Suppose that the payoff from a derivative will occur in 10 years and will equal the 3-year US dollar swap rate for a semiannual-pay swap observed at that time applied to a certain principal. Assume that the yield curve is flat at 8% (semiannually compounded) per annum in dollars and 3% (semiannually compounded) in yen. The forward swap rate volatility is 18%, the volatility of the 10-year ‘‘yen per dollar'' forward exchange rate is 12%, and the correlation between this exchange rate and US dollar interest rates is 0.25.
(a) What is the value of the derivative if the swap rate is applied to a principal of $100 million so that the payoff is in dollars?
(b) What is its value of the derivative if the swap rate is applied to a principal of 100 million yen so that the payoff is in yen?