The American Put and European Options Near Expiry, Under Levy Processes

29 Pages Posted: 23 Mar 2004

Date Written: February 26, 2004

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 time interval up to expiry, the expiry date excluding. 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 time interval up to expiry, the expiry date excluding. The implications for parameters' fitting are discussed.

Keywords: Levy processes, early exercise boundary, option pricimg

JEL Classification: G12, G13

Suggested Citation

Levendorskii, Sergei Z., The American Put and European Options Near Expiry, Under Levy Processes (February 26, 2004). Available at SSRN: https://ssrn.com/abstract=520062 or http://dx.doi.org/10.2139/ssrn.520062

Sergei Z. Levendorskii (Contact Author)

Calico Science Consulting ( email )

Austin, TX
United States

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