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Canonical valuation of options in the presence of stochastic volatility

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  • Philip Gray
  • Scott Newman

Abstract

Proposed by M. Stutzer (1996), canonical valuation is a new method for valuing derivative securities under the risk‐neutral framework. It is nonparametric, simple to apply, and, unlike many alternative approaches, does not require any option data. Although canonical valuation has great potential, its applicability in realistic scenarios has not yet been widely tested. This article documents the ability of canonical valuation to price derivatives in a number of settings. In a constant‐volatility world, canonical estimates of option prices struggle to match a Black‐Scholes estimate based on historical volatility. However, in a more realistic stochastic‐volatility setting, canonical valuation outperforms the Black‐Scholes model. As the volatility generating process becomes further removed from the constant‐volatility world, the relative performance edge of canonical valuation is more evident. In general, the results are encouraging that canonical valuation is a useful technique for valuing derivatives. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:1–19, 2005

Suggested Citation

  • Philip Gray & Scott Newman, 2005. "Canonical valuation of options in the presence of stochastic volatility," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 25(1), pages 1-19, January.
    • Handle: RePEc:wly:jfutmk:v:25:y:2005:i:1:p:1-19
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    Cited by:

    1. Omid M. Ardakani, 2022. "Option pricing with maximum entropy densities: The inclusion of higher‐order moments," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(10), pages 1821-1836, October.
    2. Jamie Alcock & Godfrey Smith, 2017. "Non-parametric American option valuation using Cressie–Read divergences," Australian Journal of Management, Australian School of Business, vol. 42(2), pages 252-275, May.
    3. Yu, Xisheng, 2021. "A unified entropic pricing framework of option: Using Cressie-Read family of divergences," The North American Journal of Economics and Finance, Elsevier, vol. 58(C).
    4. Liu, Yanxin & Li, Johnny Siu-Hang & Ng, Andrew Cheuk-Yin, 2015. "Option pricing under GARCH models with Hansen's skewed-t distributed innovations," The North American Journal of Economics and Finance, Elsevier, vol. 31(C), pages 108-125.

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