Multi-factor approximation of rough volatility models
Abi jaber, Eduardo; El Euch, Omar (2019), Multi-factor approximation of rough volatility models, SIAM Journal on Financial Mathematics, 10, 2, p. 309–349
TypeArticle accepté pour publication ou publié
Journal nameSIAM Journal on Financial Mathematics
SIAM - Society for Industrial and Applied Mathematics
MetadataShow full item record
Author(s)Abi jaber, Eduardo
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
El Euch, Omar
Abstract (EN)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.
Subjects / Keywordslimit theorems; affine Volterra processes; Rough volatility models; rough Heston models; stochastic Volterra equations; fractional Riccati equations
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