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Simulation of the CEV process and the local martingale property

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  • Lindsay, A.E.
  • Brecher, D.R.

Abstract

We consider the constant elasticity of variance (CEV) process, reviewing the relationships between its transition density and that of the non-central chi-squared distribution. When the CEV parameter exceeds one, the forward price process is a strictly local martingale, and the price of a plain vanilla European call option reflects this fact. We develop techniques for Monte Carlo simulation of the CEV process, for all parameter regimes, and compare the results against the analytic expressions for plain vanilla European option prices. Using these techniques, we also verify the local martingale property.

Suggested Citation

  • Lindsay, A.E. & Brecher, D.R., 2012. "Simulation of the CEV process and the local martingale property," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(5), pages 868-878.
    • Handle: RePEc:eee:matcom:v:82:y:2012:i:5:p:868-878
    DOI: 10.1016/j.matcom.2011.12.006
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    1. Hsu, Y.L. & Lin, T.I. & Lee, C.F., 2008. "Constant elasticity of variance (CEV) option pricing model: Integration and detailed derivation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(1), pages 60-71.
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    3. Emanuel, David C. & MacBeth, James D., 1982. "Further Results on the Constant Elasticity of Variance Call Option Pricing Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 17(4), pages 533-554, November.
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    5. Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv, December.
    6. Schroder, Mark Douglas, 1989. " Computing the Constant Elasticity of Variance Option Pricing Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 211-219, March.
    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. Antoine Jacquier & Patrick Roome, 2015. "Black-Scholes in a CEV random environment," Papers 1503.08082, arXiv.org, revised Nov 2017.
    2. Axel A. Araneda & Marcelo J. Villena, 2018. "Computing the CEV option pricing formula using the semiclassical approximation of path integral," Papers 1803.10376, arXiv.org.
    3. Wang, Hengxu & O’Hara, John G. & Constantinou, Nick, 2015. "A path-independent approach to integrated variance under the CEV model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 109(C), pages 130-152.
    4. Nawdha Thakoor & Désiré Yannick Tangman & Muddun Bhuruth, 2019. "A Spectral Approach to Pricing of Arbitrage-Free SABR Discrete Barrier Options," Computational Economics, Springer;Society for Computational Economics, vol. 54(3), pages 1085-1111, October.
    5. Blanka Horvath & Oleg Reichmann, 2018. "Dirichlet Forms and Finite Element Methods for the SABR Model," Papers 1801.02719, arXiv.org.
    6. Francesca Biagini & Lukas Gonon & Andrea Mazzon & Thilo Meyer-Brandis, 2022. "Detecting asset price bubbles using deep learning," Papers 2210.01726, arXiv.org, revised Dec 2022.

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