a. A bank uses Black's model to price European bond options. Suppose that an implied price volatility for a 5-year option on a bond maturing in 10 years is used to price a 9-year option on the bond. Would you expect the resultant price to be too high or too low? Explain.
b. Calculate the value of a 4-year European call option on bond that will mature 5 years from today using Black's model. The 5-year cash bond price is $105, the cash price of a 4-year bond with the same coupon is $102, the strike price is $100, the 4-year risk-free interest rate is 10% per annum with continuous compounding, and the volatility for the bond price in 4 years is 2% per annum.