The Difference between LSMC and Replicating Portfolio in Insurance Liability Modeling

Solvency II requires insurers to calculate the one-year Value at Risk (VaR) of their balance sheet. This involves the valuation of the balance sheet in one years 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 additionally a projection error is present, which cannot be eliminated. It is revealed that the replicating portfolio technique enjoys numerous advantages and is therefore an attractive model choice