Displaced Diffusion as an Approximation of the Constant Elasticity of Variance

Simona Svoboda-Greenwood

Applied Mathematical Finance, 2009, vol. 16, issue 3, 269-286

Abstract: The CEV (constant elasticity of variance) and displaced diffusion processes have been posited as suitable alternatives to a lognormal process in modelling the dynamics of market variables such as stock prices and interest rates. Marris (1999) noted that, for a certain parameterization, option prices produced by the two processes display close correspondence across a range of strikes and maturities. This parametrization is a simple linearization of the CEV dynamics around the initial value of the underlying and we quantify the observed agreement in option prices by performing a small time expansion of the option prices around the forward-at-the-money value of the underlying. We show further results regarding the comparability of the conditional probability density functions of the two processes and hence the associated moments.

Keywords: Constant elasticity of variance (CEV); displaced diffusion; option pricing; asymptotic expansions (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (3)

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DOI: 10.1080/13504860802628553

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