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Displaced Diffusion as an Approximation of the Constant Elasticity of Variance


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  • Simona Svoboda-Greenwood
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    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.

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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

    Volume (Year): 16 (2009)
    Issue (Month): 3 ()
    Pages: 269-286

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    Handle: RePEc:taf:apmtfi:v:16:y:2009:i:3:p:269-286

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    Keywords: Constant elasticity of variance (CEV); displaced diffusion; option pricing; asymptotic expansions;


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