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

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  • Young Shin Kim

    (Stony Brook University)

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.

Suggested Citation

  • Young Shin Kim, 2019. "Tempered stable process, first passage time, and path-dependent option pricing," Computational Management Science, Springer, vol. 16(1), pages 187-215, February.
    • Handle: RePEc:spr:comgts:v:16:y:2019:i:1:d:10.1007_s10287-018-0326-9
    DOI: 10.1007/s10287-018-0326-9
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    References listed on IDEAS

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    1. Neil Shephard & Ole E. Barndorff-Nielsen & University of Aarhus, 2001. "Normal Modified Stable Processes," Economics Series Working Papers 72, University of Oxford, Department of Economics.
    2. O.E. Barndorff-Nielsen & S.Z. Levendorskii, 2001. "Feller processes of normal inverse Gaussian type," Quantitative Finance, Taylor & Francis Journals, vol. 1(3), pages 318-331, March.
    3. Svetlana I. Boyarchenko & Sergei Z. Levendorskiǐ, 2000. "Option Pricing For Truncated Lévy Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 549-552.
    4. Alan L. Lewis, 2001. "A Simple Option Formula for General Jump-Diffusion and other Exponential Levy Processes," Related articles explevy, Finance Press.
    5. Gerber, Hans U. & Shiu, Elias S.W., 1994. "Martingale Approach to Pricing Perpetual American Options," ASTIN Bulletin, Cambridge University Press, vol. 24(2), pages 195-220, November.
    6. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
    7. Kim, Young Shin & Lee, Jaesung & Mittnik, Stefan & Park, Jiho, 2015. "Quanto option pricing in the presence of fat tails and asymmetric dependence," Journal of Econometrics, Elsevier, vol. 187(2), pages 512-520.
    8. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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    More about this item

    Keywords

    Lévy process; Tempered stable process; First passage time; Barrier option pricing; Perpetual American option pricing;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C42 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Survey Methods

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