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Displaced Diffusion as an Approximation of the Constant Elasticity of Variance

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  • Simona Svoboda-Greenwood

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.

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  • Simona Svoboda-Greenwood, 2009. "Displaced Diffusion as an Approximation of the Constant Elasticity of Variance," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(3), pages 269-286.
    • Handle: RePEc:taf:apmtfi:v:16:y:2009:i:3:p:269-286
    DOI: 10.1080/13504860802628553
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    References listed on IDEAS

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    1. Sam Howison & Mario Steinberg, 2007. "A Matched Asymptotic Expansions Approach to Continuity Corrections for Discretely Sampled Options. Part 1: Barrier Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(1), pages 63-89.
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    5. Sam Howison, 2007. "A Matched Asymptotic Expansions Approach to Continuity Corrections for Discretely Sampled Options. Part 2: Bermudan Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(1), pages 91-104.
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    7. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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    Cited by:

    1. Jaehyuk Choi & Minsuk Kwak & Chyng Wen Tee & Yumeng Wang, 2021. "A Black-Scholes user's guide to the Bachelier model," Papers 2104.08686, arXiv.org, revised Feb 2022.
    2. Roger Lee & Dan Wang, 2012. "Displaced lognormal volatility skews: analysis and applications to stochastic volatility simulations," Annals of Finance, Springer, vol. 8(2), pages 159-181, May.
    3. Thomas A. McWalter & Erik Schlögl & Jacques van Appel, 2023. "Analysing Quantiles in Models of Forward Term Rates," Risks, MDPI, vol. 11(2), pages 1-18, January.

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