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What Type of Process Underlies Options? A Simple Robust Test

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Author Info
Peter Carr (Bloomberg LP and the Courant Institute, New York University)
Liuren Wu (Zicklin School of Business, Baruch College, CUNY)

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Abstract

We develop a simple robust method to distinguish the presence of continuous and discontinuous components in the price of an asset underlying options. Our method examines the prices of at-the-money and out-of-the-money options as the option's time-to-maturity approaches zero. We show that these prices converge to zero at speeds that depend upon whether the underlying asset price process is purely continuous, purely discontinuous, or a combination of both. We apply the method to S&P 500 index options and find the existence of both a continuous component and a jump component in the index. Copyright 2003 by the American Finance Association.

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Publisher Info
Article provided by American Finance Association in its journal The Journal of Finance.

Volume (Year): 58 (2003)
Issue (Month): 6 (December)
Pages: 2581-2610
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Handle: RePEc:bla:jfinan:v:58:y:2003:i:6:p:2581-2610

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  1. Peter Christoffersen & Steve Heston & Kris Jacobs, 2003. "Option Valuation with Conditional Skewness," CIRANO Working Papers 2003s-50, CIRANO. [Downloadable!]
    Other versions:
  2. Sergei Levendorskii, 2004. "The American put and European options near expiry, under Levy processes," Quantitative Finance Papers cond-mat/0404103, arXiv.org. [Downloadable!]
  3. George J. Jiang & Ingrid Lo & Adrien Verdelhan, 2008. "Information Shocks, Jumps, and Price Discovery -- Evidence from the U.S. Treasury Market," Working Papers 08-22, Bank of Canada. [Downloadable!]
  4. Peter Carr & Liuren Wu, 2004. "Static Hedging of Standard Options," Finance 0409016, EconWPA. [Downloadable!]
  5. Li, Minqiang, 2008. "Price Deviations of S&P 500 Index Options from the Black-Scholes Formula Follow a Simple Pattern," MPRA Paper 11530, University Library of Munich, Germany. [Downloadable!]
  6. Tim Bollerslev & Viktor Todorov, 2009. "Tails, Fears and Risk Premia," CREATES Research Papers 2009-26, School of Economics and Management, University of Aarhus. [Downloadable!]
  7. Marian Micu, 2005. "Extracting expectations from currency option prices: a comparison of methods," Computing in Economics and Finance 2005 226, Society for Computational Economics. [Downloadable!]
  8. Jing-zhi Huang & Liuren Wu, 2004. "Specification Analysis of Option Pricing Models Based on Time-Changed Levy Processes," Econometric Society 2004 North American Winter Meetings 405, Econometric Society. [Downloadable!]
    Other versions:
  9. Alvaro Cartea, 2005. "Dynamic Hedging of Financial Instruments When the Underlying Follows a Non-Gaussian Process," Birkbeck Working Papers in Economics and Finance 0508, Birkbeck, Department of Economics, Mathematics & Statistics. [Downloadable!]
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