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

Author

Listed:
  • Guenter Franke

    (Center of Finance and Econometrics)

  • Richard C. Stapleton

    (University of Strathclyde)

  • Marti G. Subrahmanyam

    (Stern School of Business, New York University)

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.

Suggested Citation

  • Guenter Franke & Richard C. Stapleton & Marti G. Subrahmanyam, 1999. "When are Options Overpriced? The Black-Scholes Model and Alternative Characterisations of the Pricing Kernel," Finance 9904004, EconWPA.
  • Handle: RePEc:wpa:wuwpfi:9904004 Note: 30 pages
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    File URL: http://econwpa.repec.org/eps/fin/papers/9904/9904004.pdf
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    References listed on IDEAS

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    1. Longstaff, Francis A, 1995. "Option Pricing and the Martingale Restriction," Review of Financial Studies, Society for Financial Studies, pages 1091-1124.
    2. 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.
    3. 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.
    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 425-442, June.
    5. Canina, Linda & Figlewski, Stephen, 1993. "The Informational Content of Implied Volatility," Review of Financial Studies, Society for Financial Studies, pages 659-681.
    6. Heston, Steven L, 1993. " Invisible Parameters in Option Prices," Journal of Finance, American Finance Association, vol. 48(3), pages 933-947, July.
    7. 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 637-654, May-June.
    8. 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.
    9. Stapleton, R C & Subrahmanyam, M G, 1990. "Risk Aversion and the Intertemporal Behavior of Asset Prices," Review of Financial Studies, Society for Financial Studies, pages 677-693.
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    Citations

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    Cited by:

    1. Lüders, Erik, 2002. "Why Are Asset Returns Predictable?," ZEW Discussion Papers 02-48, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
    2. Chiaki Hara & James Huang & Christoph Kuzmics, 2006. "Representative Consumer's Risk Aversion and Efficient Risk-Sharing Rules," KIER Working Papers 620, Kyoto University, Institute of Economic Research.
    3. Bjarne Astrup Jensen & Jørgen Aase Nielsen, 2016. "How suboptimal are linear sharing rules?," Annals of Finance, Springer, pages 221-243.
    4. Christoph Böhringer & Andreas Lange, 2005. "Mission Impossible !? On the Harmonization of National Allocation Plans under the EU Emissions Trading Directive," Journal of Regulatory Economics, Springer, vol. 27(1), pages 81-94, September.
    5. Sutthisit Jamdee & Cornelis A. Los, 2005. "Multifractal Modeling of the US Treasury Term Structure and Fed Funds Rate," Finance 0502021, EconWPA.
    6. 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.
    7. Frank Niehaus, 2001. "The Influence of Heterogeneous Preferences on Asset Prices in an Incomplete Market Model," CeNDEF Workshop Papers, January 2001 2A.2, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    8. Hara, Chiaki & Huang, James & Kuzmics, Christoph, 2007. "Representative consumer's risk aversion and efficient risk-sharing rules," Journal of Economic Theory, Elsevier, pages 652-672.
    9. Niehaus, Frank, 2001. "The Influence of Heterogeneous Preferences on Asset Prices in an Incomplete Market Model," Hannover Economic Papers (HEP) dp-234, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    10. 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.
    11. Jan Wenzelburger, 2013. "Risk sharing in a financial market with endogenous option prices," The European Journal of Finance, Taylor & Francis Journals, pages 491-517.
    12. Frank Niehaus, 2000. "A Simple Option Pricing Model With Heterogeneous Agents," Computing in Economics and Finance 2000 342, Society for Computational Economics.
    13. 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.
    14. Bertram Düring & Erik Lüders, 2005. "Option Prices Under Generalized Pricing Kernels," Review of Derivatives Research, Springer, pages 97-123.
    15. James Huang, 2003. "Impact of Divergent Consumer Confidence on Option Prices," Review of Derivatives Research, Springer, pages 165-177.
    16. Luiz Vitiello & Ser-Huang Poon, 2014. "Non-monotonic pricing kernel and an extended class of mixture of distributions for option pricing," Review of Derivatives Research, Springer, pages 241-259.
    17. Schröder, Michael & Lüders, Erik, 2004. "Modeling Asset Returns: A Comparison of Theoretical and Empirical Models," ZEW Discussion Papers 04-19 [rev.], ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.

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    • G - Financial Economics

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