Markovian Approximation of the Rough Bergomi Model for Monte Carlo Option Pricing

Abstract

The recently developed rough Bergomi (rBergomi) model is a rough fractional stochastic volatility (RFSV) model which can generate a 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 well-approximated by the forward-variance Bergomi model with wisely chosen weights and mean-reversion speed parameters (aBergomi), which has the Markovian property. We establish an explicit bound on the L2-error between the respective kernels of these two models, which is explicitly controlled by the number of terms in the aBergomi model. We establish and describe the affine structure of the rBergomi model, and show the convergence of the affine structure of the aBergomi model to the one of the rBergomi model. We demonstrate the efficiency and accuracy of our method by implementing a classical Markovian Monte Carlo simulation scheme for the aBergomi model, which we compare to the hybrid scheme of the rBergomi model.

Keywords

• rough fractional stochastic volatility
• forward variance model
• markovian representation
• volatility skew
• Volterra integral
• rough heston