IDEAS home Printed from https://ideas.repec.org/p/cns/cnscwp/201112.html
   My bibliography  Save this paper

The risk neutral valuation paradox

Author

Listed:
  • A. Fiori Maccioni

Abstract

This paper highlights the role of risk neutral investors in generating endogenous bubbles in derivatives markets. We propose the following theorem. A market for derivatives, which has all the features of a perfect market except completeness and has some risk neutral investors, may exhibit almost surely extreme price movements which represent a violation to the Gaussian random walk hypothesis. This can be viewed as a paradox because it contradicts wide-held conjectures about prices in informationally efficient markets with rational investors. The theorem implies that prices are not always good approximations of the fundamental values of derivatives, and that extreme price movements like price peaks or crashes may have endogenous origin and happen with a higher-than-normal frequency. In the paper, we demonstrate the theorem and we propose an application that solves the Grossman- Stiglitz paradox on the value of information.

Suggested Citation

  • A. Fiori Maccioni, 2011. "The risk neutral valuation paradox," Working Paper CRENoS 201112, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.
    • Handle: RePEc:cns:cnscwp:201112
    as

    Download full text from publisher

    File URL: https://crenos.unica.it/crenos/node/3302
    Download Restriction: no
    File URL: https://crenos.unica.it/crenos/sites/default/files/WP11-12.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Philip H. Dybvig, Chi-fu Huang, 1988. "Nonnegative Wealth, Absence of Arbitrage, and Feasible Consumption Plans," The Review of Financial Studies, Society for Financial Studies, vol. 1(4), pages 377-401.
    2. Manuel S. Santos & Michael Woodford, 1997. "Rational Asset Pricing Bubbles," Econometrica, Econometric Society, vol. 65(1), pages 19-58, January.
    3. Grossman, Sanford J & Stiglitz, Joseph E, 1980. "On the Impossibility of Informationally Efficient Markets," American Economic Review, American Economic Association, vol. 70(3), pages 393-408, June.
    4. Steven L. Heston & Mark Loewenstein & Gregory A. Willard, 2007. "Options and Bubbles," The Review of Financial Studies, Society for Financial Studies, vol. 20(2), pages 359-390.
    5. Ernst Eberlein & Jean Jacod, 1997. "On the range of options prices (*)," Finance and Stochastics, Springer, vol. 1(2), pages 131-140.
    6. De Long, J Bradford & Andrei Shleifer & Lawrence H. Summers & Robert J. Waldmann, 1990. "Noise Trader Risk in Financial Markets," Journal of Political Economy, University of Chicago Press, vol. 98(4), pages 703-738, August.
    7. Kamara, Avraham & Miller, Thomas W., 1995. "Daily and Intradaily Tests of European Put-Call Parity," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 30(4), pages 519-539, December.
    8. Tirole, Jean, 1982. "On the Possibility of Speculation under Rational Expectations," Econometrica, Econometric Society, vol. 50(5), pages 1163-1181, September.
    9. Robert A. Jarrow, 2015. "Asset Price Bubbles," Annual Review of Financial Economics, Annual Reviews, vol. 7(1), pages 201-218, December.
    10. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    11. Peter Lakner, 1993. "Martingale Measures For A Class of Right‐Continuous Processes," Mathematical Finance, Wiley Blackwell, vol. 3(1), pages 43-53, January.
    12. Freddy Delbaen, 1992. "Representing Martingale Measures When Asset Prices Are Continuous And Bounded," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 107-130, April.
    13. David C. Heath & Robert A. Jarrow, 2008. "Arbitrage, Continuous Trading, and Margin Requirements," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 2, pages 33-46, World Scientific Publishing Co. Pte. Ltd..
    14. Eli Ofek & Matthew Richardson, 2003. "DotCom Mania: The Rise and Fall of Internet Stock Prices," Journal of Finance, American Finance Association, vol. 58(3), pages 1113-1137, June.
    15. Sonnenschein, Hugo, 1973. "Do Walras' identity and continuity characterize the class of community excess demand functions?," Journal of Economic Theory, Elsevier, vol. 6(4), pages 345-354, August.
    16. Sonnenschein, Hugo, 1972. "Market Excess Demand Functions," Econometrica, Econometric Society, vol. 40(3), pages 549-563, May.
    17. Eli Ofek & Matthew Richardson, 2003. "DotCom Mania: The Rise and Fall of Internet Stock Prices," Journal of Finance, American Finance Association, vol. 58(3), pages 1113-1138, June.
    18. (**), Hui Wang & Jaksa Cvitanic & (*), Walter Schachermayer, 2001. "Utility maximization in incomplete markets with random endowment," Finance and Stochastics, Springer, vol. 5(2), pages 259-272.
    19. Mantel, Rolf R., 1974. "On the characterization of aggregate excess demand," Journal of Economic Theory, Elsevier, vol. 7(3), pages 348-353, March.
    20. Kreps, David M., 1981. "Arbitrage and equilibrium in economies with infinitely many commodities," Journal of Mathematical Economics, Elsevier, vol. 8(1), pages 15-35, March.
    21. Alexander Cox & David Hobson, 2005. "Local martingales, bubbles and option prices," Finance and Stochastics, Springer, vol. 9(4), pages 477-492, October.
    22. O'Connell, Stephen A & Zeldes, Stephen P, 1988. "Rational Ponzi Games," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(3), pages 431-450, August.
    23. Camerer, Colin, 1989. "Bubbles and Fads in Asset Prices," Journal of Economic Surveys, Wiley Blackwell, vol. 3(1), pages 3-41.
    24. Dieter Sondermann, 2006. "Introduction to Stochastic Calculus for Finance," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-34837-5, December.
    25. Cox, John C & Ross, Stephen A, 1976. "A Survey of Some New Results in Financial Option Pricing Theory," Journal of Finance, American Finance Association, vol. 31(2), pages 383-402, May.
    26. Schachermayer, W., 1992. "A Hilbert space proof of the fundamental theorem of asset pricing in finite discrete time," Insurance: Mathematics and Economics, Elsevier, vol. 11(4), pages 249-257, December.
    27. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    28. Duffie, Darrell & Huang, Chi-fu, 1986. "Multiperiod security markets with differential information : Martingales and resolution times," Journal of Mathematical Economics, Elsevier, vol. 15(3), pages 283-303, June.
    29. Debreu, Gerard, 1974. "Excess demand functions," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 15-21, March.
    30. 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.
    31. Tirole, Jean, 1985. "Asset Bubbles and Overlapping Generations," Econometrica, Econometric Society, vol. 53(6), pages 1499-1528, November.
    32. Martin Schweizer & Johannes Wissel, 2008. "Term Structures Of Implied Volatilities: Absence Of Arbitrage And Existence Results," Mathematical Finance, Wiley Blackwell, vol. 18(1), pages 77-114, January.
    33. J. Michael Harrison & David M. Kreps, 1978. "Speculative Investor Behavior in a Stock Market with Heterogeneous Expectations," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 92(2), pages 323-336.
    Full references (including those not matched with items on IDEAS)

