TITLE:
The Sum and Difference of Two Constant Elasticity of Variance Stochastic Variables
AUTHORS:
Chi-Fai Lo
KEYWORDS:
Constant Elasticity of Variance Stochastic Variables; Probability Distribution Functions; Backward Kolmogorov Equation; Lie-Trotter Splitting Approximation
JOURNAL NAME:
Applied Mathematics,
Vol.4 No.11,
November
5,
2013
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.