AI 中文总结
本文针对因子HJM随机波动率模型，提出对冻结互换利率载荷的一阶泰勒修正，在不增加校准参数的情况下，降低了随机波动率参数偏差和外样本定价误差，改进了互换期权校准效果。
AI 中文摘要
Sepp和Rakhmonov（2025）提出的因子HJM随机波动率模型通过沿确定性期望状态路径冻结非线性互换利率载荷，实现了易处理的互换期权定价，这消除了条件互换利率方差对当前收益率曲线状态的依赖。我们对该载荷引入了一阶泰勒修正，且不增加任何校准参数。在保留冻结年金测度漂移的条件下，我们证明互换利率变换的一阶变化与中心化利率状态呈仿射关系，并在波动率中简化为一维方程。对于二次漂移对数正态随机波动率，这些方程产生有限维常微分方程（ODE）表示和直接的对数波动率公式。对独立生成的非线性模型价格进行校准的结果显示，随机波动率参数偏差显著降低，且保留了外样本定价误差，仅局部校准可识别性发生适度变化。
英文摘要
The factor HJM stochastic volatility model introduced by Sepp and Rakhmonov (2025) obtains tractable swaption pricing by freezing the nonlinear swap-rate loading along a deterministic expected-state path. This removes the dependence of conditional swap-rate variance on the current yield-curve state. We introduce a first-order Taylor correction to the loading that adds no calibration parameters. Conditional on retaining the frozen annuity-measure drift, we show that the first variation of the swap-rate transform is affine in the centered rate states and reduces to one-dimensional equations in volatility. For quadratic-drift lognormal stochastic volatility, these equations yield a finite-dimensional ODE representation and a direct log-volatility formulation. Calibrations to independently generated nonlinear-model prices show substantially lower stochastic volatility parameter bias and held-out pricing error, with only modest changes in local calibration identifiability.
Comments38 pages, code available at https://github.com/quaere-verum/FHJM-SV-Calibration
