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Suppose that the payoff from a derivative will occur in 6 years and will equal the 3-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 6% (semiannually compounded) per annum in dollars and 2% (semiannually compounded) in yen. The forward swap rate volatility is 15%, the volatility of the 6-year “yen per dollar” forward exchange rate is 10%, and the correlation between this exchange rate and U.S. dollar interest rates is 0.3. Assume that risk-free rates are 1% in yen and 3.5% in dollars (both semiannually compounded). (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?
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