The Sum and Difference of Two Constant Elasticity of Variance Stochastic Variables

Abstract

We have applied the Lie-Trotter operator splitting method to model the dynamics of both the sum and difference of two correlated constant elasticity of variance (CEV) stochastic variables. Within the Lie-Trotter splitting approximation, both the sum and difference are shown to follow a shifted CEV stochastic process, and approximate probability distributions are determined in closed form. Illustrative numerical examples are presented to demonstrate the validity and accuracy of these approximate distributions. These approximate probability distributions can be used to valuate two-asset options, e.g. spread options and basket options, where the CEV variables represent the forward prices of the underlying assets. Moreover, we believe that this new approach can be extended to study the algebraic sum of N CEV variables with potential applications in pricing multi-asset options.

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Lo, C. (2013) The Sum and Difference of Two Constant Elasticity of Variance Stochastic Variables. Applied Mathematics, 4, 1503-1511. doi: 10.4236/am.2013.411203.

Conflicts of Interest

The authors declare no conflicts of interest.

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