基于Heston随机局部波动率模型的带退保期权的GMMB riders的市场知情估值
Market-Informed Valuation of GMMB Riders with Surrender Options under a Heston Stochastic-Local Volatility Model
中文总结 AI 辅助
本研究针对Heston随机局部波动率模型下带退保期权的GMMB riders，构建市场知情估值框架，提出混合树/有限差分算法，发现允许退保时SLV与LV估值差异显著，匹配单日边际分布无法消除相关保险负债的模型风险。
中文摘要 AI 辅助
我们针对Heston随机局部波动率（SLV）模型下带理性退保的最低到期收益保证（GMMB） riders，构建了一种市场知情估值框架。该保证以扣除费用后的账户价值为标的，分别考虑仅期末形式和含提前退保权利的情形。Heston SLV设定将随机波动率与校准至规定局部波动率曲面的杠杆函数相结合，该杠杆曲面通过前向马尔可夫投影方程得到，使得在模型层面，SLV动力学受限于与对应局部波动率（LV）模型相同的一维边际分布。后者仅作为单因子基准，使我们能够在保留相同期权校准局部波动率目标的同时，分离随机波动率对延续价值和退保决策的影响。我们推导了相关的后向定价方程，并针对带校准杠杆函数的SLV模型提出了一种混合树/有限差分算法。合成实验与市场知情案例研究表明，对于仅期末保证，SLV与LV估值在数值上接近，符合共同边际目标的预期；而一旦允许退保，二者会出现显著差异，这些差异体现在保证价值、公平保险费率及依赖波动率的退保区域中。结果表明，匹配香草期权价格隐含的单日边际分布，并不能消除其价值取决于条件延续动力学和内生退保决策的保险负债的模型风险。
英文摘要
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.
