IDEAS home Printed from https://ideas.repec.org/p/ams/cdws01/2a.2.html
   My bibliography  Save this paper

The Influence of Heterogeneous Preferences on Asset Prices in an Incomplete Market Model

Author

Listed:
  • Frank Niehaus

    (University of Hannover)

Abstract

In this paper, we examine an exchange economy with a financial market composed of three assets: shares of a stock, European call options written on the stock, and riskless bonds. The financial market is assumed to be incomplete and the option is not a redundant asset. In such a case the construction of a riskless hedge-portfolio to valuate the option is unfeasible and therefore the pricing of the assets becomes a simultaneous valuation problem, nonlineary depending on the preferences of the agents. First, the case of homogeneous agents (or equivalently of a representative agent) is studied. By means of numerical analysis, it can be found that individual preferences have a major impact on the price relation of the assets, including the price of the option. This stays in contrast to the Black-Scholes analysis, where the option is a redundant asset. A unique price relation exists and no trading takes place. In the case of heterogeneous agents the price relation of the assets crucially depends on the span of the heterogeneity of the preferences. Now, trading takes place. The more risk averse agents buy the bond and sell the share and the option, whereas the less risk averse agents buy the option and the share and sell the riskless bond. More surprisingly we find that the representative asset-pricing-model overprices the riskless bond and underprices the option in relation to our model of heterogeneous agents.

Suggested Citation

  • 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.
    • Handle: RePEc:ams:cdws01:2a.2
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Dietmar P.J. Leisen and Kenneth L. Judd, 2001. "A Partial Equilibrium Model of Option Markets," Computing in Economics and Finance 2001 219, Society for Computational Economics.
    2. Detemple, Jerome B & Selden, Larry, 1991. "A General Equilibrium Analysis of Option and Stock Market Interactions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 32(2), pages 279-303, May.
    3. Günter Franke & Richard C. Stapleton & Marti G. Subrahmanyam, 1999. "When are Options Overpriced? The Black—Scholes Model and Alternative Characterisations of the Pricing Kernel," Review of Finance, European Finance Association, vol. 3(1), pages 79-102.
    4. 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.
    5. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, April.
    6. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
    7. Leland, Hayne E, 1980. "Who Should Buy Portfolio Insurance?," Journal of Finance, American Finance Association, vol. 35(2), pages 581-594, May.
    8. repec:bla:scandj:v:97:y:1995:i:3:p:459-67 is not listed on IDEAS
    9. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    10. 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.
    11. 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.
    12. Rubinstein, Mark, 1974. "An aggregation theorem for securities markets," Journal of Financial Economics, Elsevier, vol. 1(3), pages 225-244, September.
    13. Bailey, Warren & Stulz, René M., 1989. "The Pricing of Stock Index Options in a General Equilibrium Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 24(1), pages 1-12, March.
    14. 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.
    15. 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.
    16. 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, University Library of Munich, Germany.
    17. 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-.
    18. Franke, Günter & Stapleton, Richard C. & Subrahmanyam, Marti G., 1999. "When are Options Overpriced? The Black-Scholes Model and Alternative Characterisations of the Pricing Kernel," CoFE Discussion Papers 99/01, University of Konstanz, Center of Finance and Econometrics (CoFE).
    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. Bosi, Gianni & Herden, Gerhard, 2012. "Continuous multi-utility representations of preorders," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 212-218.
    2. Sabrina Ecca & Michele Marchesi & Alessio Setzu, 2008. "Modeling and Simulation of an Artificial Stock Option Market," Computational Economics, Springer;Society for Computational Economics, vol. 32(1), pages 37-53, September.

    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. Frank Niehaus, 2000. "A Simple Option Pricing Model With Heterogeneous Agents," Computing in Economics and Finance 2000 342, Society for Computational Economics.
    2. James Huang, 2003. "Impact of Divergent Consumer Confidence on Option Prices," Review of Derivatives Research, Springer, vol. 6(3), pages 165-177, October.
    3. Lüders, Erik, 2002. "Asset Prices and Alternative Characterizations of the Pricing Kernel," ZEW Discussion Papers 02-10, ZEW - Leibniz Centre for European Economic Research.
    4. 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.
    5. Bertram Düring & Erik Lüders, 2005. "Option Prices Under Generalized Pricing Kernels," Review of Derivatives Research, Springer, vol. 8(2), pages 97-123, August.
    6. 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.
    7. Bertram Düring, 2009. "Asset pricing under information with stochastic volatility," Review of Derivatives Research, Springer, vol. 12(2), pages 141-167, July.
    8. René Garcia & Richard Luger & Eric Renault, 2000. "Asymmetric Smiles, Leverage Effects and Structural Parameters," Working Papers 2000-57, Center for Research in Economics and Statistics.
    9. Luiz Vitiello & Ser-Huang Poon, 2022. "Option pricing with random risk aversion," Review of Quantitative Finance and Accounting, Springer, vol. 58(4), pages 1665-1684, May.
    10. Bakshi, Gurdip S. & Zhiwu, Chen, 1997. "An alternative valuation model for contingent claims," Journal of Financial Economics, Elsevier, vol. 44(1), pages 123-165, April.
    11. Bakshi, Gurdip & Madan, Dilip & Panayotov, George, 2010. "Returns of claims on the upside and the viability of U-shaped pricing kernels," Journal of Financial Economics, Elsevier, vol. 97(1), pages 130-154, July.
    12. Lüders, Erik & Franke, Günter, 2005. "Return predictability and stock market crashes in a simple rational expectations model," CoFE Discussion Papers 05/05, University of Konstanz, Center of Finance and Econometrics (CoFE).
    13. 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.
    14. Franke, Günter & Weber, Martin, 2001. "Heterogeneity of Investors and Asset Pricing in a Risk-Value World," CoFE Discussion Papers 01/08, University of Konstanz, Center of Finance and Econometrics (CoFE).
    15. Tarik Driouchi & Lenos Trigeorgis & Raymond H. Y. So, 2018. "Option implied ambiguity and its information content: Evidence from the subprime crisis," Annals of Operations Research, Springer, vol. 262(2), pages 463-491, March.
    16. Franke, Günter & Lüders, Erik, 2006. "Return predictability and stock market crashes in a simple rational expectation models," CoFE Discussion Papers 06/05, University of Konstanz, Center of Finance and Econometrics (CoFE).
    17. Ait-Sahalia, Yacine & Lo, Andrew W., 2000. "Nonparametric risk management and implied risk aversion," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 9-51.
    18. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    19. repec:dgr:rugsom:00e08 is not listed on IDEAS
    20. Nizar Riane, 2023. "The inverse Black-Scholes problem in Radon measures space revisited: towards a new measure of market uncertainty," Papers 2303.16773, arXiv.org.
    21. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.

    More about this item

    Keywords

    Asset pricing; Incomplete markets; Option pricing; Heterogeneous agents;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

    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:ams:cdws01:2a.2. 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: Christopher F. Baum (email available below). General contact details of provider: https://edirc.repec.org/data/cnuvanl.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.