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Quasi Mean Reversion in an Efficient Stock Market: The Characterisation of Economic Equilibria which Support Black-Scholes Option Pricing

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  • Hodges, Stewart
  • Carverhill, Andrew

Abstract

This paper is concerned with the behavior of the risk premium on the market portfolio of risky assets. The paper provides a characterization of the evolution of the market risk prem ium in economies where the variance of the return on the market has constant variance and market index options can be priced using the 1 973 Black Scholes model. It is shown that the risk premium satisfies a n on linear partial differential equation called Burgers' equation. The analysis has potentially important implications for empirical work, where for example, it is undecided whether observed mean reversion i n stock prices can be explained by time varying risk premia within an efficient market. Copyright 1993 by Royal Economic Society.

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  • Hodges, Stewart & Carverhill, Andrew, 1993. "Quasi Mean Reversion in an Efficient Stock Market: The Characterisation of Economic Equilibria which Support Black-Scholes Option Pricing," Economic Journal, Royal Economic Society, vol. 103(417), pages 395-405, March.
    • Handle: RePEc:ecj:econjl:v:103:y:1993:i:417:p:395-405
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    Cited by:

    1. Mirosław Lachowicz & Henryk Leszczyński, 2020. "Modeling Asymmetric Interactions in Economy," Mathematics, MDPI, vol. 8(4), pages 1-14, April.
    2. Zura Kakushadze, 2014. "Mean-Reversion and Optimization," Papers 1408.2217, arXiv.org, revised Feb 2016.
    3. Lüders, Erik, 2002. "Asset Prices and Alternative Characterizations of the Pricing Kernel," ZEW Discussion Papers 02-10, ZEW - Leibniz Centre for European Economic Research.
    4. Lüders, Erik & Peisl, Bernhard, 2001. "How do investors' expectations drive asset prices?," ZEW Discussion Papers 01-15, ZEW - Leibniz Centre for European Economic Research.
    5. 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.
    6. Weinbaum, David, 2009. "Investor heterogeneity, asset pricing and volatility dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 33(7), pages 1379-1397, July.
    7. Englezos, Nikolaos & Frangos, Nikolaos E. & Kartala, Xanthi-Isidora & Yannacopoulos, Athanasios N., 2013. "Stochastic Burgers PDEs with random coefficients and a generalization of the Cole–Hopf transformation," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 3239-3272.
    8. Leonenko, N. N. & Woyczynski, W. A., 1998. "Exact parabolic asymptotics for singular -D Burgers' random fields: Gaussian approximation," Stochastic Processes and their Applications, Elsevier, vol. 76(2), pages 141-165, August.
    9. Jiang-Lun Wu & Wei Yang, 2013. "A Galerkin approximation scheme for the mean correction in a mean-reversion stochastic differential equation," Papers 1305.1868, arXiv.org.

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