Paper #1475

Title:

Pricing and hedging Margrabe options with stochastic volatilities

Authors:

Elisa Alòs and Thorsten Rheinländer

Date:

March 2015 (Revised: February 2017)

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.

Keywords:

Stochastic volatility; Margrabe options; change of numeraire; mean-variance hedging; Malliavin calculus

Area of Research:

Statistics, Econometrics and Quantitative Methods

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