Year 1 cumulative probability of default = 1 - exp(-0.1*1) = 9.52% (marginal probability (PD1)) Year 2 cumulative probability of default = 1 - exp(-0.1*2) = 18.13%; thus, marginal probability (PD2) = 18.13 - 9.52 = 8.61%. Year 3 cumulative probability of default = 1 - exp(-0.1*3) = 25.92%; thus, marginal probability (PD2) = 25.92 - 18.13 = 7.79%. Collateral amounts of AUD 14 million for each of the years 1, 2 and 3 are considered. Therefore, the rest of the derivation becomes: Year0 Year 1 Year 2 Year 3 Marginal probability of default [PD(t)] 9.52% 8.61% 7.79% Discount factor (DF) 0.9704 0.9418 0.9139 Recovery rate (RR) 80% 70% 60% Expected exposure (EE) (AUD million) 14 14 14 Collateral (C) (AUD million) 11 11 11 EE' (netted) (AUD million) 3 3 3 (1-RR)*(EE')*PD(t)*(DF) (AUD million) 0.0554 0.0730 0.0854 n CVA = (1 - RRt)(EEt)(PDt)(DFt) = 0.0554 + 0.0730 + 0.0854 = 0.2138 t=0

The correct answer to the question is A, which involves calculating the Credit Valuation Adjustment (CVA) using a specific formula. The formula for CVA is given by: \[ CVA = E_{r=0}^{\infty}(1 - RR_t)(EExposure_t)(PD_t)(DF_t) \] In this formula: - \( RR_t \) is the recovery rate at time \( t \). - \( EE_t \) is the expected exposure at time \( t \). - \( PD_t \) is the probability of default at time \( t \). - \( DF_t \) is the discount factor at time \( t \), which is calculated using the risk-free rate. For the given problem: - The risk-free rate is 3%, and the discount factors for years 1, 2, and 3 are calculated using \( exp(-0.03 \times t) \), resulting in 0.9704, 0.9418, and 0.9139, respectively. - The hazard rate is constant at 10%, and the recovery rates for years 1, 2, and 3 are 80%, 70%, and 60%, respectively. - The marginal probabilities of default (PD) for each year are calculated using the cumulative probability of default and subtracting the previous year's cumulative probability. The expected exposure (EE) is AUD 14 million for each year, and collateral (C) is AUD 11 million for each year. After netting the collateral, the net expected exposure (EE') is AUD 3 million for each year. The calculation for each year is then performed as follows: \[ (1-RR) \times EE' \times PD(t) \times DF \] For Year 1: \( (1 - 0.80) \times 3 \times 0.0952 \times 0.9704 = 0.0554 \) AUD million For Year 2: \( (1 - 0.70) \times 3 \times 0.0861 \times 0.9418 = 0.0730 \) AUD million For Year 3: \( (1 - 0.60) \times 3 \times 0.0779 \times 0.9139 = 0.0854 \) AUD million Finally, the total CVA is the sum of the annual contributions: \[ CVA = 0.0554 + 0.0730 + 0.0854 = 0.2138 \] AUD million The incorrect options (B, C, and D) are explained as follows: - Option B is incorrect because it uses the hazard rate as the marginal default probability for each year. - Option C is incorrect because it uses the recovery rate instead of the loss given default (LGD). - Option D is incorrect because it does not consider collateral in the calculation. The question tests the understanding of calculating CVA and related concepts such as netting, collateralization, and the use of the hazard rate to define default probabilities.