Consider a swaption to enter into a standard equity swap as a fixed-rate payer, equity receiver, in which the notional principal is fixed.

If the strike is K. the underlying swap starts at time 0=n and terminates at m.

Then the swap will have a value at the expiration of

$$SW(0,m)=Max(0,R-K) \sum_{i=1}^{m}B(0,i)$$

where $B(0, i)$ stand for zero-coupon bond with 1\$ face value that matures at $i$. And $R=\frac{1-B(0, m)}{\sum_{i=1}^{m}B(0,i) }$.

My question is how to derive this equation? (Since R is the swap rate, is it possible that swap rate can replace equity return?) Please give me some hints regarding this question. enter image description here This result was from “The Pricing of Equity Swaps and Swaptions.” The Journal of Derivatives, 5 (Summer, 1998), page 29.


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