Question

Use the DerivaGem software to value a European swaption that gives you the right in 2 years to enter into a 5 -year swap in which you pay a fixed rate of $6 \%$ and receive floating. Cash flows are exchanged semiannually on the swap. The continuously compounded 1-year, 2-year, 5-year, and 10-year risk-free (OIS) zero rates are $5 \%$, $6 \%, 6.5 \%$, and $7 \%$, respectively. Assume a principal of $$\$ 100$$. The forward swap rate is $7 \%$ (compounded semiannually) and its volatility is $15 \%$ per annum. Give an example of how the swaption might be used by a corporation. What bond option is equivalent to the swaption?

   Use the DerivaGem software to value a European swaption that gives you the right in 2 years to enter into a 5 -year swap in which you pay a fixed rate of $6 \%$ and receive floating. Cash flows are exchanged semiannually on the swap. The continuously compounded 1-year, 2-year, 5-year, and 10-year risk-free (OIS) zero rates are $5 \%$, $6 \%, 6.5 \%$, and $7 \%$, respectively. Assume a principal of $$\$ 100$$. The forward swap rate is $7 \%$ (compounded semiannually) and its volatility is $15 \%$ per annum. Give an example of how the swaption might be used by a corporation. What bond option is equivalent to the swaption?

Options, Futures, and Other Derivatives

John C. Hull 10th Edition

Chapter 29, Problem 25

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Step 1

The fixed leg pays $6\%$ semiannually, so the present value can be calculated as follows: $$PV_{\text{fixed}} = \frac{6\%}{2} \times \left(1 - \frac{1}{(1 + 6\%/2)^{10}}\right) \times \frac{100}{(1 + 5\%/2)^2}$$ Simplifying this expression, we find that Show more…

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Use the DerivaGem software to value a European swaption that gives you the right in 2 years to enter into a 5 -year swap in which you pay a fixed rate of $6 \%$ and receive floating. Cash flows are exchanged semiannually on the swap. The continuously compounded 1-year, 2-year, 5-year, and 10-year risk-free (OIS) zero rates are $5 \%$, $6 \%, 6.5 \%$, and $7 \%$, respectively. Assume a principal of $$\$ 100$$. The forward swap rate is $7 \%$ (compounded semiannually) and its volatility is $15 \%$ per annum. Give an example of how the swaption might be used by a corporation. What bond option is equivalent to the swaption?

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