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The American put and European options near expiry, under Levy processes

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Sergei Levendorskii
Abstract

We derive explicit formulas for time decay, for the European call and put options at expiry, and use them to calculate analytical approximations to the price of the American put and early exercise boundary near expiry. We show that for many families of non-Gaussian processes used in empirical studies of financial markets, the early exercise boundary for the American put without dividends is separated from the strike price by a non-vanishing margin on the interval [0,T). As the riskless rate vanishes and the drift decreases accordingly so that the stock remains a martingale, the optimal exercise price goes to zero uniformly over the interval [0, T). The implications for parameters' fitting are discussed.

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File URL: http://arxiv.org/abs/cond-mat/0404103
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Paper provided by arXiv.org in its series Quantitative Finance Papers with number cond-mat/0404103.

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Date of creation: Apr 2004
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Handle: RePEc:arx:papers:cond-mat/0404103

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References listed on IDEAS
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  1. Peter Carr & Liuren Wu, 2003. "What Type of Process Underlies Options? A Simple Robust Test," Journal of Finance, American Finance Association, vol. 58(6), pages 2581-2610, December. [Downloadable!] (restricted)
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  2. Rama Cont & Marc Potters & Jean-Philippe Bouchaud, 1997. "Scaling in stock market data: stable laws and beyond," Quantitative Finance Papers cond-mat/9705087, arXiv.org. [Downloadable!]
  3. Andrew Matacz, 1997. "Financial modeling and option theory with the truncated Lévy process," Science & Finance (CFM) working paper archive 500035, Science & Finance, Capital Fund Management. [Downloadable!]
  4. Yacine Aït-Sahalia, 2002. "Telling from Discrete Data Whether the Underlying Continuous-Time Model Is a Diffusion," Journal of Finance, American Finance Association, vol. 57(5), pages 2075-2112, October. [Downloadable!] (restricted)
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  5. Eberlein, Ernst & Keller, Ulrich & Prause, Karsten, 1998. "New Insights into Smile, Mispricing, and Value at Risk: The Hyperbolic Model," Journal of Business, University of Chicago Press, vol. 71(3), pages 371-405, July. [Downloadable!] (restricted)
  6. Rama Cont & Marc Potters & Jean-Philippe Bouchaud, 1997. "Scaling in stock market data: stable laws and beyond," Science & Finance (CFM) working paper archive 9705087, Science & Finance, Capital Fund Management. [Downloadable!]
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Cited by:
(explanations, 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. Michael Roper, 2008. "Implied volatility explosions: European calls and implied volatilities close to expiry in exponential L\'evy models," Quantitative Finance Papers 0809.3305, arXiv.org, revised Sep 2008. [Downloadable!]
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