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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2006; 43(2): 383-398

Printed March 1, 2006

Copyright © The Korean Mathematical Society.

Approximations of option prices for a jump-diffusion model

In-Suk Wee

Korea University

Abstract

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We consider a geometric L\'{e}vy process for an underlying asset. We prove first that the option price is the unique solution of certain integro-differential equation without assuming differentiability and boundedness of derivatives of the payoff function. Second result is to provide convergence rate for option prices when the small jumps are removed from the L\'{e}vy process.

Keywords: Black-Scholes model, jump-diffusion model, L\'{e}vy process, option price

MSC numbers: Primary 91B28, 60H30

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