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A Multifractal Model of Assets Returns

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Author Info
Laurent Calvet
Adlai Fisher
Benoit Mandelbrot

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Abstract

An important determinant of option prices is the elasticity of the pricing kernel used to price all decline in the economy. In this paper, we first show that for a given forward price of the underlying asset, option prices are higher when the elasticity of pricing kernel is declining than when it is constant. We then investigate the implications of the elasticity of the pricing kernel for the stochastic process followed by the underlying asset. Given that the underlying information process follows a geometric Brownlan motion, we demonstrate that constant elasticity of the pricing kernel is equivalent to a Brownlan motion for the forward price of the underlying asset, so that the Black-Scholes formula correctly prices option on the asset. In contrast, declining elasticity implies that he forward price process is no longer a Brownlan motion. It has higher volatility and exhibits autocorrelation. In this case, the Black-Scholes formula and underprices all options.

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Paper provided by New York University, Leonard N. Stern School of Business- in its series New York University, Leonard N. Stern School Finance Department Working Paper Seires with number 99-072.

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Date of creation: Mar 1999
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Handle: RePEc:fth:nystfi:99-072

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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.:
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  1. Lux, Thomas, 2004. "The Markov-switching multi-fractal model of asset returns : GMM estimation and linear forecasting of volatility," Economics Working Papers 2004,11, Christian-Albrechts-University of Kiel, Department of Economics. [Downloadable!]
    Other versions:
  2. Lux, Thomas, 2003. "The multi-fractal model of asset returns : its estimation via GMM and its use for volatility forecasting," Economics Working Papers 2003,13, Christian-Albrechts-University of Kiel, Department of Economics. [Downloadable!]
    Other versions:
  3. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 1999. "The Distribution of Exchange Rate Volatility," Center for Financial Institutions Working Papers 99-08, Wharton School Center for Financial Institutions, University of Pennsylvania. [Downloadable!]
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  4. Challet, Damien & Peirano, Pier Paolo, 2008. "The Ups and Downs of Modeling Financial Time Series with Wiener Process Mixtures," MPRA Paper 9770, University Library of Munich, Germany. [Downloadable!]
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  5. Laurent E. Calvet & Adlai J. Fisher, 2006. "Multifrequency Jump-Diffusions: An Equilibrium Approach," NBER Working Papers 12797, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  6. Thomas Lux, 2008. "Stochastic Behavioral Asset Pricing Models and the Stylized Facts," Kiel Working Papers 1426, Kiel Institute for the World Economy. [Downloadable!]
  7. Marc Henry & Paolo Zaffaroni, 2002. "The long range dependence paradigm for macroeconomics and finance," Discussion Papers 0102-19, Columbia University, Department of Economics. [Downloadable!]
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    Other versions:
  9. Paul Eitelman & Justin Vitanza, 2008. "A non-random walk revisited: short- and long-term memory in asset prices," International Finance Discussion Papers 956, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
  10. Dr. Brian J. Jacobsen, 2005. "The Use of Downside Risk Measures in Portfolio Construction and Evaluation," Computing in Economics and Finance 2005 5, Society for Computational Economics. [Downloadable!]
  11. Per Frederiksen & Frank S. Nielsen, 2008. "Estimation of Dynamic Models with Nonparametric Simulated Maximum Likelihood," CREATES Research Papers 2008-59, School of Economics and Management, University of Aarhus. [Downloadable!]
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  14. Laurent Calvet & Adlai Fisher, 1999. "Forecasting Multifractal Volatility," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-017, New York University, Leonard N. Stern School of Business-. [Downloadable!]
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  15. Giuseppe Garofalo & Alessandro Sansone, 2005. "Asset Price Dynamics in a Financial Market with Heterogeneous Trading Strategies and Time Delays," Working Papers 88, Sapienza University of Rome, Department of Public Economics. [Downloadable!]
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  16. Sijing Zong & Cornelis A. Los & Nyonyo Kyaw, 2004. "Persistence Characteristics of Latin American Financial Markets," Finance 0411013, EconWPA. [Downloadable!]
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  17. Laurent Calvet & Adlai Fisher & Benoit Mandelbrot, 1997. "Large Deviations and the Distribution of Price Changes," Cowles Foundation Discussion Papers 1165, Cowles Foundation, Yale University. [Downloadable!]
  18. TEYSSIERE, Gilles, 2003. "Interaction models for common long-range dependence in asset price volatilities," CORE Discussion Papers 2003026, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
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  22. Adlai Fisher & Laurent Calvet & Benoit Mandelbrot, 1997. "Multifractality of Deutschemark/US Dollar Exchange Rates," Cowles Foundation Discussion Papers 1166, Cowles Foundation, Yale University. [Downloadable!]
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