Question 1: a) Consider a corporate bond with 1-year, 4% annual coupon payment, is priced at par value (=$100). Assume that default can occur only at year-end immediately before coupon payment, and the recovery rate is 40%. Also, assume that 1-year risk-free rate is 3%. what's the risk-neutral probability of default implied by the price of the corporate bond? (3pt) b) Assume that the cumulative default rate over a 10-year horizon for some category of corporate bonds is 15%, based on the reduced form model, what's the average hazard rate per year over the 10-year period? (2pt) c) An AA rated corporate bond that matures in 5 years, has a coupon rate of 6%, and a modified duration of 4.2. Assume that credit spread associated with AA and A ratings are 1% and 1.75% respectively. All else being equal, what would be the bond's approximate percentage price change (using only duration) if its credit rating changed to A? (2pt) Question 1: a) Consider a corporate bond with 1-year, 4% annual coupon payment, is priced at par value (=$100). Assume that default can occur only at year-end immediately before coupon payment, and the recovery rate is 40%. Also, assume that 1-year risk-free rate is 3%. what's the risk-neutral probability of default implied by the price of the corporate bond? (3pt) b) Assume that the cumulative default rate over a 10-year horizon for some category of corporate bonds is 15%, based on the reduced form model, what's the average hazard rate per year over the 10-year period? (2pt) c) An AA rated corporate bond that matures in 5 years, has a coupon rate of 6%, and a modified duration of 4.2. Assume that credit spread associated with AA and A ratings are 1% and 1.75% respectively. All else being equal, what would be the bond's approximate percentage price change (using only duration) if its credit rating changed to A? (2pt)