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dc.contributor.authorBayer, Christian
dc.contributor.authorBen Hammouda, Chiheb
dc.contributor.authorTempone, Raul
dc.description.abstractWhen approximating the expectation of a functional of a certain stochastic process, the robustness and performance of multilevel Monte Carlo (MLMC) method, may be highly deteriorated by the low regularity of the integrand with respect to the input parameters. To overcome this issue, a smoothing procedure is needed to uncover the available regularity and improve the performance of the MLMC estimator. In this work, we consider cases where we cannot perform an analytic smoothing. Thus, we introduce a novel numerical smoothing technique based on root-finding combined with a one dimensional integration with respect to a single well-chosen variable. Our study is motivated by option pricing problems and our main focus is on dynamics where a discretization of the asset price is needed. Through our analysis and numerical experiments, we demonstrate how numerical smoothing significantly reduces the kurtosis at the deep levels of MLMC, and also improves the strong convergence rate, when using Euler scheme. Due to the complexity theorem of MLMC, and given a pre-selected tolerance, $\text{TOL}$, this results in an improvement of the complexity from $\mathcal{O}\left(\text{TOL}^{-2.5}\right)$ in the standard case to $\mathcal{O}\left(\text{TOL}^{-2} \log(\text{TOL})^2\right)$. Moreover, we show how our numerical smoothing combined with MLMC enables us also to estimate density functions, which standard MLMC (without smoothing) fails to achieve.
dc.description.sponsorshipThis 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. T
dc.rightsCC0 1.0 Universal
dc.titleNumerical Smoothing with Multilevel Monte Carlo for Efficient Option Pricing and Density Estimation
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division Applied Mathematics and Computational Science Program
dc.conference.nameConference: 14th International Conference in Monte Carlo & Quasi-Monte Carlo Methods in Scientific Computing (MCQMC 2020)
dc.conference.locationUniversity of Oxford
dc.contributor.institutionChair of Mathematics for Uncertainty Quantification, RWTH Aachen University, Aachen 52072, Germany
dc.contributor.institutionWeierstrass Institute for Applied Analysis and Stochastics (WIAS), Berlin, Germany.

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