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The GARCH Option Pricing Model: A Modification of Lattice Approach

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  • Chun-Chou Wu

Abstract

Ritchken and Trevor (1999) proposed a lattice approach for pricing American options under discrete time-varying volatility GARCH frameworks. Even though the lattice approach worked well for the pricing of the GARCH options, it was inappropriate when the option price was computed on the lattice using standard backward recursive procedures, even if the concepts of Cakici and Topyan (2000) were incorporated. This paper shows how to correct the deficiency and that with our adjustment, the lattice method performs properly for option pricing under the GARCH process. Copyright Springer Science + Business Media, Inc. 2006

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  • Chun-Chou Wu, 2006. "The GARCH Option Pricing Model: A Modification of Lattice Approach," Review of Quantitative Finance and Accounting, Springer, vol. 26(1), pages 55-66, February.
    • Handle: RePEc:kap:rqfnac:v:26:y:2006:i:1:p:55-66
    DOI: 10.1007/s11156-006-7033-2
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    References listed on IDEAS

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    1. Jin-Chuan Duan & Evan Dudley & Geneviève Gauthier & Jean-Guy Simonato, 1999. "Pricing Discretely Monitored Barrier Options by a Markov Chain," CIRANO Working Papers 99s-15, CIRANO.
    2. Duan, Jin-Chuan & Simonato, Jean-Guy, 2001. "American option pricing under GARCH by a Markov chain approximation," Journal of Economic Dynamics and Control, Elsevier, vol. 25(11), pages 1689-1718, November.
    3. Peter Ritchken & Rob Trevor, 1999. "Pricing Options under Generalized GARCH and Stochastic Volatility Processes," Journal of Finance, American Finance Association, vol. 54(1), pages 377-402, February.
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    Cited by:

    1. Bingxin Li, 2020. "Option-implied filtering: evidence from the GARCH option pricing model," Review of Quantitative Finance and Accounting, Springer, vol. 54(3), pages 1037-1057, April.
    2. Shin-Yun Wang & Ming-Che Chuang & Shih-Kuei Lin & So-De Shyu, 2021. "Option pricing under stock market cycles with jump risks: evidence from the S&P 500 index," Review of Quantitative Finance and Accounting, Springer, vol. 56(1), pages 25-51, January.
    3. Xuemei Gao & Dongya Deng & Yue Shan, 2014. "Lattice Methods for Pricing American Strangles with Two-Dimensional Stochastic Volatility Models," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-6, April.
    4. In Kim & In-Seok Baek & Jaesun Noh & Sol Kim, 2007. "The role of stochastic volatility and return jumps: reproducing volatility and higher moments in the KOSPI 200 returns dynamics," Review of Quantitative Finance and Accounting, Springer, vol. 29(1), pages 69-110, July.
    5. Cheng Few Lee & Yibing Chen & John Lee, 2020. "Alternative Methods to Derive Option Pricing Models: Review and Comparison," World Scientific Book Chapters, in: Cheng Few Lee & John C Lee (ed.), HANDBOOK OF FINANCIAL ECONOMETRICS, MATHEMATICS, STATISTICS, AND MACHINE LEARNING, chapter 102, pages 3573-3617, World Scientific Publishing Co. Pte. Ltd..
    6. Konstantinos Skindilias & Chia Lo, 2015. "Local volatility calibration during turbulent periods," Review of Quantitative Finance and Accounting, Springer, vol. 44(3), pages 425-444, April.
    7. Ma, Jingtang & Li, Wenyuan & Han, Xu, 2015. "Stochastic lattice models for valuation of volatility options," Economic Modelling, Elsevier, vol. 47(C), pages 93-104.
    8. Ivivi J. Mwaniki, 2017. "On skewed, leptokurtic returns and pentanomial lattice option valuation via minimal entropy martingale measure," Cogent Economics & Finance, Taylor & Francis Journals, vol. 5(1), pages 1358894-135, January.

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