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S. Vanduffel, T. Hoedemakers and J. Dhaene, “Comparing Approximations for Risk Measures of Sums of NonIndependent Lognormal Random Variables,” North American Actuarial Journal, Vol. 9, No. 4, 2005, pp. 71-82.

has been cited by the following article:

• 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.