    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. Alessandro Fiori Maccioni, 2011. "Endogenous Bubbles in Derivatives Markets: The Risk Neutral Valuation Paradox," Papers 1106.5274, arXiv.org, revised Sep 2011.
    2. Robert A. Jarrow, 2015. "Asset Price Bubbles," Annual Review of Financial Economics, Annual Reviews, vol. 7(1), pages 201-218, December.
    3. Committee, Nobel Prize, 2013. "Understanding Asset Prices," Nobel Prize in Economics documents 2013-1, Nobel Prize Committee.
    4. Hardy Hulley, 2009. "Strict Local Martingales in Continuous Financial Market Models," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 19, July-Dece.
    5. Hardy Hulley, 2009. "Strict Local Martingales in Continuous Financial Market Models," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2-2009.
    6. W. Schachermayer, 1994. "Martingale Measures For Discrete‐Time Processes With Infinite Horizon," Mathematical Finance, Wiley Blackwell, vol. 4(1), pages 25-55, January.
    7. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," 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 11, pages 639-742, Elsevier.
    8. Jouini, Elyes, 2001. "Arbitrage and control problems in finance: A presentation," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 167-183, April.
    9. Loewenstein, Mark & Willard, Gregory A., 2000. "Rational Equilibrium Asset-Pricing Bubbles in Continuous Trading Models," Journal of Economic Theory, Elsevier, vol. 91(1), pages 17-58, March.
    10. repec:dau:papers:123456789/5590 is not listed on IDEAS
    11. John Conlon, 2005. "Should Central Banks Burst Bubbles?," Game Theory and Information 0508007, University Library of Munich, Germany.
    12. 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.
    13. Jaime A. Londo~no, 2003. "State Tameness: A New Approach for Credit Constrains," Papers math/0305274, arXiv.org, revised Feb 2004.
    14. Brunnermeier, Markus K. & Oehmke, Martin, 2013. "Bubbles, Financial Crises, and Systemic Risk," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 1221-1288, Elsevier.
    15. John R. Conlon, 2015. "Should Central Banks Burst Bubbles? Some Microeconomic Issues," Economic Journal, Royal Economic Society, vol. 125(582), pages 141-161, February.
    16. Peter Temin & Hans-Joachim Voth, 2004. "Riding the South Sea Bubble," American Economic Review, American Economic Association, vol. 94(5), pages 1654-1668, December.
    17. repec:dau:papers:123456789/5374 is not listed on IDEAS
    18. Napp, Clotilde, 2001. "Pricing issues with investment flows Applications to market models with frictions," Journal of Mathematical Economics, Elsevier, vol. 35(3), pages 383-408, June.
    19. repec:dau:papers:123456789/5603 is not listed on IDEAS
    20. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    21. Charalambos Aliprantis & Kim Border & Owen Burkinshaw, 1996. "Market economies with many commodities," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 19(1), pages 113-185, March.
    22. Fergusson, Kevin, 2020. "Less-Expensive Valuation And Reserving Of Long-Dated Variable Annuities When Interest Rates And Mortality Rates Are Stochastic," ASTIN Bulletin, Cambridge University Press, vol. 50(2), pages 381-417, May.
    23. repec:uts:finphd:40 is not listed on IDEAS
    24. John Fender, 2020. "Beyond the efficient markets hypothesis: Towards a new paradigm," Bulletin of Economic Research, Wiley Blackwell, vol. 72(3), pages 333-351, July.

    More about this item

    Keywords

    risk neutral; martingale; derivatives; efficient market; fundamental theorem; bubble;
    All these keywords.

    JEL classification:

    • G1 - Financial Economics - - General Financial Markets
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

    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:cns:cnscwp:201112. 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: CRENoS (email available below). General contact details of provider: https://edirc.repec.org/data/crenoit.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.