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Monte Carlo Simulation of the CGMY Process and Option Pricing

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  • Laura Ballotta
  • Ioannis Kyriakou

Abstract

We present a joint Monte Carlo‐Fourier transform sampling scheme for pricing derivative products under a Carr–Geman–Madan–Yor (CGMY) model (Carr et al. [Journal of Business, 75, 305–332, 2002]) exhibiting jumps of infinite activity and finite or infinite variation. The approach relies on numerical transform inversion with computable error estimates, which allow generating the unknown cumulative distribution function of the CGMY process increments at the desired accuracy level. We use this to generate samples and simulate the entire trajectory of the process without need of truncating the process small jumps. We illustrate the computational efficiency of the proposed method by comparing it to the existing methods in the literature on pricing a wide range of option contracts, including path‐dependent univariate and multivariate products. © 2014 Wiley Periodicals, Inc. Jrl Fut Mark 34:1095–1121, 2014

Suggested Citation

  • Laura Ballotta & Ioannis Kyriakou, 2014. "Monte Carlo Simulation of the CGMY Process and Option Pricing," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 34(12), pages 1095-1121, December.
    • Handle: RePEc:wly:jfutmk:v:34:y:2014:i:12:p:1095-1121
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    Cited by:

    1. Ting He, 2020. "Nonparametric Predictive Inference for Asian options," Papers 2008.13082, arXiv.org.
    2. Ballotta, Laura & Rayée, Grégory, 2022. "Smiles & smirks: Volatility and leverage by jumps," European Journal of Operational Research, Elsevier, vol. 298(3), pages 1145-1161.
    3. Gianluca Fusai & Ioannis Kyriakou, 2016. "General Optimized Lower and Upper Bounds for Discrete and Continuous Arithmetic Asian Options," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 531-559, May.
    4. He, Ting, 2023. "An imprecise pricing model for Asian options based on Nonparametric predictive inference," Pacific-Basin Finance Journal, Elsevier, vol. 77(C).
    5. Michele Azzone & Roberto Baviera, 2023. "A fast Monte Carlo scheme for additive processes and option pricing," Computational Management Science, Springer, vol. 20(1), pages 1-34, December.
    6. Chengwei Zhang & Zhiyuan Zhang, 2017. "Sequential Sampling for CGMY Processes via Decomposition of their Time Changes," Papers 1708.00189, arXiv.org, revised Aug 2018.
    7. Søren Asmussen, 2022. "On the role of skewness and kurtosis in tempered stable (CGMY) Lévy models in finance," Finance and Stochastics, Springer, vol. 26(3), pages 383-416, July.
    8. Michele Bianchi & Frank Fabozzi, 2014. "Discussion of ‘on simulation and properties of the stable law’ by Devroye and James," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(3), pages 353-357, August.
    9. Svetlana Boyarchenko & Sergei Levendorskiĭ, 2019. "Sinh-Acceleration: Efficient Evaluation Of Probability Distributions, Option Pricing, And Monte Carlo Simulations," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(03), pages 1-49, May.
    10. Piergiacomo Sabino, 2021. "Pricing Energy Derivatives in Markets Driven by Tempered Stable and CGMY Processes of Ornstein-Uhlenbeck Type," Papers 2103.13252, arXiv.org.
    11. Michele Azzone & Roberto Baviera, 2021. "A fast Monte Carlo scheme for additive processes and option pricing," Papers 2112.08291, arXiv.org, revised Jul 2023.
    12. Xu Guo & Yutian Li, 2016. "Valuation of American options under the CGMY model," Quantitative Finance, Taylor & Francis Journals, vol. 16(10), pages 1529-1539, October.
    13. Svetlana Boyarchenko & Sergei Levendorskii, 2023. "Simulation of a L\'evy process, its extremum, and hitting time of the extremum via characteristic functions," Papers 2312.03929, arXiv.org.
    14. Chengwei Zhang & Zhiyuan Zhang, 2018. "Sequential sampling for CGMY processes via decomposition of their time changes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(6-7), pages 522-534, September.
    15. Winston Buckley & Sandun Perera, 2019. "Optimal demand in a mispriced asymmetric Carr–Geman–Madan–Yor (CGMY) economy," Annals of Finance, Springer, vol. 15(3), pages 337-368, September.
    16. Wang, Chuan-Ju & Kao, Ming-Yang, 2016. "Optimal search for parameters in Monte Carlo simulation for derivative pricing," European Journal of Operational Research, Elsevier, vol. 249(2), pages 683-690.
    17. Chiu, Chun-Yuan & Dai, Tian-Shyr & Lyuu, Yuh-Dauh, 2015. "Pricing Asian option by the FFT with higher-order error convergence rate under Lévy processes," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 418-437.

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