High order approximations and simulation schemes for the log-Heston process

Aurélien Alfonsi () and Edoardo Lombardo ()
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Aurélien Alfonsi: CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - ENPC - École nationale des ponts et chaussées - IP Paris - Institut Polytechnique de Paris, MATHRISK - Mathematical Risk Handling - UPEM - Université Paris-Est Marne-la-Vallée - Centre Inria de Paris - Inria - Institut National de Recherche en Informatique et en Automatique - ENPC - École nationale des ponts et chaussées - IP Paris - Institut Polytechnique de Paris
Edoardo Lombardo: CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - ENPC - École nationale des ponts et chaussées - IP Paris - Institut Polytechnique de Paris, MATHRISK - Mathematical Risk Handling - UPEM - Université Paris-Est Marne-la-Vallée - Centre Inria de Paris - Inria - Institut National de Recherche en Informatique et en Automatique - ENPC - École nationale des ponts et chaussées - IP Paris - Institut Polytechnique de Paris, Università degli Studi di Roma Tor Vergata [Roma, Italia] = University of Rome Tor Vergata [Rome, Italy] = Université de Rome Tor Vergata [Rome, Italie]

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Abstract: We present weak approximations schemes of any order for the Heston model that are obtained by using the method developed by Alfonsi and Bally (2021). This method consists in combining approximation schemes calculated on different random grids to increase the order of convergence. We apply this method with either the Ninomiya-Victoir scheme (2008) or a second-order scheme that samples exactly the volatility component, and we show rigorously that we can achieve then any order of convergence. We give numerical illustrations on financial examples that validate the theoretical order of convergence. We also present promising numerical results for the multifactor/rough Heston model and hint at applications to other models, including the Bates model and the double Heston model.

Keywords: Rough Heston model.; Heston model; Random grids; Weak approximation schemes (search for similar items in EconPapers)
Date: 2024-07-24
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Published in SIAM Journal on Financial Mathematics, 2024, 16 (2), pp.516-544. ⟨10.1137/24M1679720⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-04826997

DOI: 10.1137/24M1679720

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