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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.

Suggested Citation

  • Sergei Levendorskii, 2004. "The American put and European options near expiry, under Levy processes," Papers cond-mat/0404103, arXiv.org.
    • Handle: RePEc:arx:papers:cond-mat/0404103
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    References listed on IDEAS

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    Cited by:

    1. Elizondo Rocío & Padilla Pablo & Bladt Mogens, 2009. "An Alternative Formula to Price American Options," Working Papers 2009-06, Banco de México.
    2. Leif Andersen & Alexander Lipton, 2012. "Asymptotics for Exponential Levy Processes and their Volatility Smile: Survey and New Results," Papers 1206.6787, arXiv.org.
    3. Michael Roper, 2008. "Implied volatility explosions: European calls and implied volatilities close to expiry in exponential L\'evy models," Papers 0809.3305, arXiv.org, revised Sep 2008.
    4. Leif Andersen & Alexander Lipton, 2013. "Asymptotics For Exponential Lévy Processes And Their Volatility Smile: Survey And New Results," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(01), pages 1-98.

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