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An Alternative Valuation Model for Contingent Claims

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  • Gurdip S. Bakshi

    ()
    (University of Maryland, Robert H. Smith School of Business)

  • Zhiwu Chen

    ()
    (International Center for Finance)

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    Abstract

    The fundamental valuation equation of Cox, Ingersoll and Ross was expressed in terms of the indirect utility of wealth function. As closed-form solution for the indirect utility is generally unobtainable when investment opportunities are stochastic, existing contingent claims models involving general stochastic processes were almost all derived under the restrictive log utility assumption. An alternative valuation equation is proposed here that depends only on the direct utility function. This alternative valuation approach is applied to derive closed-form solutions for bonds, bond options, individual stocks, and stock options under both power utility and exponential utility functions. Allowable processes for aggregate output, firms' dividends, and state variables are quite general and empirically plausible. The resulting interest rate and stock price dynamics have many empirically plausible properties. Our bond and stock option pricing models with stochastic volatility and stochastic interest rates have most existing models nested. The stock option pricing model is also shown to have the ability to reconcile certain puzzling empirical regularities such as the volatility smile.

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    Bibliographic Info

    Paper provided by Yale School of Management in its series Yale School of Management Working Papers with number ysm78.

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    Date of creation: 29 Feb 1996
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    Handle: RePEc:ysm:somwrk:ysm78

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    Web page: http://icf.som.yale.edu/
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