Explanation:
The correct answer is C. Utilizing a direct CVA formula is more efficient computationally, especially when minimizing computational time is a priority. The direct CVA calculation converges more quickly because it assumes that the default time, exposure at default, and loss given default (LGD) are independent, which allows using only a single average LGD and makes it unnecessary to simulate default events. This approach focuses on evaluating the value of the portfolio at a single potential default date in the future and multiplies the final result by the counterparty default probability in the interval.
A is incorrect because the path-wise CVA formula, although intuitive, is not the most efficient approach when computational time is a concern. It requires multiple valuations of the underlying portfolio according to the number of time intervals, which increases computational cost and affects the speed of convergence due to the autocorrelation between successive points in the simulation.
B is incorrect because the path-wise simulation does not demonstrate better computational performance; in fact, it is shown to converge more slowly due to the strong positive correlation between successive valuation points in the simulation. This high correlation makes the method quite inefficient compared to the direct approach.
D is incorrect because the direct CVA formula is preferred specifically because it does NOT require simulating multiple valuations of the underlying portfolio at various time intervals. Instead, it converges more quickly by using single average LGD and by focusing on a single potential default date.
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Q.5474 Eastpointe Bank has entered into a 10-year receiver interest rate swap with Counterparty A, where it will receive a fixed rate and pay a floating rate. The risk management team at Eastpointe Bank is aware that the credit value adjustment (CVA) is a crucial measure for counterparty credit risk and is evaluating the best method for computing CVA for this uncollateralized swap. They consider implementing either a direct or path-wise CVA formula. Given the bank's requirement to minimize computational time without sacrificing accuracy, which approach would be more effective?
A
Implementing a path-wise CVA formula, because it offers a more intuitive representation of CVA as a product of the exposure at default, the probability of default, and the loss given default.
B
Utilizing a path-wise CVA formula, because it demonstrates better computational performance due to the low correlation between successive points in the simulation.
C
Utilizing a direct CVA formula, because it assumes independence of default time, exposure at default, and loss given default, leading to faster convergence and more efficient computationally.
D
Implementing a direct CVA formula, because it requires simulating multiple valuations of the underlying portfolio to define exposure at different time intervals, improving accuracy.