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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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Paper provided by Center of Finance and Econometrics, University of Konstanz in its series CoFE Discussion Paper with number 99-01.

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Length: 30 pages
Date of creation: Jan 1999
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Handle: RePEc:knz:cofedp:9901

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. 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. [Downloadable!] (restricted)
  2. 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. [Downloadable!] (restricted)
  3. Stapleton, R C & Subrahmanyam, M G, 1990. "Risk Aversion and the Intertemporal Behavior of Asset Prices," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 3(4), pages 677-93. [Downloadable!] (restricted)
  4. Mark Rubinstein, 1976. "The Valuation of Uncertain Income Streams and the Pricing of Options," Bell Journal of Economics, The RAND Corporation, vol. 7(2), pages 407-425, Autumn. [Downloadable!] (restricted)
  5. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring. [Downloadable!] (restricted)
  6. 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. [Downloadable!]
  7. Canina, Linda & Figlewski, Stephen, 1993. "The Informational Content of Implied Volatility," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 6(3), pages 659-81. [Downloadable!] (restricted)
  8. Heston, Steven L, 1993. " Invisible Parameters in Option Prices," Journal of Finance, American Finance Association, vol. 48(3), pages 933-47, July. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
  10. 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. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. 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. [Downloadable!]
  2. 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.
    Other versions:
  3. Günter Franke & Thomas Weber, 2006. "Wieweit tragen rationale Modelle in der Finanzmarktforschung?," CoFE Discussion Paper 06-09, Center of Finance and Econometrics, University of Konstanz. [Downloadable!]
  4. Frank Niehaus, 2000. "A Simple Option Pricing Model With Heterogeneous Agents," Computing in Economics and Finance 2000 342, Society for Computational Economics. [Downloadable!]
  5. 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. [Downloadable!]
  6. Hara, C. & Christoph Kuzmics, 2004. "Representative Consumer's Risk Aversion and Efficient Risk-Sharing Rules," Cambridge Working Papers in Economics 0452, Faculty of Economics, University of Cambridge. [Downloadable!]
    Other versions:
  7. Shiyi Chen & Wolfgang Härdle & Rouslan Moro, 2006. "Estimation of Default Probabilities with Support Vector Machines," SFB 649 Discussion Papers SFB649DP2006-077, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  8. 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. [Downloadable!]
  9. 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. [Downloadable!]
  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. [Downloadable!]
  11. 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. [Downloadable!]
  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. [Downloadable!]
  13. Guenter Franke & James Huang & Richard Stapleton, 2006. "Two-dimensional risk-neutral valuation relationships for the pricing of options," Review of Derivatives Research, Springer, vol. 9(3), pages 213-237, November. [Downloadable!] (restricted)
    Other versions:
  14. 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. [Downloadable!]
  15. Lüders, Erik, 2002. "Why Are Asset Returns Predictable?," ZEW Discussion Papers 02-48, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research. [Downloadable!]
  16. Bertram Düring, 2008. "Asset Pricing Under Information with Stochastic Volatility," CoFE Discussion Paper 08-04, Center of Finance and Econometrics, University of Konstanz. [Downloadable!]
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