Question-4

a. Derive the probability distribution of the 1-year HPR on a 30-year U.S. Treasury bond with a coupon of 3.0% if it is currently selling at par and the probability distribution of its yield to maturity a year from now is as shown in the table below. (Assume the entire 3.0% coupon is paid at the end of the year rather than every 6 months. Assume a par value of $100.) (Negative values should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 2 decimal places.)

b. Use the Black-Scholes formula for the following stock:

b. Use the Black-Scholes formula for the following stock: Time to expiration Standard deviation Exercise price Stock price Annual interest rate Dividend 6 months 54% per year $54 $52 4% 0 Required: Calculate the value of a put option