Markovian approximation of the rough Bergomi model for Monte Carlo option pricing

Qinwen Zhu (1) , Gregoire Loeper (2) , Wen Chen (3) , Nicolas Langrené (3)

1 NNU - Nanjing Normal University
2 Monash University [Melbourne]
3 CSIRO - Commonwealth Scientific and Industrial Research Organisation [Canberra]

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.

Mots clés: Volterra integral; volatility skew; Markovian representation; forward variance model; rough fractional stochastic volatility; rough Heston; hybrid scheme; sum of Ornstein-Uhlenbeck processes

Domaines: Probabilités [math.PR]; Finance quantitative [q-fin.CP]

Qinwen Zhu, Gregoire Loeper, Wen Chen, Nicolas Langrené. Markovian approximation of the rough Bergomi model for Monte Carlo option pricing. Mathematics , 2021, 9 (5), pp.528. ⟨10.3390/math9050528⟩. ⟨hal-02910724v2⟩