Market-Informed Valuation of GMMB Riders with Surrender Options under a Heston Stochastic-Local Volatility Model

2026-08-28

AI Summary

本文使用Heston随机局部波动模型，通过结合市场信息来评估具有提前退保选项的保证最低到期收益（GMMB）附加条款的价值。

Abstract

We develop a market-informed valuation framework for guaranteed minimum maturity benefit (GMMB) riders with rational surrender under the Heston stochastic-local volatility (SLV) model. The guarantee is written on the fee-deducted account value and is considered both in its terminal-only form and in the presence of early surrender rights. The Heston SLV specification combines stochastic volatility with a leverage function calibrated to a prescribed local-volatility surface. The leverage surface is obtained through a forward Markovian-projection equation so that, at the model level, the SLV dynamics are constrained to the same one-dimensional marginals as the corresponding local-volatility (LV) model. The latter is used only as a one-factor benchmark, allowing us to isolate the effect of stochastic volatility on continuation values and surrender decisions while preserving the same option-calibrated local-volatility target. We derive the associated backward pricing equations and propose a hybrid tree/finite-difference algorithm for the SLV model with a calibrated leverage function. Synthetic experiments and a market-informed case study show that SLV and LV valuations are numerically close for terminal-only guarantees, as expected from the common marginal target, whereas materially larger differences can arise once surrender is allowed. These differences are reflected in guarantee values, fair insurance fees and volatility-dependent surrender regions. The results indicate that matching one-date marginals implied by vanilla-option prices does not eliminate model risk for insurance liabilities whose value depends on conditional continuation dynamics and endogenous surrender decisions.

Problem

• Guaranteed Minimum Maturity Benefit (GMMB)
• Surrender Options
• Heston Stochastic-Local Volatility Model
• Market-Informed Valuation

Innovation

• Heston SLV model
• guaranteed minimum maturity benefit (GMMB)
• surrender options
• leverage function
• hybrid tree/finite-difference algorithm