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On the multiplicity of option prices under CEV with positive elasticity of variance

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  • Dirk Veestraeten

    (University of Amsterdam)

Abstract

The discounted stock price under the Constant Elasticity of Variance model is not a martingale when the elasticity of variance is positive. Two expressions for the European call price then arise, namely the price for which put-call parity holds and the price that represents the lowest cost of replicating the call option’s payoffs. The greeks of European put and call prices are derived and it is shown that the greeks of the risk-neutral call can substantially differ from standard results. For instance, the relation between the call price and variance may become non-monotonic. Such unfamiliar behavior then might yield option-based tests for the potential presence of a bubble in the underlying stock price.

Suggested Citation

  • Dirk Veestraeten, 2017. "On the multiplicity of option prices under CEV with positive elasticity of variance," Review of Derivatives Research, Springer, vol. 20(1), pages 1-13, April.
    • Handle: RePEc:kap:revdev:v:20:y:2017:i:1:d:10.1007_s11147-016-9122-2
    DOI: 10.1007/s11147-016-9122-2
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    References listed on IDEAS

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    1. Steven L. Heston & Mark Loewenstein & Gregory A. Willard, 2007. "Options and Bubbles," Review of Financial Studies, Society for Financial Studies, vol. 20(2), pages 359-390.
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    5. Alexander Cox & David Hobson, 2005. "Local martingales, bubbles and option prices," Finance and Stochastics, Springer, vol. 9(4), pages 477-492, October.
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    8. 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.
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    Cited by:

    1. Oleg L. Kritski & Vladimir F. Zalmezh, 2017. "Asymptotics for Greeks under the constant elasticity of variance model," Papers 1707.04149, arXiv.org, revised Jul 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. Jia‐Hau Guo & Lung‐Fu Chang, 2020. "Repeated Richardson extrapolation and static hedging of barrier options under the CEV model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(6), pages 974-988, June.
    4. Yukihiro Tsuzuki, 2024. "Boundary conditions at infinity for Black-Scholes equations," Papers 2401.05549, arXiv.org, revised Mar 2024.
    5. José Carlos Dias & João Pedro Vidal Nunes & Aricson Cruz, 2020. "A note on options and bubbles under the CEV model: implications for pricing and hedging," Review of Derivatives Research, Springer, vol. 23(3), pages 249-272, October.
    6. Yukihiro Tsuzuki, 2023. "Pitman's Theorem, Black-Scholes Equation, and Derivative Pricing for Fundraisers," Papers 2303.13956, arXiv.org.

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    More about this item

    Keywords

    Bubbles; Constant elasticity of variance; Option pricing; Put-call parity; Risk-neutral valuation;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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