Insurance Portfolio Valuation under Market Jumps: A Framework Combining Kou Jump-Diffusion Forecasting and Dynamic CPPI Hedging

Abstract

This study develops an integrated valuation framework for insurance portfolios under discontinuous market conditions. The framework combines asset-price forecasting based on the Kou jump-diffusion model with Dynamic Constant Proportion Portfolio Insurance (D-CPPI) to support portfolio protection and capital guarantee management. The Kou jump-diffusion model is employed to capture asymmetric jumps and extreme market movements, while D-CPPI dynamically allocates wealth between risky and risk-free assets. To address gap risk, a volatility-adjusted risk multiplier with a non-negativity constraint is incorporated into the portfolio insurance mechanism. The proposed framework is evaluated using S&P 500 index data from 2006–2010 at daily, weekly, and monthly observation frequencies. The forecasting results demonstrate satisfactory predictive performance, with Mean Absolute Percentage Error (MAPE) values of 4.76%, 5.04%, and 5.36% for the daily, weekly, and monthly models, respectively. Portfolio simulations indicate that arbitrarily selected multipliers can lead to substantial losses and floor violations, whereas the constrained volatility-adjusted multiplier maintains portfolio values above the guaranteed floor across all observation frequencies and effectively mitigates gap risk. These findings suggest that integrating Kou jump-diffusion forecasting with D-CPPI provides an effective approach for insurance portfolio valuation under volatile market conditions. The proposed framework contributes to the literature by jointly addressing asset-price jumps, dynamic portfolio allocation, and gap-risk mitigation within a unified insurance portfolio management framework.