What difference does it make in Problem if the swap rate is observed in 5 years, but the exchange of payments takes place in
(a) 6 years, and
(b) 7 years? Assume that the volatilities of all forward rates are 20%.
Assume also that the forward swap rate for the period between years 5 and 7 has a correlation of 0.8 with the forward interest rate between years 5 and 6 and a correlation of 0.95 with the forward interest rate between years 5 and 7.
Problem :
The yield curve is flat at 10% per annum with annual compounding. Calculate the value of an instrument where, in 5 years' time, the 2-year swap rate (with annual compounding) is received and a fixed rate of 10% is paid. Both are applied to a notional principal of $100.
Assume that the volatility of the swap rate is 20% per annum. Explain why the value of the instrument is different from zero.