Multi-factor approximation of rough volatility models

Rough volatility models are very appealing because of their fit of both historical and implied volatilities. However due to the non-Markovian and non-semimartingale nature of the volatility process, there is no obvious way to... [ view full abstract ]

Rough volatility models are very appealing because of their fit of both historical and implied volatilities. However due to the non-Markovian and non-semimartingale nature of the volatility process, there is no obvious 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 case of the rough Heston model. This enables us to derive a numerical method for solving fractional Riccati equations appearing in the characteristic function of the log-price.