A Unified Longevity–Financial Risk Framework for Evaluating Pension Funding Ratios

Defined-benefit pension funds face simultaneous exposure to longevity risk and financial market volatility, yet most regulatory frameworks assess these risks in isolation using deterministic methods. This paper examines how their joint occurrence affects fund solvency measured by the funding ratio. We develop an integrated stochastic framework combining a generalized Lee–Carter model with cohort effects for mortality, a two-state Markov regime-switching process for asset returns, and a Cox–Ingersoll–Ross model for stochastic interest rates; liabilities are valued under the risk-neutral measure. The model is calibrated to Italian ISTAT/HMD mortality data and institutional benchmarks over 2000–2023; solvency risk is quantified via value-at-risk and conditional value-at-risk of the funding ratio at one-, five-, and ten-year horizons ($M=50,000$ Monte Carlo scenarios). Financial risk dominates at the one-year horizon (${\mathrm{CVaR}}_{0.99}=59.1$ percentage points), while longevity risk grows from $4\%$ of the total tail risk at one year to $21\%$ at ten years. The stochastic ${\mathrm{VaR}}_{0.99}$ exceeds deterministic reserves by a factor of $4.8\times$, and the standard modular aggregation formula overestimates combined risk by up to five percentage points due to its Gaussian copula assumption. These results demonstrate that integrated stochastic modeling is essential for sound regulatory capital assessment under the IORP II framework.