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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.

Suggested Citation

  • 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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    References listed on IDEAS

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    1. Angus Deaton & Guy Laroque, 1992. "On the Behaviour of Commodity Prices," Review of Economic Studies, Oxford University Press, pages 1-23.
    2. Robert S. Pindyck & Julio J. Rotemberg, 1993. "The Comovement of Stock Prices," The Quarterly Journal of Economics, Oxford University Press, vol. 108(4), pages 1073-1104.
    3. Robert S. Pindyck, 1994. "Inventories and the Short-Run Dynamics of Commodity Prices," RAND Journal of Economics, The RAND Corporation, pages 141-159.
    4. repec:crs:wpaper:8909 is not listed on IDEAS
    5. Campbell, John Y & Shiller, Robert J, 1987. "Cointegration and Tests of Present Value Models," Journal of Political Economy, University of Chicago Press, vol. 95(5), pages 1062-1088, October.
    6. French, Kenneth R., 1983. "A comparison of futures and forward prices," Journal of Financial Economics, Elsevier, vol. 12(3), pages 311-342, November.
    7. N. Gregory Mankiw & David Romer & Matthew D. Shapiro, 1991. "Stock Market Forecastability and Volatility: A Statistical Appraisal," Review of Economic Studies, Oxford University Press, pages 455-477.
    8. John Y. Campbell, Robert J. Shiller, 1988. "The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors," Review of Financial Studies, Society for Financial Studies, vol. 1(3), pages 195-228.
    9. James A. Kahn, 1992. "Why is Production More Volatile than Sales? Theory and Evidence on the Stockout-Avoidance Motive for Inventory-Holding," The Quarterly Journal of Economics, Oxford University Press, vol. 107(2), pages 481-510.
    10. Fama, Eugene F & French, Kenneth R, 1988. " Business Cycles and the Behavior of Metals Prices," Journal of Finance, American Finance Association, vol. 43(5), pages 1075-1093, December.
    11. David M. Cutler & James M. Poterba & Lawrence H. Summers, 1991. "Speculative Dynamics," Review of Economic Studies, Oxford University Press, vol. 58(3), pages 529-546.
    12. repec:hoo:wpaper:91-7 is not listed on IDEAS
    13. Cox, John C. & Ingersoll, Jonathan Jr. & Ross, Stephen A., 1981. "The relation between forward prices and futures prices," Journal of Financial Economics, Elsevier, vol. 9(4), pages 321-346, December.
    14. James G. MacKinnon, 1990. "Critical Values for Cointegration Tests," Working Papers 1227, Queen's University, Department of Economics.
    15. Dusak, Katherine, 1973. "Futures Trading and Investor Returns: An Investigation of Commodity Market Risk Premiums," Journal of Political Economy, University of Chicago Press, vol. 81(6), pages 1387-1406, Nov.-Dec..
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    Cited by:

    1. Lüders, Erik, 2002. "Asset Prices and Alternative Characterizations of the Pricing Kernel," ZEW Discussion Papers 02-10, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
    2. 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.
    3. 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.
    4. Zura Kakushadze, 2014. "Mean-Reversion and Optimization," Papers 1408.2217, arXiv.org, revised Feb 2016.
    5. Lüders, Erik & Peisl, Bernhard, 2001. "How do investors' expectations drive asset prices?," ZEW Discussion Papers 01-15, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
    6. 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.
    7. 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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