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When are Options Overpriced? The Black-Scholes Model and Alternative Characterisations of the Pricing Kernel

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Author Info

  • Guenter Franke

    (Center of Finance and Econometrics)

  • Richard C. Stapleton

    (University of Strathclyde)

  • Marti G. Subrahmanyam

    (Stern School of Business, New York University)

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    Abstract

    An important determinant of option prices is the elasticity of the pricing kernel used to price all claims in the economy. In this paper, we first show that for a given forward price of the underlying asset, option prices are higher when the elasticity of the pricing kernel is declining than when it is constant. We then investigate the implications of the elasticity of the pricing kernel for the stochastic process followed by the underlying asset. Given that the underlying information process follows a geometric Brownian motion, we demonstrate that constant elasticity of the pricing kernel is equivalent to a Brownian Motion for the forward price of the underlying asset, so that the Black- Scholes formula correctly prices options on the asset. In contrast, declining elasticity implies that the forward price process is no longer a Brownian motion: it has higher volatility and exhibits autocorrelation. In this case, the Black-Scholes formula underprices all options.

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    File URL: http://128.118.178.162/eps/fin/papers/9904/9904004.pdf
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    Bibliographic Info

    Paper provided by EconWPA in its series Finance with number 9904004.

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    Length: 30 pages
    Date of creation: 14 Apr 1999
    Date of revision:
    Handle: RePEc:wpa:wuwpfi:9904004

    Note: 30 pages
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    Web page: http://128.118.178.162

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    References

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    1. Canina, Linda & Figlewski, Stephen, 1993. "The Informational Content of Implied Volatility," Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 659-81.
    2. Brennan, M J, 1979. "The Pricing of Contingent Claims in Discrete Time Models," Journal of Finance, American Finance Association, vol. 34(1), pages 53-68, March.
    3. Longstaff, Francis A, 1995. "Option Pricing and the Martingale Restriction," Review of Financial Studies, Society for Financial Studies, vol. 8(4), pages 1091-1124.
    4. Franke, Gunter, 1984. " Conditions for Myopic Valuation and Serial Independence of the Market Excess Return in Discrete Time Models," Journal of Finance, American Finance Association, vol. 39(2), pages 425-42, June.
    5. Franke, Gunter & Stapleton, Richard C. & Subrahmanyam, Marti G., 1998. "Who Buys and Who Sells Options: The Role of Options in an Economy with Background Risk," Journal of Economic Theory, Elsevier, vol. 82(1), pages 89-109, September.
    6. Stapleton, R C & Subrahmanyam, M G, 1990. "Risk Aversion and the Intertemporal Behavior of Asset Prices," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 677-93.
    7. Bick, Avi, 1987. "On the Consistency of the Black-Scholes Model with a General Equilibrium Framework," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(03), pages 259-275, September.
    8. Heston, Steven L, 1993. " Invisible Parameters in Option Prices," Journal of Finance, American Finance Association, vol. 48(3), pages 933-47, July.
    9. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
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    Citations

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    Cited by:
    1. Hara, Chiaki & Huang, James & Kuzmics, Christoph, 2007. "Representative consumer's risk aversion and efficient risk-sharing rules," Journal of Economic Theory, Elsevier, vol. 137(1), pages 652-672, November.
    2. Frank Niehaus, 2000. "A Simple Option Pricing Model With Heterogeneous Agents," Computing in Economics and Finance 2000 342, Society for Computational Economics.
    3. Jan Beran & Yuanhua Feng & Günter Franke & Dieter Hess & Dirk Ocker, 1999. "SEMIFAR Models, with Applications to Commodities, Exchange Rates and the Volatility of Stock Market Indices," CoFE Discussion Paper 99-18, Center of Finance and Econometrics, University of Konstanz.
    4. 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.
    5. Lüders, Erik, 2002. "Why Are Asset Returns Predictable?," ZEW Discussion Papers 02-48, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
    6. Günter Franke & Erik Lüders, 2006. "Return Predictability and Stock Market Crashes in a Simple Rational Expectations Model¤," CoFE Discussion Paper 06-05, Center of Finance and Econometrics, University of Konstanz.
    7. Günter Franke & Erik Lüders, 2005. "Return Predictability and Stock Market Crashes in a Simple Rational Expectations Model," CoFE Discussion Paper 05-05, Center of Finance and Econometrics, University of Konstanz.
    8. Günter Franke & Erik Lüders, 2004. "Why Do Asset Prices Not Follow Random Walks?," CoFE Discussion Paper 04-05, Center of Finance and Econometrics, University of Konstanz.
    9. 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.
    10. Lüders, Erik & Schröder, Michael, 2004. "Modeling Asset Returns: A Comparison of Theoretical and Empirical Models," ZEW Discussion Papers 04-19, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
    11. Frank Niehaus, 2001. "The Influence of Heterogeneous Preferences on Asset Prices in an Incomplete Market Model," Computing in Economics and Finance 2001 60, Society for Computational Economics.
    12. Lüders, Erik & Lüders-Amann, Inge & Schröder, Michael, 2004. "The Power Law and Dividend Yields," ZEW Discussion Papers 04-51, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.

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