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

Author

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  • Guntar Franke
  • Richard C. Stapleton
  • Marti G. Subrahmanyam

Abstract

This paper examines the convexity bias introduced by pricing interest rate swaps off the Eurocurrency futures curve and the market's adjustment of this bias in prices over time. The convexity bias arises because of the difference between a futures contract and a forward contract on interest rates, since the payoff to the latter is non-linear in interest rates. Using daily data from 1987-1996, the differences between market swap rates and the swap rates implied from Eurocurrency futures prices are studied for the four major interest rate swap markets - $, £, DM and ¥. The evidence suggests that swaps were being priced off the futures curve (i.e. by ignoring the convexity adjustment) during the earlier years of the study, after which the market swap rates drifted below the rates implied by futures prices. The empirical analysis shows that this spread between the market and futures-implied swap rates cannot be explained by default risk differences, liquidity differences or information asymmetries between the swap and the futures markets. Using alternative term structure models (one-factor Vasicek, Cox-Ingersoll and Ross, Hull and White, Black and Karasinski, and the two-factor Heath, Jarrow and Morton), the theoretical value of the convexity bias is found to be related to the empirically observed swap-futures differential. We interpret these results as evidence of mispricing of swap contracts during the earlier years of the study, with a gradual elimination of that mispricing by incorporation of a convexity adjustment in swap pricing over time.

Suggested Citation

  • Guntar Franke & Richard C. Stapleton & Marti G. Subrahmanyam, 1999. "When are Options Overpriced? The Black-Scholes Model and Alternative Characterizations of the Pricing Kernel," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-003, New York University, Leonard N. Stern School of Business-.
  • Handle: RePEc:fth:nystfi:99-003
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    File URL: http://www.stern.nyu.edu/fin/workpapers/papers99/wpa99003.pdf
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    Cited by:

    1. 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.
    2. Lüders, Erik, 2002. "Why Are Asset Returns Predictable?," ZEW Discussion Papers 02-48, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
    3. Bertram Düring, 2009. "Asset pricing under information with stochastic volatility," Review of Derivatives Research, Springer, vol. 12(2), pages 141-167, July.
    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. 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.
    6. Jan Wenzelburger, 2013. "Risk sharing in a financial market with endogenous option prices," The European Journal of Finance, Taylor & Francis Journals, vol. 19(6), pages 491-517, July.
    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.
    8. Bjarne Astrup Jensen & Jørgen Aase Nielsen, 2016. "How suboptimal are linear sharing rules?," Annals of Finance, Springer, vol. 12(2), pages 221-243, May.
    9. 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.
    10. Frank Niehaus, 2000. "A Simple Option Pricing Model With Heterogeneous Agents," Computing in Economics and Finance 2000 342, Society for Computational Economics.
    11. Franke, Günter & Weber, Martin, 2003. "Heterogeneity of Investors and Asset Pricing in a Risk-Value World," CEPR Discussion Papers 3832, C.E.P.R. Discussion Papers.
    12. Sutthisit Jamdee & Cornelis A. Los, 2005. "Multifractal Modeling of the US Treasury Term Structure and Fed Funds Rate," Finance 0502021, EconWPA.
    13. 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.
    14. 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.
    15. 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.
    16. Bertram Düring & Erik Lüders, 2005. "Option Prices Under Generalized Pricing Kernels," Review of Derivatives Research, Springer, vol. 8(2), pages 97-123, August.
    17. James Huang, 2003. "Impact of Divergent Consumer Confidence on Option Prices," Review of Derivatives Research, Springer, vol. 6(3), pages 165-177, October.
    18. 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, vol. 17(2), pages 241-259, July.
    19. repec:spr:annopr:v:262:y:2018:i:2:d:10.1007_s10479-015-2079-y is not listed on IDEAS

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