Bond Power Exchange Options

Abstract

We study power exchange options written on zero-coupon bonds under a stochastic string frame- work. We obtain closed-form expressions for pricing and hedging bond power exchange options and, as particular cases, the corresponding expressions for call power options and constant un- derlying elasticity in strikes (CUES) options. Suffi cient 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 this kind of option is also stated. Finally, we consider several applications of our results including duration and convexity measures for bond power exchange options, pric- ing 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.

Keywords: Stochastic string, power option, pricing, hedging, Malliavin calculus

JEL Classification: F1, G4