On Margrabe options written on stochastic volatility models

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 second order approximative pricing formulae for Margrabe options. This can only be done under certain crucial assumptions, which, by way of example, we show to hold in the 3/2 model where we also can perform explicit computations. 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.