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The Finite Moment Log Stable Process and Option Pricing

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Author Info
Peter Carr (New York University)
Liuren Wu (Fordham University)

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Abstract

We document a surprising pattern in market prices of S&P 500 index options. When implied volatilities are graphed against a standard measure of moneyness, the implied volatility smirk does not flatten out as maturity increases up to the observable horizon of two years. This behavior contrasts sharply with the implications of many pricing models and with the asymptotic behavior implied by the central limit theorem (CLT). We develop a parsimonious model which deliberately violates the CLT assumptions and thus captures the observed behavior of the volatility smirk over the maturity horizon. Calibration exercises demonstrate its superior performance against several widely used alternatives.

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Publisher Info
Paper provided by EconWPA in its series Finance with number 0207012.

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Length: 42 pages
Date of creation: 30 Aug 2002
Date of revision:
Handle: RePEc:wpa:wuwpfi:0207012

Note: Type of Document - pdf; prepared on MikTex; to print on postscript; pages: 42 ; figures: included. produced via dvipdfm
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Web page: http://129.3.20.41

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Related research
Keywords: Volatility smirk; central limit theorem; Levy a­lpha-stable motion; self­similarity; option pricing.;

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Find related papers by JEL classification:
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
F31 - International Economics - - International Finance - - - Foreign Exchange
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods

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.:

  1. Markus Leippold & Liuren Wu, 2002. "Asset Pricing Under The Quadratic Class," Finance 0207015, EconWPA. [Downloadable!]
    Other versions:
  2. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July. [Downloadable!] (restricted)
  3. Peter Carr & Liuren Wu, 2002. "Time-Changed Levy Processes and Option Pricing," Finance 0207011, EconWPA. [Downloadable!]
    Other versions:
  4. Ding, Zhuanxin & Granger, Clive W. J., 1996. "Modeling volatility persistence of speculative returns: A new approach," Journal of Econometrics, Elsevier, vol. 73(1), pages 185-215, July. [Downloadable!] (restricted)
    Other versions:
  5. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 9(1), pages 69-107. [Downloadable!] (restricted)
  6. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," Journal of Business, University of Chicago Press, vol. 36, pages 394. [Downloadable!]
  7. David Backus & Silverio Foresi & Liuren Wu, 2002. "Accouting for Biases in Black-Scholes," Finance 0207008, EconWPA. [Downloadable!]
  8. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring. [Downloadable!] (restricted)
  9. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-33, March. [Downloadable!] (restricted)
  10. Zhuanxin Ding & Clive Granger & Robert Engle, 1992. "A Long Memory Property of Stock Market Returns and a New Model," University of California at San Diego, Economics Working Paper Series 92-21, Department of Economics, UC San Diego.
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  11. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144. [Downloadable!] (restricted)
    Other versions:
  12. Heston, Steven L, 1993. " Invisible Parameters in Option Prices," Journal of Finance, American Finance Association, vol. 48(3), pages 933-47, July. [Downloadable!] (restricted)
  13. 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. [Downloadable!] (restricted)
  14. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley. [Downloadable!]
  15. Yacine Aït-Sahalia & Andrew W. Lo, 1998. "Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices," Journal of Finance, American Finance Association, vol. 53(2), pages 499-547, 04. [Downloadable!] (restricted)
    Other versions:
  16. Das, Sanjiv Ranjan & Sundaram, Rangarajan K., 1999. "Of Smiles and Smirks: A Term Structure Perspective," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(02), pages 211-239, June. [Downloadable!]
  17. Bates, David S., 2000. "Post-'87 crash fears in the S&P 500 futures option market," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 181-238. [Downloadable!] (restricted)
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