Pricing Equity Swaps in a Stochastic Interest Rate Economy

Abstract

“A swap is a package of forward contracts, and the standard Òcost of carryÓ model for valuing forwards, like other-risk neutral valuation relationships, involves the riskless interest rate but not the expected price change on the underlying asset. Thus, in a basic equity swap, the current term structure of interest determines the swap rate, while the equity price process plays no role. It has been demonstrated that under non-stochastic interest rates, this result holds whether a swap has fixed or variable notional principal. Kijima and Muromachi introduce stochastic interest rates, and show that when notional principal is constant, the result is the same, but with variable notional principal, the stock price process does enter the swap valuation equation in the correlation between interest rate changes and stock returns. They derive valuation formulas for capped equity swaps in the same framework.”