Exercise 6.9 (Equity Swap) In the framework of Example 4.5, we want to use the rate of return of an equity instead of the LIBOR rate. Such a swap is called an equity swap. Let I(t) be the time-t price of an equity. In the “plain vanilla” equity swap, two parties agree to exchange the cash flows based on the fixed interest rate S and those based on the return

Suppose that the equity swap starts at t = 0. Prove that the swap rate S is given by (4.26), that is,

It should be noted that the equity swap rate S does not depend on the equity return. See Chance and Rich (1998) and Kijima and Muromachi (2001) for details of equity swaps.

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I(Ti+1) - I(Ti) I(Ti+1) I(T;) -1, 0, 1,...,n - 1. I(Ti)