Hierarchical adaptive sparse grids and quasi-Monte Carlo for option pricing under the rough Bergomi model
KAUST DepartmentApplied Mathematics & Computational Sci
Applied Mathematics and Computational Science Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Stochastic Numerics Research Group
KAUST Grant NumberURF/1/2584-01-01
Online Publication Date2020-04-20
Print Publication Date2020-09-01
Permanent link to this recordhttp://hdl.handle.net/10754/630796
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AbstractThe rough Bergomi (rBergomi) model, introduced recently in Bayer et al. [Pricing under rough volatility. Quant. Finance, 2016, 16(6), 887–904], is a promising rough volatility model in quantitative finance. It is a parsimonious model depending on only three parameters, and yet remarkably fits empirical implied volatility surfaces. In the absence of analytical European option pricing methods for the model, and due to the non-Markovian nature of the fractional driver, the prevalent option is to use the Monte Carlo (MC) simulation for pricing. Despite recent advances in the MC method in this context, pricing under the rBergomi model is still a time-consuming task. To overcome this issue, we have designed a novel, hierarchical approach, based on: (i) adaptive sparse grids quadrature (ASGQ), and (ii) quasi-Monte Carlo (QMC). Both techniques are coupled with a Brownian bridge construction and a Richardson extrapolation on the weak error. By uncovering the available regularity, our hierarchical methods demonstrate substantial computational gains with respect to the standard MC method. They reach a sufficiently small relative error tolerance in the price estimates across different parameter constellations, even for very small values of the Hurst parameter. Our work opens a new research direction in this field, i.e. to investigate the performance of methods other than Monte Carlo for pricing and calibrating under the rBergomi model.
CitationBayer, C., Ben Hammouda, C., & Tempone, R. (2020). Hierarchical adaptive sparse grids and quasi-Monte Carlo for option pricing under the rough Bergomi model. Quantitative Finance, 1–17. doi:10.1080/14697688.2020.1744700
SponsorsC. Bayer gratefully acknowledges support from the German Research Foundation (DFG), via the Cluster of Excellence MATH+ (project AA4-2) and the individual grant BA5484/1. This work was supported by the KAUST Office of Sponsored Research (OSR) under Award No. URF/1/2584-01-01 and the Alexander von Humboldt Foundation. C. Ben Hammouda and R. Tempone are members of the KAUST SRI Center for Uncertainty Quantification in Computational Science and Engineering. The authors would like to thank Joakim Beck, Eric Joseph Hall and Erik von Schwerin for their helpful and constructive comments. The authors are also very grateful to the anonymous referees for their valuable comments and suggestions that greatly contributed to shape the final version of the paper.
PublisherInforma UK Limited