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

Author

Listed:
  • Qinwen Zhu

    (School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China)

  • Grégoire Loeper

    (School of Mathematics & Centre for Quantitative Finance and Investment Strategies, Monash University, Clayton, VIC 3800, Australia)

  • Wen Chen

    (Data61, Commonwealth Scientific and Industrial Research Organisation, Melbourne, VIC 3008, Australia)

  • Nicolas Langrené

    (Data61, Commonwealth Scientific and Industrial Research Organisation, Melbourne, VIC 3008, Australia)

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.

Suggested Citation

  • Qinwen Zhu & Grégoire Loeper & Wen Chen & Nicolas Langrené, 2021. "Markovian Approximation of the Rough Bergomi Model for Monte Carlo Option Pricing," Mathematics, MDPI, vol. 9(5), pages 1-21, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:5:p:528-:d:509580
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    References listed on IDEAS

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    Cited by:

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    3. Eduardo Abi Jaber & Camille Illand & Shaun Xiaoyuan Li, 2022. "Joint SPX-VIX calibration with Gaussian polynomial volatility models: deep pricing with quantization hints," Working Papers hal-03902513, HAL.
    4. Eduardo Abi Jaber & Camille Illand & Shaun & Li, 2022. "Joint SPX-VIX calibration with Gaussian polynomial volatility models: deep pricing with quantization hints," Papers 2212.08297, arXiv.org.

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