The difference between LSMC and replicating portfolio in insurance liability modeling

Area of Science:

• Quantitative Finance
• Insurance Risk Management

Background:

• Solvency II mandates the calculation of 1-year value at risk for insurer balance sheets.
• Valuing insurance liabilities often requires estimation due to the lack of closed-form solutions.
• Pure Monte Carlo simulations are often impractical for these valuations.

Purpose of the Study:

• To compare the accuracy and feasibility of approximation methods for Solvency II valuations.
• To analyze the error structures of least squares Monte Carlo (LSMC) and portfolio replication methods.
• To determine the advantages of portfolio replication over LSMC for insurance risk management.

Main Methods:

• Comparative analysis of regression-based Monte Carlo methods.
• Examination of approximation errors in LSMC and portfolio replication.
• Theoretical assessment of error convergence and elimination.

Main Results:

• LSMC introduces a non-eliminable projection error alongside approximation error.
• Portfolio replication methods only contain approximation error, which converges to zero.
• The portfolio replication technique demonstrates significant advantages over LSMC.

Conclusions:

• The portfolio replication method is a more robust and accurate approach for Solvency II balance sheet valuations.
• Insurers should favor the portfolio replication technique for its superior error characteristics.
• This finding offers practical guidance for regulatory compliance and risk assessment in the insurance industry.