Question

A swaption gives the holder the right to receive $7.6 \%$ in a 5 -year swap starting in 4 years. Payments are made annually. The forward swap rate is $8 \%$ with annual compounding and its volatility is $25 \%$ per annum. The principal is $$\$ 1$$ million and risk-free (OIS) rates for all maturities are $7.8 \%$ (with continuous compounding). Use Black's model to price the swaption. Compare your answer to that given by DerivaGem.

   A swaption gives the holder the right to receive $7.6 \%$ in a 5 -year swap starting in 4 years. Payments are made annually. The forward swap rate is $8 \%$ with annual compounding and its volatility is $25 \%$ per annum. The principal is $$\$ 1$$ million and risk-free (OIS) rates for all maturities are $7.8 \%$ (with continuous compounding). Use Black's model to price the swaption. Compare your answer to that given by DerivaGem.
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Options, Futures, and Other Derivatives
Options, Futures, and Other Derivatives
John C. Hull 10th Edition
Chapter 29, Problem 23 ↓

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Step 1

The fixed leg of the swap pays $7.6\%$ annually on a notional principal of $1$ million for 5 years. The present value of this fixed leg can be calculated using the formula for the present value of a fixed rate bond: $$PV_{\text{fixed}} = \frac{C}{r} \left(1 -  Show more…

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A swaption gives the holder the right to receive $7.6 \%$ in a 5 -year swap starting in 4 years. Payments are made annually. The forward swap rate is $8 \%$ with annual compounding and its volatility is $25 \%$ per annum. The principal is $$\$ 1$$ million and risk-free (OIS) rates for all maturities are $7.8 \%$ (with continuous compounding). Use Black's model to price the swaption. Compare your answer to that given by DerivaGem.
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