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Multi-factor approximation of rough volatility models

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AJEE_20180407_Final.pdf (637.0Kb)
Date
2019
Dewey
Probabilités et mathématiques appliquées
Sujet
limit theorems; affine Volterra processes; Rough volatility models; rough Heston models; stochastic Volterra equations; fractional Riccati equations
Journal issue
SIAM Journal on Financial Mathematics
Volume
10
Number
2
Publication date
2019
Article pages
309–349
Publisher
SIAM - Society for Industrial and Applied Mathematics
URI
https://basepub.dauphine.fr/handle/123456789/17921
Collections
  • CEREMADE : Publications
Metadata
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Author
Abi jaber, Eduardo
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
El Euch, Omar
141112 École Polytechnique
Type
Article accepté pour publication ou publié
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.

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