IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Log in (now much improved!) to save this article

The Black-Scholes model as a determinant of the implied volatility smile: A simulation study

  • Vagnani, Gianluca
Registered author(s):

    The paper represents an initial effort to shed light on the determinants of the implied volatility smile in financial (derivative) markets. It fully details the implications of the institutionalization of the Black-Scholes model in an uncertain world populated by individuals who are bounded by the amount of calculation or accounting which is technically possible. Combining model simulations, empirical analysis, and mathematical derivations, the paper proposes that the determinants of the volatility smile might be related to the behavior of traders. In pricing options, they use the widely accepted Black-Scholes formula with a measure of stock volatility that they derive from their subjective beliefs. Moreover, heterogeneity of traders' beliefs and the way traders update their expectations have nontrivial effects, both on equilibrium prices and on the emergence of the implied volatility smile.

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-2681(09)00166-8
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Article provided by Elsevier in its journal Journal of Economic Behavior & Organization.

    Volume (Year): 72 (2009)
    Issue (Month): 1 (October)
    Pages: 103-118

    as
    in new window

    Handle: RePEc:eee:jeborg:v:72:y:2009:i:1:p:103-118
    Contact details of provider: Web page: http://www.elsevier.com/locate/jebo

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

    as in new window
    1. Herbert Dawid & Michael Neugart, 2011. "Agent-based Models for Economic Policy Design," Eastern Economic Journal, Palgrave Macmillan, vol. 37(1), pages 44-50.
    2. Jackwerth, Jens Carsten & Rubinstein, Mark, 1996. " Recovering Probability Distributions from Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1611-32, December.
    3. Ehrentreich, Norman, 2006. "Technical trading in the Santa Fe Institute Artificial Stock Market revisited," Journal of Economic Behavior & Organization, Elsevier, vol. 61(4), pages 599-616, December.
    4. LeBaron, Blake & Arthur, W. Brian & Palmer, Richard, 1999. "Time series properties of an artificial stock market," Journal of Economic Dynamics and Control, Elsevier, vol. 23(9-10), pages 1487-1516, September.
    5. Figlewski, Stephen, 1989. " Options Arbitrage in Imperfect Markets," Journal of Finance, American Finance Association, vol. 44(5), pages 1289-1311, December.
    6. Sanford J Grossman & Joseph E Stiglitz, 1997. "On the Impossibility of Informationally Efficient Markets," Levine's Working Paper Archive 1908, David K. Levine.
    7. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    8. 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 703-38, August.
    9. Eric Renault & Nizar Touzi, 1996. "Option Hedging And Implied Volatilities In A Stochastic Volatility Model," Mathematical Finance, Wiley Blackwell, vol. 6(3), pages 279-302.
    10. Thomas H. Naylor & J. M. Finger, 1967. "Verification of Computer Simulation Models," Management Science, INFORMS, vol. 14(2), pages B92-B101, October.
    11. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. " Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-49, December.
    12. Kliger, Doron & Levy, Ori, 2003. "Mood-induced variation in risk preferences," Journal of Economic Behavior & Organization, Elsevier, vol. 52(4), pages 573-584, December.
    13. Schmalensee, Richard & Trippi, Robert R, 1978. "Common Stock Volatility Expectations Implied by Option Premia," Journal of Finance, American Finance Association, vol. 33(1), pages 129-47, March.
    14. Ziegler, Alexandre, 2002. "State-price densities under heterogeneous beliefs, the smile effect, and implied risk aversion," European Economic Review, Elsevier, vol. 46(8), pages 1539-1557, September.
    15. Arthur, W Brian, 1994. "Inductive Reasoning and Bounded Rationality," American Economic Review, American Economic Association, vol. 84(2), pages 406-11, May.
    16. Brandt, Michael W. & Jones, Christopher S., 2006. "Volatility Forecasting With Range-Based EGARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 470-486, October.
    17. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    18. R. W. Conway & B. M. Johnson & W. L. Maxwell, 1959. "Some Problems of Digital Systems Simulation," Management Science, INFORMS, vol. 6(1), pages 92-110, October.
    19. Alvin E. Roth, 2002. "The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics," Econometrica, Econometric Society, vol. 70(4), pages 1341-1378, July.
    20. Rubinstein, Mark, 1985. " Nonparametric Tests of Alternative Option Pricing Models Using All Reported Trades and Quotes on the 30 Most Active CBOE Option Classes from August 23, 1976 through August 31, 1978," Journal of Finance, American Finance Association, vol. 40(2), pages 455-80, June.
    21. Jean-Marie, Alain & Tidball, Mabel, 2006. "Adapting behaviors through a learning process," Journal of Economic Behavior & Organization, Elsevier, vol. 60(3), pages 399-422, July.
    22. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    23. Holland, John H & Miller, John H, 1991. "Artificial Adaptive Agents in Economic Theory," American Economic Review, American Economic Association, vol. 81(2), pages 365-71, May.
    24. Routledge, Bryan R, 1999. "Adaptive Learning in Financial Markets," Review of Financial Studies, Society for Financial Studies, vol. 12(5), pages 1165-1202.
    25. Hansen, Lars Peter & Singleton, Kenneth J, 1982. "Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models," Econometrica, Econometric Society, vol. 50(5), pages 1269-86, September.
    26. Gadi Barlevy & Pietro Veronesi, . "Information Acquisition in Financial Markets," CRSP working papers 484, Center for Research in Security Prices, Graduate School of Business, University of Chicago.
    27. Longstaff, Francis A, 1995. "Option Pricing and the Martingale Restriction," Review of Financial Studies, Society for Financial Studies, vol. 8(4), pages 1091-1124.
    28. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    29. Richard L. Van Horn, 1971. "Validation of Simulation Results," Management Science, INFORMS, vol. 17(5), pages 247-258, January.
    30. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    31. Jack P. C. Kleijnen, 1988. "Analyzing Simulation Experiments with Common Random Numbers," Management Science, INFORMS, vol. 34(1), pages 65-74, January.
    32. Rama Cont & Jose da Fonseca, 2002. "Dynamics of implied volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 45-60.
    33. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    34. K. Ronnie Sircar & George Papanicolaou, 1999. "Stochastic volatility, smile & asymptotics," Applied Mathematical Finance, Taylor & Francis Journals, vol. 6(2), pages 107-145.
    35. Canina, Linda & Figlewski, Stephen, 1993. "The Informational Content of Implied Volatility," Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 659-81.
    36. 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 637-54, May-June.
    37. Mthuli Ncube & Stephen Satchell, 1997. "The Statistical Properties of the Black-Scholes Option Price," Mathematical Finance, Wiley Blackwell, vol. 7(3), pages 287-305.
    Full references (including those not matched with items on IDEAS)

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    When requesting a correction, please mention this item's handle: RePEc:eee:jeborg:v:72:y:2009:i:1:p:103-118. 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: (Shamier, Wendy)

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 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.

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.