Question

What is the value of a European swap option that gives the holder the right to enter into a 3-year annual-pay swap in 4 years where a fixed rate of 5% is paid and LIBOR is received? The swap principal is $10 million. Assume that the yield curve is flat at 5% per annum with annual compounding and the volatility of the swap rate is 20%.

Answer 1

A yield curve flattens at a place where both the options (LIBOR as well as fixed rate pay) are equal to one another.

A volatility of a swap ratio is the rate at which the LIBOR is valued. Hence, the value of the swap option will be the amount saved due to opting for LIBOR over the fixed interest part.

Hence, LIBOR % = fixed rate - (volatility of swap rate * fixed interest rate) = 5% - 5*20% = 5-1 = 4%.

therefore, value of European swap option for 3years = 10million * (5-4)% * 3 = $ 0.30million.