riskmanagementhw5

# riskmanagementhw5 - Portfolio Models of Credit Risk Merton...

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Portfolio Models of Credit Risk, Merton Model, and KMV 1. A risk analyst is trying to estimate the Credit VaR for a risky bond. The Credit VaR is defined here as the maximum unexpected loss at a confidence level of 99.9% over a one-month horizon. Assume that the bond is valued at \$1,000,000 one-month forward, and the one-year cumulative default probability is 2% for this bond, what is the best estimate of the Credit VaR for this bond assuming no recovery? a) 20,000 b) 1,682 c) 998,318 d) 0 Solution: c First, transform the annual default probability into a monthly probability. Using (1- 2%)=(1-d)^12, find d=0.00168, which assumes a constant probability of default during the year. The expected credit loss is d*\$1M = \$1,682. Finally, we calculate the WCL at the 99.9% confidence level, which is the lowest number CL i such that P (CL CL i ) 99 . 9%. We have P (CL = 0) = 99 . 83%; P (CL 1 , 000 , 000) = 100 . 00%. Therefore, the WCL is \$1,000,000, and the CVAR is \$1 , 000 , 000 \$1 , 682 = \$998 , 318 2. A senior unsecured BB rated bond matures exactly in 5 years, and is paying an annual coupon of 6%. The 1-year forward price of the bond, if the obligor stays BB is __________ Solution: 102.0063 3. Following is a set of identical transactions. Assuming all counterparties have the same credit rating, which transaction should preferably be executed? a. Buying gas from a trading firm b. Buying gas from a gas producer c. Buying gas from a distributor d. Indifferent between a), b), and c). Solution: b. This is an example of right-way trade. To have lower credit risk, it would be preferable to engage in a trade where there is a lower probability of a default by the counterparty when the contract is in-the-money. This will happen if the counterparty enters a transaction to hedge an operating exposure. For instance, a gas producer has a natural operating exposure to

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## This note was uploaded on 02/27/2010 for the course MA 535 taught by Professor Prasad during the Spring '10 term at Stevens.

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riskmanagementhw5 - Portfolio Models of Credit Risk Merton...

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