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A generalization of the rational rough Heston approximation

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  • Jim Gatheral
  • Radov{s} Radoiv{c}i'c

Abstract

Previously, in [GR19], we derived a rational approximation of the solution of the rough Heston fractional ODE in the special case \lambda = 0, which corresponds to a pure power-law kernel. In this paper we extend this solution to the general case of the Mittag-Leffler kernel with \lambda \geq 0. We provide numerical evidence of the convergence of the solution.

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  • Jim Gatheral & Radov{s} Radoiv{c}i'c, 2023. "A generalization of the rational rough Heston approximation," Papers 2310.09181, arXiv.org, revised Feb 2024.
    • Handle: RePEc:arx:papers:2310.09181
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    References listed on IDEAS

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    1. Jim Gatheral & Martin Keller-Ressel, 2019. "Affine forward variance models," Finance and Stochastics, Springer, vol. 23(3), pages 501-533, July.
    2. 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.
    3. Omar El Euch & Mathieu Rosenbaum, 2019. "The characteristic function of rough Heston models," Mathematical Finance, Wiley Blackwell, vol. 29(1), pages 3-38, January.
    4. Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv, December.
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