Explanation:
The correct approach to calculate the present value of the expected payoff in the event of default involves considering the loss given default, which is represented by the notional amount minus the recovery. The default probability for the specific year (third year in this case) is then used to estimate the expected loss. This amount is discounted back to the present value using the risk-free interest rate, and for a mid-year default assumption, the discount factor is applied for half the year duration (2.5 years for the third year).
B is incorrect. Adding the recovery rate to the default probability does not accurately represent the calculation of the expected payoff in CDS valuation. The recovery rate is used to adjust the loss given default, not to be added to the default probability.
C is incorrect. The survival probability is not used to calculate the expected payoff in the event of a default. Additionally, the recovery rate is not multiplied by the survival probability but is used to adjust the loss given default.
D is incorrect. While the default probability is used, it is not correct to multiply it by the recovery rate. The recovery rate is used to adjust the notional amount to represent the loss-given default, and the discount factor should be applied for 2.5 years for a mid-year default, not 3 years.
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Q.6075 Consider a scenario where a financial analyst is valuing a 5-year CDS with a constant hazard rate of 1.5% per annum for the reference entity, and the market's risk-free interest rate is set at 3% per annum with continuous compounding. The recovery rate is observed at 50%. Which of the following methods correctly describes how the analyst should calculate the present value of the expected payoff in the event of a default during the third year of the contract considering the loss-given default?
A
Multiply the third year’s default probability by the notional amount minus recovery, and then apply the discount factor for 2.5 years.
B
Add the recovery rate to the third year’s default probability, then multiply by the notional amount and apply the discount factor for 2.5 years.
C
Multiply the third year’s survival probability by the notional amount and the recovery rate, then apply the discount factor for 3.5 years.
D
Multiply the third year’s default probability by the recovery rate and the notional amount, then apply the discount factor for 3 years.
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