Weighted Monte Carlo with Least Squares and Randomized Extended Kaczmarz for Option Pricing

Damir Filipović, Kathrin Glau, Yuji Nakatsukasa and Francesco Statti
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Damir Filipović: Ecole Polytechnique Fédérale de Lausanne; Swiss Finance Institute
Kathrin Glau: Queen Mary University of London
Yuji Nakatsukasa: University of Oxford
Francesco Statti: Ecole Polytechnique Fédérale de Lausanne

No 19-54, Swiss Finance Institute Research Paper Series from Swiss Finance Institute

Abstract: We propose a methodology for computing single and multi-asset European option prices, and more generally expectations of scalar functions of (multivariate) random variables. This new approach combines the ability of Monte Carlo simulation to handle high-dimensional problems with the efficiency of function approximation. Specifically, we first generalize the recently developed method for multivariate integration in [arXiv:1806.05492] to integration with respect to probability measures. The method is based on the principle “approximate and integrate” in three steps i) sample the integrand at points in the integration domain, ii) approximate the integrand by solving a least-squares problem, iii) integrate the approximate function. In high-dimensional applications we face memory limitations due to large storage requirements in step ii). Combining weighted sampling and the randomized extended Kaczmarz algorithm we obtain a new efficient approach to solve large-scale least-squares problems. Our convergence and cost analysis along with numerical experiments show the effectiveness of the method in both low and high dimensions, and under the assumption of a limited number of available simulations.

Keywords: sMonte Carlo; Monte Carlo under budget constraints; variance reduction; multi-asset options; Kaczmarz algorithm; weighted sampling; large-scale least-squares problems (search for similar items in EconPapers)
Pages: 31 pages
Date: 2019-10
New Economics Papers: this item is included in nep-cmp and nep-ore
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:chf:rpseri:rp1954

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