22.24. All one-year LIBOR forward rates are 5% with annual compounding and the risk-free

(OIS) rate is 4.6% with continuous compounding. In a five-year swap, company X pays a fixed rate of 6% and receives LIBOR annually on a principal of $100 million. The volatility of the two-year swap rate in three years is 20%.

(a) What is the value of the swap?

(b) Use DerivaGem to calculate the value of the swap if company X has the option to cancel after three years.

(c) Use DerivaGem to calculate the value of the swap if instead the counterparty has the option to cancel after three years.

(d) What is the value of the swap if either side can cancel at the end of three years?

Show that this is the same as the value of a three-year swap and explain why the two values are the same.