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Asymptotic analysis of the American call option with dividends

Published online by Cambridge University Press:  12 December 2002

CHARLES KNESSL
CHARLES KNESSL
Affiliation:
Department of Mathematics, Statistics and Computer Science (M/C 249), University of Illinois at Chicago, 851 South Morgan Street, Chicago, IL 60607-7045, USA email: [email protected]
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Abstract

We consider an American call option and let C(S, T0) be the price of an option corresponding to asset price S at some time T0 prior to the expiration time TF . We analyze C(S, T0) in various asymptotic limits. These include situations where the interest and dividend rates are large or small, compared to the volatility of the asset. We also analyze the optimal exercise boundary for the option. We use perturbation methods to analyze either the PDE that C(S, T0) satisfies, or a nonlinear integral equation that is satisfied by the optimal exercise boundary.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 13 , Issue 6 , December 2002 , pp. 587 - 616
Copyright
2002 Cambridge University Press

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