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A fast Monte Carlo scheme for additive processes and option pricing

Author

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  • Michele Azzone

    (Politecnico di Milano)

  • Roberto Baviera

    (Politecnico di Milano)

Abstract

In this paper, we present a very fast Monte Carlo scheme for additive processes: the computational time is of the same order of magnitude of standard algorithms for simulating Brownian motions. We analyze in detail numerical error sources and propose a technique that reduces the two major sources of error. We also compare our results with a benchmark method: the jump simulation with Gaussian approximation. We show an application to additive normal tempered stable processes, a class of additive processes that calibrates “exactly” the implied volatility surface. Numerical results are relevant. This fast algorithm is also an accurate tool for pricing path-dependent discretely-monitoring options with errors of one basis point or below.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:comgts:v:20:y:2023:i:1:d:10.1007_s10287-023-00463-1
    DOI: 10.1007/s10287-023-00463-1
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    References listed on IDEAS

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    2. Dilip B. Madan & King Wang, 2020. "Additive Processes with Bilateral Gamma Marginals," Applied Mathematical Finance, Taylor & Francis Journals, vol. 27(3), pages 171-188, May.
    3. Michele Azzone & Roberto Baviera, 2022. "Additive normal tempered stable processes for equity derivatives and power-law scaling," Quantitative Finance, Taylor & Francis Journals, vol. 22(3), pages 501-518, March.
    4. Peter Carr & Lorenzo Torricelli, 2021. "Additive logistic processes in option pricing," Finance and Stochastics, Springer, vol. 25(4), pages 689-724, October.
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    6. 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.
    7. Carolyn E. Phelan & Daniele Marazzina & Gianluca Fusai & Guido Germano, 2019. "Hilbert transform, spectral filters and option pricing," Annals of Operations Research, Springer, vol. 282(1), pages 273-298, November.
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    9. 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.
    10. Fabio Baschetti & Giacomo Bormetti & Silvia Romagnoli & Pietro Rossi, 2022. "The SINC way: a fast and accurate approach to Fourier pricing," Quantitative Finance, Taylor & Francis Journals, vol. 22(3), pages 427-446, March.
    11. Michele Azzone & Roberto Baviera, 2019. "Additive normal tempered stable processes for equity derivatives and power law scaling," Papers 1909.07139, arXiv.org, revised Jan 2022.
    12. Helyette Geman & C. Peter M. Dilip Y. Marc, 2007. "Self decomposability and option pricing," Post-Print halshs-00144193, HAL.
    13. Ernst Eberlein & Dilip Madan, 2009. "Sato processes and the valuation of structured products," Quantitative Finance, Taylor & Francis Journals, vol. 9(1), pages 27-42.
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    Cited by:

    1. Jimin Lin & Guixin Liu, 2024. "Neural Term Structure of Additive Process for Option Pricing," Papers 2408.01642, arXiv.org, revised Oct 2024.

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    More about this item

    Keywords

    Additive process; Simulation; Fast Fourier transform; Lewis formula;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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