An aspect of optimal regression design for LSMC

Weiß Christian () and Nikolić Zoran ()
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Weiß Christian: Institut Naturwissenschaften, Hochschule Ruhr West, Duisburger Str. 100, 45479Mülheim an der Ruhr, Germany
Nikolić Zoran: Mathematical Institute, University Cologne, Weyertal 86-90, 50931Cologne, Germany

Monte Carlo Methods and Applications, 2019, vol. 25, issue 4, 283-290

Abstract: Practitioners sometimes suggest to use a combination of Sobol sequences and orthonormal polynomials when applying an LSMC algorithm for evaluation of option prices or in the context of risk capital calculation under the Solvency II regime. In this paper, we give a theoretical justification why good implementations of an LSMC algorithm should indeed combine these two features in order to assure numerical stability. Moreover, an explicit bound for the number of outer scenarios necessary to guarantee a prescribed degree of numerical stability is derived. We embed our observations into a coherent presentation of the theoretical background of LSMC in the insurance setting.

Keywords: Least squares Monte Carlo; numerical stability; Sobol sequences; low-discrepancy sequences; orthonormal polynomials (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1515/mcma-2019-2049

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