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The Valuation of American Options for a Class of Diffusion Processes

  • Jérôme Detemple

    ()

    (Boston University School of Management, 595 Commonwealth Avenue, Boston, Massachusetts 02215, and CIRANO, 2020 University Street, 25th Floor, Montreal, Quebec, Canada H3A 2A5, and Wholesale Group Quantitative Research, Reliant Resource, Louisiana #1111, Houston, Texas 77210-4567)

  • Weidong Tian

    ()

    (Boston University School of Management, 595 Commonwealth Avenue, Boston, Massachusetts 02215, and CIRANO, 2020 University Street, 25th Floor, Montreal, Quebec, Canada H3A 2A5, and Wholesale Group Quantitative Research, Reliant Resource, Louisiana #1111, Houston, Texas 77210-4567)

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    We present an integral equation approach for the valuation of American-style derivatives when the underlying asset price follows a general diffusion process and the interest rate is stochastic. Our contribution is fourfold. First, we show that the exercise region is determined by a single exercise boundary under very general conditions on the interest rate and the dividend yield. Second, based on this result, we derive a recursive integral equation for the exercise boundary and provide a parametric representation of the American option price. Third, we apply the results to models with stochastic volatility or stochastic interest rate, and to American bond options in one-factor models. For the cases studied, explicit parametric valuation formulas are obtained. Finally, we extend results on American capped options to general diffusion prices. Numerical schemes based on approximations of the optimal stopping time (such as approximations based on a lower bound, or on a combination of lower and upper bounds) are shown to be valid in this context.

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    File URL: http://dx.doi.org/10.1287/mnsc.48.7.917.2815
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    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 48 (2002)
    Issue (Month): 7 (July)
    Pages: 917-937

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    Handle: RePEc:inm:ormnsc:v:48:y:2002:i:7:p:917-937
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