Abstract
The recently developed rough Bergomi (rBergomi) model is a rough fractional stochastic volatility (RFSV) model which can generate more realistic term structure of at-the-money volatility skews compared with other RFSV models. However, its non-Markovianity brings mathematical and computational challenges for model calibration and simulation. To overcome these difficulties, we show that the rBergomi model can be approximated by the Bergomi model, which has the Markovian property. Our main theoretical result is to establish and describe the affine structure of the rBergomi model. We demonstrate the efficiency and accuracy of our method by implementing a Markovian approximation algorithm based on a hybrid scheme.
Highlights
The rough Bergomi model introduced by Bayer et al (2016) has gained acceptance for stochastic volatility modelling due to its power-law at-the-money volatility skew which is consistent with empirical studies and the market impact function under the noarbitrage assumption
In particular we provide for the first time a proof that the ATM volatility skew of the rBergomi model is equivalent to the power
In order to implement the hybrid scheme to the rBergomi model, we need to introduce a particular class of nonstationary processes, namely truncated Brownian semi-stationary processes, t
Summary
The rough Bergomi (rBergomi) model introduced by Bayer et al (2016) has gained acceptance for stochastic volatility modelling due to its power-law at-the-money volatility skew which is consistent with empirical studies (see Forde and Zhang 2017, Fukasawa 2017, Gatheral et al 2018) and the market impact function under the noarbitrage assumption (see Jusselin and Rosenbaum 2018). The Volterra kernel corresponds to a superposition of infinitely many Ornstein-Uhlenbeck (O-U) processes with different speeds of mean reversion. Truncating this infinite sum into a finite sum of O-U processes yields an approximation of the rBergomi model which is a Markovian approximated.
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