A Natural Hedging Framework for Longevity Risk with Graphical Risk Assessment

Battle Count: 59

The paper is primarily focused on actuarial risk management and life insurance longevity hedging rather than quantitative trading. However, it has tangential relevance to quantitative finance through its use of stochastic mortality models, Monte Carlo simulation, VaR/CVaR risk measures, and portfolio optimization techniques. The graphical risk metric concept could potentially inspire visualization tools for trading risk assessment. The framework is more relevant to insurance risk management and actuarial science than to algorithmic trading or market-making strategies.

The framework requires: (1) Stochastic mortality model fitting (Lee-Carter, CBD) using R packages like StMoMo, (2) Monte Carlo simulation of survival probabilities, (3) Valuation of annuity and insurance portfolios with multiple products and weights, (4) Calibration of hedge ratios using closed-form solutions or numerical optimization, (5) Construction of joint prediction regions using Mahalanobis distances and convex hulls, (6) Multiple confidence levels for graphical visualization. The mathematical formulations are well-defined but implementation requires careful handling of mortality projections, portfolio weighting, and graphical construction. The three-step structure is modular, but full implementation across multiple models and calibration methods adds complexity.

The paper provides detailed mathematical formulations, algorithmic procedures for constructing the graphical metric, and specifies the use of R packages (StMoMo, HMDHFDplus). Mortality data is from the publicly available Human Mortality Database. However, replication code is only available upon reasonable request from the corresponding author, and no GitHub repository is provided. The three numerical illustrations are well-specified with portfolio details in Appendix C.