Pricing and hedging Margrabe options with stochastic volatilities

Alòs, Elisa; Rheinländer, Thorsten

Pricing and hedging Margrabe options with stochastic volatilities

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Alòs, E, Rheinländer, T. Pricing and hedging Margrabe options with stochastic volatilities. 2015. handle: http://hdl.handle.net/10230/23366

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Abstract

A Margrabe or exchange option is an option to exchange one asset for another. In a general stochastic volatility framework, by taking the second asset as a numeraire,we derive pricing as well as approximate pricing formulae for Margrabe options. The correlated Stein & Stein and the 3=2 model are studied as particular examples. Moreover, we derive the general mean-variance optimal hedging strategy and show that it is a delta-hedge only in case of zero correlation between asset prices and volatility.