Question 5

Question5 (CreditRisk): You are holding 1 unit of a zero bond issued by XYZ. The face value and the recovery rate are respectively $100 and 40%. The term to maturity is 5 years. If XYZ defaults at any time in the coming ve years, the recovery rate will be paid at the maturity day. The price of the bond is $60. a) If the bond is Ba-rated, find the probability of defaults using the table of historical default rate. b) Suppose a four-year zero coupon US treasrny bond with face value of $100 is selling at $93, what would be the default probability of the junk bond implied from the market price? c) Using each of the probabilities obtained from a) & b) calculate the expected value and variance of your credit loss. d) (Ignore parts a to c) As a risk analyst, you are trying to estimate the C-VaR (Credit VaR) for a portfolio that includes two risky bonds. We define C-VaR as the maximum unexpected loss with a very high confidence (99.9%) in a rather short time (typically 1 month). Suppose each of the two bond are worth $1,000,000 one month forward, and that the one-year cumulative default probability is 4% for each of the two bonds. Find the C- VaR of this portfolio assuming no default correlation and no zero recovery rate. (Note: For this part is an application of finding default probability using bond prices)