Chapter 21: Credit Value at Risk
21.10.
Explain carefully the distinction between real-world and risk-neutral default probabilities.
Which is higher? A bank enters into a credit derivative where it agrees to pay $100 at the end of
one year if a certain company’s credit rating falls from A to Baa or lower during the year. The
one-year risk-free rate is 5%. Using Table 21.1, estimate a value for the derivative. What
assumptions are you making? Do they tend to overstate or understate the value of the
derivative?
Real world default probabilities are the true probabilities of defaults. They can be estimated from
historical data. Risk-neutral default probabilities are the probabilities of default in a world where
Table 21.1 the probability of a company moving from A to Baa or lower in one year is 6.65%. An
estimate of the value of the derivative is therefore 0.0665 × 100 × e−0.05×1 = 6.33. The
21.11.
Suppose that a bank has a total of $10 million of small exposures of a certain type. The one-year
probability of default is 1% and the recovery rate averages 40%. Estimate the 99.5% one-year
credit VaR using Vasicek’s model if the copula correlation parameter is 0.2.
21.12. (Spreadsheet Provided)
Use the transition matrix in Table 21.1 and software on the author’s web site to calculate the
transition matrix over 1.25 years.
The transition matrix is shown in the spreadsheet.