Pricing and Hedging Bond Power Exchange Options in a Stochastic String Term-Structure Model

Abstract

We study power exchange options written on zero-coupon bonds under a stochastic string term-structure framework. Closed-form expressions for pricing and hedging bond power exchange options are obtained and, as particular cases, the corresponding expressions for call power options and constant underlying elasticity in strikes (CUES) options. Sufficient conditions for the equivalence of the European and the American versions of bond power exchange options are provided and the put-call parity relation for European bond power exchange options is established. Finally, we consider several applications of our results including duration and convexity measures for bond power exchange options, pricing extendable/accelerable maturity zero-coupon bonds, options to price a zero-coupon bond off of a shifted term-structure, and options on interest rates and rate spreads. In particular, we show that standard formulas for interest rate caplets and floorlets in a LIBOR market model can be obtained as special cases of bond power exchange options under a stochastic string term-structure model.