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Computational Management Science

, Volume 16, Issue 1–2, pp 187–215 | Cite as

Tempered stable process, first passage time, and path-dependent option pricing

  • Young Shin KimEmail author
Original Paper

Abstract

In this paper, we will discuss an approximation of the characteristic function of the first passage time for a Lévy process using the martingale approach. The characteristic function of the first passage time of the tempered stable process is provided explicitly or by an indirect numerical method. This will be applied to the perpetual American option pricing and the barrier option pricing. For the numerical illustration, we calibrate risk neutral process parameters using S&P 500 index option prices and apply those parameters to find prices of perpetual American option and barrier option.

Keywords

Lévy process Tempered stable process First passage time Barrier option pricing Perpetual American option pricing 

JEL Classification

G13 C21 C42 

Notes

Acknowledgements

I am grateful to Professor Kyuong Jin Choi, in Haskayne School of Business, University of Calgary, who gave the motivation to complete of this research. Also, all remaining errors are entirely my own.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of BusinessStony Brook UniversityNew YorkUSA

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