On the optimal choice of strike conventions in exchange option pricing

TL;DR

This paper introduces a Malliavin Calculus-based method to determine the optimal strike convention for exchange options, minimizing pricing errors across stochastic volatility models.

Contribution

It presents a novel, model-independent approach to select strike conventions for exchange options, improving pricing accuracy for exotic derivatives.

Findings

The optimal strike convention minimizes the difference between Margrabe and true prices.

The method is robust across different stochastic volatility models.

Numerical examples validate the effectiveness of the proposed approach.

Abstract

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 optimal log-linear strikevconvention 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. Numerical examples are given which provide strong support to the new methodology.