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A Framework for Valuing Derivative Securities

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  • Philip Gray
  • Stephen F. Gray

Abstract

This paper develops a general framework for valuing a wide range of derivative securities. Rather than focusing on the stochastic process of the underlying security and developing an instantaneously‐riskless hedge portfolio, we focus on the terminal distribution of the underlying security. This enables the derivative security to be valued as the weighted sum of a number of component pieces. The component pieces are simply the different payoffs that the security generates in different states of the world, and they are weighted by the probability of the particular state of the world occurring. A full set of derivations is provided. To illustrate its use, the valuation framework is applied to plain‐vanilla call and put options, as well as a range of derivatives including caps, floors, collars, supershares, and digital options.

Suggested Citation

  • Philip Gray & Stephen F. Gray, 2001. "A Framework for Valuing Derivative Securities," Financial Markets, Institutions & Instruments, John Wiley & Sons, vol. 10(5), pages 253-276.
    • Handle: RePEc:wly:finmar:v:10:y:2001:i:5:p:253-276
    DOI: 10.1111/1468-0416.00047
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