Question: Suppose that the payoff from a derivative will occur in ten years and will equal the three-year U.S. dollar swap rate for a semiannual-pay swap

Suppose that the payoff from a derivative will occur in ten years and will equal the three-year U.S. dollar swap rate for a semiannual-pay swap observed at that time applied to a certain principal. Assume that the swap 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 ten year "yen per dollar" forward exchange rate is 12%, and the correlation between this exchange rate and U.S. 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?

Assume that risk-free rates are 2% in yen and 6% in dollars (both semiannually compounded).

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