Replicating Portfolio vs LSMC for ALM

Details

Supervisors

Hainaut, Donatien

Faculty

Faculté des sciences

Degree label

Master [120] en sciences actuarielles, à finalité spécialisée

Abstract

enThis thesis studies the valuation of participating life insurance liabilities in a stochastic Asset--Liability Management framework. The financial market is modeled using a hybrid Equity-Hull-White model with stochastic interest rates and equity dynamics, while mortality risk is represented using the Makeham mortality law. The analysis considers two insurance products: a participating endowment contract and a participating temporary life annuity. Three investment strategies are investigated for the benchmark portfolio: Fixed Maturity Bucket (FMB), Constant Duration Bucket (CDB), and Partial Cash-Flow Matching (PCFM). Best estimate liabilities are computed using nested Monte Carlo simulation, Least Squares Monte Carlo (LSMC), and replicating portfolio techniques. Numerical results show that replicating portfolios provide highly accurate approximations of Monte Carlo valuations with limited replication errors. The study also highlights the impact of investment strategies and equity allocation on liability valuation and risk measures such as the Value-at-Risk. The results indicate that Partial Cash-Flow Matching generally produces lower liability risk and improved replication quality, while participating endowment contracts exhibit higher sensitivity to financial market risk than temporary life annuities.