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    Hierarchical adaptive sparse grids and quasi-Monte Carlo for option pricing under the rough Bergomi model

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    Type
    Article
    Authors
    Bayer, Christian
    Ben Hammouda, Chiheb cc
    Tempone, Raul cc
    KAUST Department
    Applied Mathematics & Computational Sci
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Stochastic Numerics Research Group
    KAUST Grant Number
    URF/1/2584-01-01
    Date
    2020-04-20
    Online Publication Date
    2020-04-20
    Print Publication Date
    2020-09-01
    Permanent link to this record
    http://hdl.handle.net/10754/630796
    
    Metadata
    Show full item record
    Abstract
    The 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.
    Citation
    Bayer, 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
    Sponsors
    C. 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.
    Publisher
    Informa UK Limited
    Journal
    Quantitative Finance
    DOI
    10.1080/14697688.2020.1744700
    arXiv
    1812.08533
    Additional Links
    https://www.tandfonline.com/doi/full/10.1080/14697688.2020.1744700
    http://arxiv.org/pdf/1812.08533
    ae974a485f413a2113503eed53cd6c53
    10.1080/14697688.2020.1744700
    Scopus Count
    Collections
    Preprints; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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