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Pricing of spread and exchange options in a rough jump-diffusion market

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  • Hainaut, Donatien

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

Abstract

This article studies the pricing of spread and exchange options in a market made up of two risky assets driven by a rough Heston model with jumps. Firstly, we rewrite this non-Markov model as an infinite dimensional Markov process. We next consider a finite dimensional approximation and show that the characteristic function of log-returns admits a representation in terms of forward differential equations. By passing to the limit, we infer that the characteristic function of the rough jump Heston model depends on a hybrid system of ordinary and fractional differential equations. Bivariate options are next priced with a one or two dimensional discrete Fourier Transform. We conclude by a numerical illustration analyzing the impact of roughness on exchange and spread options.

Suggested Citation

  • Hainaut, Donatien, 2022. "Pricing of spread and exchange options in a rough jump-diffusion market," LIDAM Discussion Papers ISBA 2022012, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvad:2022012
    DOI: https://
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    References listed on IDEAS

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    1. Dupret, Jean-Loup & Hainaut, Donatien, 2021. "Portfolio insurance under rough volatility and Volterra processes," LIDAM Discussion Papers ISBA 2021026, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Hainaut, Donatien, 2021. "Moment generating function of non-Markov self-excited claims processes," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 406-424.
    3. Mesias Alfeus & Erik Schlögl, 2019. "On Spread Option Pricing Using Two-Dimensional Fourier Transform," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(05), pages 1-20, August.
    4. Omar El Euch & Mathieu Rosenbaum, 2019. "The characteristic function of rough Heston models," Mathematical Finance, Wiley Blackwell, vol. 29(1), pages 3-38, January.
    5. Petter Bjerksund & Gunnar Stensland, 2014. "Closed form spread option valuation," Quantitative Finance, Taylor & Francis Journals, vol. 14(10), pages 1785-1794, October.
    6. Christian Bayer & Peter Friz & Jim Gatheral, 2016. "Pricing under rough volatility," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 887-904, June.
    7. Dupret, Jean-Loup & Hainaut, Donatien, 2021. "Portfolio insurance under rough volatility and Volterra processes," LIDAM Reprints ISBA 2021051, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Caldana, Ruggero & Fusai, Gianluca, 2013. "A general closed-form spread option pricing formula," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 4893-4906.
    9. Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, vol. 33(1), pages 177-186, March.
    10. Jim Gatheral & Thibault Jaisson & Mathieu Rosenbaum, 2018. "Volatility is rough," Quantitative Finance, Taylor & Francis Journals, vol. 18(6), pages 933-949, June.
    11. Hainaut, Donatien, 2021. "Moment generating function of non-Markov self-excited claims processes," LIDAM Discussion Papers ISBA 2021028, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    12. Eduardo Abi Jaber & Omar El Euch, 2019. "Multi-factor approximation of rough volatility models," Post-Print hal-01697117, HAL.
    13. Hainaut, Donatien, 2021. "Moment generating function of non-Markov self-excited claims processes," LIDAM Reprints ISBA 2021046, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    14. Li, Minqiang, 2008. "Closed-Form Approximations for Spread Option Prices and Greeks," MPRA Paper 6994, University Library of Munich, Germany.
    15. Dupret, Jean-Loup & Barbarin, Jérôme & Hainaut, Donatien, 2021. "Impact of rough stochastic volatility models on long-term life insurance pricing," LIDAM Discussion Papers ISBA 2021017, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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