The American Put and European Options Near Expiry, Under Levy Processes
29 Pages Posted: 23 Mar 2004
Date Written: February 26, 2004
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: Suggested Citation