Hierarchical adaptive sparse grids and quasi-Monte Carlo for option pricing under the rough Bergomi model
KAUST Grant NumberURF/1/2584-01-01
Permanent link to this recordhttp://hdl.handle.net/10754/662401
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AbstractThe rough Bergomi (rBergomi) model, introduced recently in (Bayer, Friz, Gatheral, 2016), is a promising rough volatility model in quantitative finance. It is a parsimonious model depending on only three parameters, and yet remarkably fits with 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, when reaching 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.
SponsorsThis 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. 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.
Conference/Event nameSeminar talk at RWTH Aachen University
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