IDEAS home Printed from https://ideas.repec.org/p/zbw/tbsifw/if37v1.html
   My bibliography  Save this paper

Piecewise continuous cumulative prospect theory and behavioral financial engineering

Author

Listed:
  • Gürtler, Marc
  • Stolpe, Julia

Abstract

We extend the continuous Cumulative Prospect Theory (CPT) by considering piecewise con-tinuous distributions with a finite number of jump discontinuities. Such distributions are rele-vant in practice, for example, within the framework of financial engineering since cash flow distributions of most types of derivatives are only piecewise continuous. In addition, we ex-pand the model with a (piecewise) continuous version of hedonic framing which is, until now, only available in a discrete model setting. We show how to apply the model to a broad class of structured products. Finally, we apply Prospect Theory (PT), CPT, and expected utility theory to a set of different real-life certificates with piecewise continuous and discrete distributions in order to analyze whether there are any significant differences between the theories, and which theory is able to explain the demand behavior of a market participant best. As a result, we recommend the use of the piecewise continuous version of CPT to design products within the framework of behavioral financial engineering.

Suggested Citation

  • Gürtler, Marc & Stolpe, Julia, 2011. "Piecewise continuous cumulative prospect theory and behavioral financial engineering," Working Papers IF37V1, Technische Universität Braunschweig, Institute of Finance.
    • Handle: RePEc:zbw:tbsifw:if37v1
    DOI: 10.2139/ssrn.1965558
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/55253/1/684986450.pdf
    Download Restriction: no
    File URL: https://libkey.io/10.2139/ssrn.1965558?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Wu, George, 1994. "An Empirical Test of Ordinal Independence," Journal of Risk and Uncertainty, Springer, vol. 9(1), pages 39-60, July.
    3. Nicholas Barberis & Ming Huang, 2008. "Stocks as Lotteries: The Implications of Probability Weighting for Security Prices," American Economic Review, American Economic Association, vol. 98(5), pages 2066-2100, December.
    4. Breuer, Wolfgang & Hauten, Guido & Kreuz, Claudia, 2009. "Financial instruments with sports betting components: Marketing gimmick or a domain for behavioral finance?," Journal of Banking & Finance, Elsevier, vol. 33(12), pages 2241-2252, December.
    5. Richard H. Thaler, 2008. "Mental Accounting and Consumer Choice," Marketing Science, INFORMS, vol. 27(1), pages 15-25, 01-02.
    6. 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.
    7. Camerer, Colin F & Ho, Teck-Hua, 1994. "Violations of the Betweenness Axiom and Nonlinearity in Probability," Journal of Risk and Uncertainty, Springer, vol. 8(2), pages 167-196, March.
    8. Michael Birnbaum, 2005. "A Comparison of Five Models that Predict Violations of First-Order Stochastic Dominance in Risky Decision Making," Journal of Risk and Uncertainty, Springer, vol. 31(3), pages 263-287, December.
    9. Mohammed Abdellaoui & Frank Vossmann & Martin Weber, 2005. "Choice-Based Elicitation and Decomposition of Decision Weights for Gains and Losses Under Uncertainty," Management Science, INFORMS, vol. 51(9), pages 1384-1399, September.
    10. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    11. Humphrey, Steven J, 1995. "Regret Aversion or Event-Splitting Effects? More Evidence under Risk and Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 11(3), pages 263-274, December.
    12. Birnbaum, Michael H & Navarrete, Juan B, 1998. "Testing Descriptive Utility Theories: Violations of Stochastic Dominance and Cumulative Independence," Journal of Risk and Uncertainty, Springer, vol. 17(1), pages 49-78, October.
    13. Marc Rieger & Mei Wang, 2006. "Cumulative prospect theory and the St. Petersburg paradox," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(3), pages 665-679, August.
    14. Luce, R Duncan, 1998. "Coalescing, Event Commutativity, and Theories of Utility," Journal of Risk and Uncertainty, Springer, vol. 16(1), pages 87-114, April.
    15. Marc Rieger & Mei Wang, 2008. "Prospect theory for continuous distributions," Journal of Risk and Uncertainty, Springer, vol. 36(1), pages 83-102, February.
    16. George Wu & Jiao Zhang & Mohammed Abdellaoui, 2005. "Testing Prospect Theories Using Probability Tradeoff Consistency," Journal of Risk and Uncertainty, Springer, vol. 30(2), pages 107-131, January.
    17. George Wu & Richard Gonzalez, 1996. "Curvature of the Probability Weighting Function," Management Science, INFORMS, vol. 42(12), pages 1676-1690, December.
    18. 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.
    19. 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.
    20. 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.
