American and European Options Near Expiry, Under Markov Processes with Jumps

19 Pages Posted: 2 Nov 2004

Abstract

We derive an explicit formula for time decay, theta, for out-of-the-money European options at expiry, in terms of the density of jumps and payoff $g$. We use this formula to show that in the presence of jumps, the limit of the no-exercise region as time to expiry tends to 0 is typically larger than in the pure Gaussian case. In particular, 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).

Keywords: European out-of-the-money options, early exercise boundary, processes with jumps

JEL Classification: D81, C61

Suggested Citation

Levendorskii, Sergei Z., American and European Options Near Expiry, Under Markov Processes with Jumps. Available at SSRN: https://ssrn.com/abstract=610544 or http://dx.doi.org/10.2139/ssrn.610544

Sergei Z. Levendorskii (Contact Author)

Calico Science Consulting ( email )

Austin, TX
United States

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