A nested stochastic model for evaluating required capital of guaranteed minimum surrender benefit (GMSB)

Interest rate-linked insurance contracts with an embedded Guaranteed Minimum Surrender Benefit (GMSB) option are exposed to market risks, such as interest rate fluctuations.To prevent significant losses caused by policyholders exercising their surrender options during economic downturns and low-interest-rate environments, insurance companies must hold available capital exceeding the required capital.To calculate this required capital for GMSB, which generally does not have a closed-form solution, a scenario-based approach can be used.This involves valuing the GMSB payout under different real-world outer scenarios.A nested stochastic model refers to a framework that values GMSB using inner scenarios embedded within outer scenarios.This study applies the nested stochastic modeling methodology to the calculation of required capital for GMSB guarantees, empirically analyzing the probability distribution of future GMSB values.Additionally, the study evaluates GMSB valuations under various conditions.The analysis reveals that GMSB values are negatively skewed and inversely correlated with interest rates.As the time horizon lengthens, both guarantee costs and required capital increase.Furthermore, as the policyholder's entry age increases, uncertainty rises, leading to a higher required capital ratio.