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Approximate option pricing and hedging in the CEV model via path-wise comparison of stochastic processes

Author

Listed:
  • Vladislav Krasin

    (Barclays Capital)

  • Ivan Smirnov

    (Susquehanna International Group)

  • Alexander Melnikov

    (University of Alberta)

Abstract

This paper presents a methodology of finding explicit boundaries for some financial quantities via comparison of stochastic processes. The path-wise comparison theorem is used to establish domination of the stock price process by a process with a known distribution that is relatively simple. We demonstrate how the comparison theorem can be applied in the constant elasticity of variance model to derive closed-form expressions for option price bounds, an approximate hedging strategy and a conditional value-at-risk estimate. We also provide numerical examples and compare precision of our method with the distribution-free approach.

Suggested Citation

  • Vladislav Krasin & Ivan Smirnov & Alexander Melnikov, 2018. "Approximate option pricing and hedging in the CEV model via path-wise comparison of stochastic processes," Annals of Finance, Springer, vol. 14(2), pages 195-209, May.
    • Handle: RePEc:kap:annfin:v:14:y:2018:i:2:d:10.1007_s10436-017-0309-9
    DOI: 10.1007/s10436-017-0309-9
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Stochastic differential equations; Comparison theorem; Option pricing; Constant elasticity of variance model;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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