On the Optimal Choice of Strike Conventions in Exchange Option Pricing

An important but rarely-addressed option pricing question is how to choose appropriate strikes for implied volatility inputs when pricing more exotic multi-asset derivatives. By means of Malliavin calculus, we construct an asymptotically optimal log-linear strike convention for exchange options under stochastic volatility models. This novel approach allows us to minimize the difference between the corresponding Margrabe computed price and the true option price. We show that this optimal convention does not depend on the specific stochastic volatility model chosen and, furthermore, that parameter estimation can be dramatically simplified by using market observables as inputs. Numerical examples are given that provide strong support for the new methodology