Question 4. Interest Rate Options Pricing, Valuation, Payoff, and Hedging (20 marks) Tango Bank has contracted to lend $80 million to Delta Co. in three months' time. This loan will be for a period of six months. To hedge against the risk of interest rates dropping, Tango has purchased an interest rate put option. The put option has an exercise rate of 2.15% and a maturity of three months. The underlying forward rate is based on the LIBOR, which has a current term structure of # days 90 270 LIBOR 2% 2.3% The terms of the LIBOR specify 30 days in a month and 360 days in a year. The volatility on the underlying forward rate is 0.25. Tango uses the Black Model to estimate the call premium. a. b. Calculate the contract premium the bank must pay for this put option. (7 marks) Suppose that in three months' time, the six-month LIBOR turns out to be 2%. What is the annualized rate of return on Tango's position with the put option? (7 marks) Hindsight being 20-20, should Tango have purchased the put option? (3 marks) Tango could also have used a forward rate agreement (FRA) to hedge its future lending rate. What are the similarities and differences between interest rate option and FRA? (3 marks) c. d. Question 4. Interest Rate Options Pricing, Valuation, Payoff, and Hedging (20 marks) Tango Bank has contracted to lend $80 million to Delta Co. in three months' time. This loan will be for a period of six months. To hedge against the risk of interest rates dropping, Tango has purchased an interest rate put option. The put option has an exercise rate of 2.15% and a maturity of three months. The underlying forward rate is based on the LIBOR, which has a current term structure of # days 90 270 LIBOR 2% 2.3% The terms of the LIBOR specify 30 days in a month and 360 days in a year. The volatility on the underlying forward rate is 0.25. Tango uses the Black Model to estimate the call premium. a. b. Calculate the contract premium the bank must pay for this put option. (7 marks) Suppose that in three months' time, the six-month LIBOR turns out to be 2%. What is the annualized rate of return on Tango's position with the put option? (7 marks) Hindsight being 20-20, should Tango have purchased the put option? (3 marks) Tango could also have used a forward rate agreement (FRA) to hedge its future lending rate. What are the similarities and differences between interest rate option and FRA? (3 marks) c. d