Use the Black's model to value a 1-year European put option on a 10-year bond. Assume that the current cash price of the bond is $125, the strike price is $110, the 1-year interest rate is 10% per annum, the bond's forward price volatility is 8% per annum, and the present value of the coupons to be paid during the life of the option is $10.
2. Explain carefully how you would use (a) spot volatilities and (b) flat volatilities to value a 5-year cap.