    21. Mohammed Abdellaoui, 2000. "Parameter-Free Elicitation of Utility and Probability Weighting Functions," Management Science, INFORMS, vol. 46(11), pages 1497-1512, November.
    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. Toritseju Begho & Kelvin Balcombe, 2023. "Attitudes to Risk and Uncertainty: New Insights From an Experiment Using Interval Prospects," SAGE Open, , vol. 13(3), pages 21582440231, July.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jakusch, Sven Thorsten & Meyer, Steffen & Hackethal, Andreas, 2019. "Taming models of prospect theory in the wild? Estimation of Vlcek and Hens (2011)," SAFE Working Paper Series 146, Leibniz Institute for Financial Research SAFE, revised 2019.
    2. Michael H. Birnbaum & Ulrich Schmidt & Miriam D. Schneider, 2017. "Testing independence conditions in the presence of errors and splitting effects," Journal of Risk and Uncertainty, Springer, vol. 54(1), pages 61-85, February.
    3. Diecidue, Enrico & Schmidt, Ulrich & Zank, Horst, 2009. "Parametric weighting functions," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1102-1118, May.
    4. 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.
    5. Martina Nardon & Paolo Pianca, 2019. "European option pricing under cumulative prospect theory with constant relative sensitivity probability weighting functions," Computational Management Science, Springer, vol. 16(1), pages 249-274, February.
    6. Marc Rieger & Mei Wang, 2008. "Prospect theory for continuous distributions," Journal of Risk and Uncertainty, Springer, vol. 36(1), pages 83-102, February.
    7. Jakusch, Sven Thorsten, 2017. "On the applicability of maximum likelihood methods: From experimental to financial data," SAFE Working Paper Series 148, Leibniz Institute for Financial Research SAFE, revised 2017.
    8. George Wu & Alex B. Markle, 2008. "An Empirical Test of Gain-Loss Separability in Prospect Theory," Management Science, INFORMS, vol. 54(7), pages 1322-1335, July.
    9. Martina Nardon & Paolo Pianca, 2019. "Behavioral premium principles," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(1), pages 229-257, June.
    10. Michael H. Birnbaum, 2005. "Three New Tests of Independence That Differentiate Models of Risky Decision Making," Management Science, INFORMS, vol. 51(9), pages 1346-1358, September.
    11. Dichtl, Hubert & Drobetz, Wolfgang, 2011. "Portfolio insurance and prospect theory investors: Popularity and optimal design of capital protected financial products," Journal of Banking & Finance, Elsevier, vol. 35(7), pages 1683-1697, July.
    12. Ulrich Schmidt & Horst Zank, 2008. "Risk Aversion in Cumulative Prospect Theory," Management Science, INFORMS, vol. 54(1), pages 208-216, January.
    13. 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.
    14. L'Haridon, Olivier, 2009. "Behavior in the loss domain: An experiment using the probability trade-off consistency condition," Journal of Economic Psychology, Elsevier, vol. 30(4), pages 540-551, August.
    15. Birnbaum, Michael H., 2004. "Tests of rank-dependent utility and cumulative prospect theory in gambles represented by natural frequencies: Effects of format, event framing, and branch splitting," Organizational Behavior and Human Decision Processes, Elsevier, vol. 95(1), pages 40-65, September.
    16. Wakker, Peter P., 2023. "A criticism of Bernheim & Sprenger's (2020) tests of rank dependence," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 107(C).
    17. Marie Pfiffelmann, 2011. "Solving the St. Petersburg Paradox in cumulative prospect theory: the right amount of probability weighting," Theory and Decision, Springer, vol. 71(3), pages 325-341, September.
    18. José Lara Resende & George Wu, 2010. "Competence effects for choices involving gains and losses," Journal of Risk and Uncertainty, Springer, vol. 40(2), pages 109-132, April.
    19. Andreas Glöckner & Baiba Renerte & Ulrich Schmidt, 2020. "Violations of coalescing in parametric utility measurement," Theory and Decision, Springer, vol. 89(4), pages 471-501, November.
    20. Martín Egozcue & Luis Fuentes García & Ričardas Zitikis, 2023. "The Slicing Method: Determining Insensitivity Regions of Probability Weighting Functions," Computational Economics, Springer;Society for Computational Economics, vol. 61(4), pages 1369-1402, April.

    More about this item

    Keywords

    Continuous Cumulative Prospect Theory; Continuous Hedonic Framing; Behavioral Finance; Financial Engineering;
    All these keywords.

    JEL classification:

    • G31 - Financial Economics - - Corporate Finance and Governance - - - Capital Budgeting; Fixed Investment and Inventory Studies
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
    • G35 - Financial Economics - - Corporate Finance and Governance - - - Payout Policy

    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:zbw:tbsifw:if37v1. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/iwtbsde.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.