Multi-factor approximation of rough volatility models

Eduardo Abi Jaber () and Omar El Euch ()
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Eduardo Abi Jaber: CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique
Omar El Euch: X - École polytechnique - IP Paris - Institut Polytechnique de Paris

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Abstract: Rough volatility models are very appealing because of their remarkable fit of both historical and implied volatilities. However, due to the non-Markovian and non-semimartingale nature of the volatility process, there is no simple way to simulate efficiently such models, which makes risk management of derivatives an intricate task. In this paper, we design tractable multi-factor stochastic volatility models approximating rough volatility models and enjoying a Markovian structure. Furthermore, we apply our procedure to the specific case of the rough Heston model. This in turn enables us to derive a numerical method for solving fractional Riccati equations appearing in the characteristic function of the log-price in this setting.

Keywords: fractional Riccati equations; limit theorems; affine Volterra processes; Rough volatility models; rough Heston models; stochastic Volterra equations (search for similar items in EconPapers)
Date: 2019-05-01
New Economics Papers: this item is included in nep-ets and nep-rmg
Note: View the original document on HAL open archive server: https://hal.science/hal-01697117v3
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Citations: View citations in EconPapers (57)

Published in SIAM Journal on Financial Mathematics, 2019

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01697117

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