Ultimate access to all questions.
In the context of financial risk management, calculating the Credit Valuation Adjustment (CVA) is crucial for assessing counterparty credit risk. Suppose we have a scenario where the CVA needs to be determined using the formula:
CVA = Σ(1 - RRt)(EEt)(PDt)(DFt)
In this formula:
DFt represents the discount factor, calculated from a 3% risk-free rate.PDt is the probability of default, with a constant hazard rate of 10% over 3 years.EEt represents the exposure at each time point, considering collateral amounts of AUD 14 million annually.RRt is the recovery rate.Given these parameters, how can we calculate the CVA?
A
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(-0.032)=0.9418, and exp(-0.033)=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(-0.11) = 9.52% (marginal probability (PD1)) Year 2 cumulative probability of default = 1 - exp(-0.12) = 18.13%; thus, marginal probability (PD2) = 18.13 - 9.52 = 8.61%. Year 3 cumulative probability of default = 1 - exp(-0.13) = 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
B
AUD 0.2527 million is the result obtained when the hazard rate of 10% is used as the marginal default probability for each of the 3 years.
C
AUD 0.5201 million is the result obtained when the recovery rate and not the LGD is used.
D
AUD 0.9980 million is the result obtained when collateral is not considered