A Simple Generalisation of Kirk’s Approximation for Multi-Asset Spread Options by the Lie-Trotter Operator Splitting Method

Abstract

In this paper, by means of the Lie-Trotter operator splitting method, we have presented a new unified approach not only to rigorously derive Kirk’s approximation but also to obtain a generalisation for multi-asset spread options in a straightforward manner. The derived price formula for the multi-asset spread option bears a great resemblance to Kirk’s approximation in the two-asset case. More importantly, our approach is able to provide a new perspective on Kirk’s approximation and the generalization; that is, they are simply equivalent to the Lie-Trotter operator splitting approximation to the Black-Scholes equation.