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Securities Markets, Diffusion State Processes, and Arbitrage-Free Shadow Prices

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  • Heaney, John
  • Poitras, Geoffrey

Abstract

This paper develops the parametric restrictions imposed on diffusion state processes by the requirement of arbitrage-free asset pricing. Using the equivalent martingale measure as a starting point, the diffusion property is exploited to specify the shadow pricing function, which takes conditional state variable probabilities under the reference measure into arbitrage-free contingent claim prices. The main results of the paper provide differential equations associated with the shadow price function that are used to identify restrictions on the parameters of assumed diffusion processes. The paper concludes with an application to the CIR model where the state variable, the instantaneous interest rate, is assumed to follow a square root process. Calculations are also provided for the parametric restrictions imposed on the Brownian bridge and OU state variable processes.

Suggested Citation

  • Heaney, John & Poitras, Geoffrey, 1994. "Securities Markets, Diffusion State Processes, and Arbitrage-Free Shadow Prices," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(2), pages 223-239, June.
    • Handle: RePEc:cup:jfinqa:v:29:y:1994:i:02:p:223-239_00
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    Cited by:

    1. Geoffrey Poitras & John Heaney, 2008. ""How Is The Stock Market Doing?" Using Absence Of Arbitrage To Measure Stock Market Performance," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 1-27.
    2. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.

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