IDEAS home Printed from https://ideas.repec.org/p/crf/wpaper/09-03.html
   My bibliography  Save this paper

A Cumulative Prospect Theory Approach to Option Pricing

Author

Listed:
  • Christian Wolff

    () (Luxembourg School of Finance, University of Luxembourg)

  • Thorsten Lehnert

    () (Luxembourg School of Finance, University of Luxembourg)

  • Cokki Versluis

    () (DSM Corporate Technology)

Abstract

It is a well known empirical fact that actual option prices show persistent and systematic deviations from Black-Scholes option values. While a substantial number of enhancements have been proposed in the literature, these approaches typically leave investors’ preferences towards risk unmodified. In this paper we study option prices in an economy where investors are valuing call options according to the cumulative prospect theory of Kahneman and Tversky. We distinguish two prospect option pricing models, based on whether cash flows are either considered to be segregated or aggregated over time. These models are compared with the Black-Scholes model and the stochastic volatility model of Heston. Empirical analysis of European call options on the S&P 500 index shows that prospect option pricing models significantly improve the fitting performance compared with the Black-Scholes model and that especially the aggregated version’s performance is at least equivalent to the Heston model.

Suggested Citation

  • Christian Wolff & Thorsten Lehnert & Cokki Versluis, 2009. "A Cumulative Prospect Theory Approach to Option Pricing," LSF Research Working Paper Series 09-03, Luxembourg School of Finance, University of Luxembourg.
  • Handle: RePEc:crf:wpaper:09-03
    as

    Download full text from publisher

    File URL: http://www.lsf.lu/index.php/eng/content/download/1220/6058/file/09-03.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. Heynen, Ronald & Kemna, Angelien & Vorst, Ton, 1994. "Analysis of the Term Structure of Implied Volatilities," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(01), pages 31-56, March.
    2. Christoffersen, Peter & Heston, Steve & Jacobs, Kris, 2006. "Option valuation with conditional skewness," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 253-284.
    3. repec:dgr:rugsom:96e26 is not listed on IDEAS
    4. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-291, March.
    5. Groot, J.S. de & Dijkstra, T.K., 1996. "Writing covered calls : should it be done?," Research Report 96E26, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    6. Bams, Dennis & Lehnert, Thorsten & Wolff, Christian C, 2005. "Loss Functions in Option Valuation: A Framework for Model Selection," CEPR Discussion Papers 4960, C.E.P.R. Discussion Papers.
    7. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. " Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-2049, December.
    8. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    9. Shiller, Robert J., 1999. "Human behavior and the efficiency of the financial system," Handbook of Macroeconomics,in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 20, pages 1305-1340 Elsevier.
    10. Barberis, Nicholas & Thaler, Richard, 2003. "A survey of behavioral finance," Handbook of the Economics of Finance,in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 18, pages 1053-1128 Elsevier.
    11. Fox, Craig R & Rogers, Brett A & Tversky, Amos, 1996. "Options Traders Exhibit Subadditive Decision Weights," Journal of Risk and Uncertainty, Springer, vol. 13(1), pages 5-17, July.
    12. 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.
    13. Dennis Bams & Thorsten Lehnert & Christian C. P. Wolff, 2009. "Loss Functions in Option Valuation: A Framework for Selection," Management Science, INFORMS, vol. 55(5), pages 853-862, May.
    14. Bernard Dumas & Jeff Fleming & Robert E. Whaley, 1998. "Implied Volatility Functions: Empirical Tests," Journal of Finance, American Finance Association, vol. 53(6), pages 2059-2106, December.
    15. Jin-Chuan Duan & Jean-Guy Simonato, 1995. "Empirical Martingale Simulation for Asset Prices," CIRANO Working Papers 95s-43, CIRANO.
    16. Nava Ashraf & Colin F. Camerer & George Loewenstein, 2005. "Adam Smith, Behavioral Economist," Journal of Economic Perspectives, American Economic Association, vol. 19(3), pages 131-145, Summer.
    17. Klaus Abbink & Bettina Rockenbach, 2006. "Option pricing by students and professional traders: a behavioural investigation," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 27(6), pages 497-510.
    18. Allen M. Poteshman & Vitaly Serbin, 2003. "Clearly Irrational Financial Market Behavior: Evidence from the Early Exercise of Exchange Traded Stock Options," Journal of Finance, American Finance Association, vol. 58(1), pages 37-70, February.
    19. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    20. Richard H. Thaler & Eric J. Johnson, 1990. "Gambling with the House Money and Trying to Break Even: The Effects of Prior Outcomes on Risky Choice," Management Science, INFORMS, vol. 36(6), pages 643-660, June.
    21. Michael Kilka & Martin Weber, 2001. "What Determines the Shape of the Probability Weighting Function Under Uncertainty?," Management Science, INFORMS, vol. 47(12), pages 1712-1726, December.
    22. Shefrin, Hersh & Statman, Meir, 2000. "Behavioral Portfolio Theory," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 35(02), pages 127-151, June.
    23. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    24. Nicholas Barberis & Ming Huang & Tano Santos, 2001. "Prospect Theory and Asset Prices," The Quarterly Journal of Economics, Oxford University Press, vol. 116(1), pages 1-53.
    25. Benninga, Simon & Mayshar, Joram, 2000. "Heterogeneity and option pricing," Research Report 00E08, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    26. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    27. Christensen, B. J. & Prabhala, N. R., 1998. "The relation between implied and realized volatility," Journal of Financial Economics, Elsevier, vol. 50(2), pages 125-150, November.
    28. Rockenbach, Bettina, 2004. "The behavioral relevance of mental accounting for the pricing of financial options," Journal of Economic Behavior & Organization, Elsevier, vol. 53(4), pages 513-527, April.
    29. repec:dgr:rugsom:00e08 is not listed on IDEAS
    30. Guo, Chen, 1998. "Option Pricing with Heterogeneous Expectations," The Financial Review, Eastern Finance Association, vol. 33(4), pages 81-92, November.
    31. Hersh Shefrin & Meir Statman, 1993. "Behavioral Aspects of the Design and Marketing of Financial Products," Financial Management, Financial Management Association, vol. 22(2), Summer.
    32. Peter Ritchken & Rob Trevor, 1999. "Pricing Options under Generalized GARCH and Stochastic Volatility Processes," Journal of Finance, American Finance Association, vol. 54(1), pages 377-402, February.
    33. Breuer, Wolfgang & Perst, Achim, 2007. "Retail banking and behavioral financial engineering: The case of structured products," Journal of Banking & Finance, Elsevier, vol. 31(3), pages 827-844, March.
    34. Jin-Chuan Duan & Geneviève Gauthier & Jean-Guy Simonato, 2001. "Asymptotic Distribution of the EMS Option Price Estimator," Management Science, INFORMS, vol. 47(8), pages 1122-1132, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Martina Nardon & Paolo Pianca, 2014. "European option pricing with constant relative sensitivity probability weighting function," Working Papers 2014:25, Department of Economics, University of Venice "Ca' Foscari".
    2. Martina Nardon & Paolo Pianca, 2012. "Prospect theory: An application to European option pricing," Working Papers 2012:34, Department of Economics, University of Venice "Ca' Foscari".

    More about this item

    Keywords

    Prospect Theory; Framing; Mental Accounting; Risk Attitude; Loss Aversion; Probability Perception; Weighting Function; Stochastic Volatility; Option Pricing.;

    JEL classification:

    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:crf:wpaper:09-03. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Martine Zenner). General contact details of provider: http://edirc.repec.org/data/sfsculu.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.