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An aspect of optimal regression design for LSMC

Author

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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)

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.

Suggested Citation

  • Weiß Christian & Nikolić Zoran, 2019. "An aspect of optimal regression design for LSMC," Monte Carlo Methods and Applications, De Gruyter, vol. 25(4), pages 283-290, December.
    • Handle: RePEc:bpj:mcmeap:v:25:y:2019:i:4:p:283-290:n:2
    DOI: 10.1515/mcma-2019-2049
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    References listed on IDEAS

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    1. Carriere, Jacques F., 1996. "Valuation of the early-exercise price for options using simulations and nonparametric regression," Insurance: Mathematics and Economics, Elsevier, vol. 19(1), pages 19-30, December.
    2. Giuseppe Benedetti, 2017. "On The Calculation Of Risk Measures Using Least-Squares Monte Carlo," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(03), pages 1-14, May.
    3. Anne-Sophie Krah & Zoran Nikolić & Ralf Korn, 2018. "A Least-Squares Monte Carlo Framework in Proxy Modeling of Life Insurance Companies," Risks, MDPI, vol. 6(2), pages 1-26, June.
    4. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
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    Cited by:

    1. Anne-Sophie Krah & Zoran Nikolić & Ralf Korn, 2020. "Machine Learning in Least-Squares Monte Carlo Proxy Modeling of Life Insurance Companies," Risks, MDPI, vol. 8(1), pages 1-79, February.

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