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Eur Actuar J. 2016;6(2):441-494. doi: 10.1007/s13385-016-0133-z. Epub 2016 Nov 4.

The difference between LSMC and replicating portfolio in insurance liability modeling.

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Departments of Quantitative Economics and Finance, Maastricht University, Netspar, Kleynen Consultants, P.O. Box 616, 6200 MD Maastricht, The Netherlands.
Department of Quantitative Economics, Maastricht University, Netspar, P.O. Box 616, 6200 MD Maastricht, The Netherlands.


Solvency II requires insurers to calculate the 1-year value at risk of their balance sheet. This involves the valuation of the balance sheet in 1 year's time. As for insurance liabilities, closed-form solutions to their value are generally not available, insurers turn to estimation procedures. While pure Monte Carlo simulation set-ups are theoretically sound, they are often infeasible in practice. Therefore, approximation methods are exploited. Among these, least squares Monte Carlo (LSMC) and portfolio replication are prominent and widely applied in practice. In this paper, we show that, while both are variants of regression-based Monte Carlo methods, they differ in one significant aspect. While the replicating portfolio approach only contains an approximation error, which converges to zero in the limit, in LSMC a projection error is additionally present, which cannot be eliminated. It is revealed that the replicating portfolio technique enjoys numerous advantages and is therefore an attractive model choice.


Least squares Monte Carlo; Least squares regression; Portfolio replication

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