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The Valuation of Volatility Options


  • Jérôme B. Detemple
  • Carlton Osakwe


This paper examines the valuation of European- and American-style volatility options based on a general equilibrium stochastic volatility framework. Properties of the optimal exercise region and of the option price are provided when volatility follows a general diffusion process. Explicit valuation formulas are derived in four particular cases. Emphasis is placed on the MRLP (mean-reverting in the log) volatility model which has received considerable empirical support. In this context we examine the properties and hedging behavior of volatility options. Unlike American options, European call options on volatility are found to display concavity at high levels of volatility. Cet article examine l'évaluation des options sur volatilité, de type européen ou américain, dans le cadre d'un modèle d'équilibre général avec volatilité stochastique. Certaines propriétés de la région d'exercise optimal et du prix de l'option sont établies lorsque la volatilité suit un processus général de diffusion. Des formules d'évaluation explicites sont ensuite dérivées dans quatre cas particuliers. Nous étudions en détail le cas d'un processus de volatilité de type MRLP (mean-reverting in the log) qui semble être conforme à l'évidence empirique. Les propriétés et le comportement de couverture des options sur volatilité sont examinées dans ce cadre. ¸ l'opposeé d'une option d'achat américaine, le prix d'une option d'achat européenne sur volatilité s'avère être une fonction concave lorsque le niveau de volatilité s'élève.

Suggested Citation

  • Jérôme B. Detemple & Carlton Osakwe, 1999. "The Valuation of Volatility Options," CIRANO Working Papers 99s-43, CIRANO.
  • Handle: RePEc:cir:cirwor:99s-43

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    References listed on IDEAS

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    Cited by:

    1. Piotr Pluciennik, 2010. "Forecasting Financial Processes by Using Diffusion Models," Dynamic Econometric Models, Uniwersytet Mikolaja Kopernika, vol. 10, pages 51-60.

    More about this item


    Stochastic volatility; European options; American options; optimal exercise; early exercise premium; hedging; viability; Volatilité stochastique; options européennes; options américaines; exercice optimal; prime d'exercice anticipé; couverture de risque; viabilité;

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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