AI 中文总结
本研究验证空间弱形式LASSO流程可恢复Heston随机波动率模型，经模拟及标普500数据测试，其在指定库内系数估计可靠，漂移参数恢复精度较低，无明显噪声相变。
AI 中文摘要
我们研究空间弱形式LASSO流程能否恢复Heston随机波动率模型。高斯测试函数将局部增量矩转化为漂移、扩散及收益-方差协方差的弱目标。使用50个高斯核、线性库{1,v}、列归一化、五折交叉验证LASSO及同期索引，30次独立的100年模拟恢复ξ、ρ、ρξ的中位数相对误差分别为0.90%、0.53%、1.80%，而漂移恢复精度较低（κ为12.29%，θ为6.61%）。在含噪声的方差观测下，杠杆估计值逐渐下降，无明显相变。将该方法应用于2007-2010年的标普500数据，估计得κ=2.361、θ=0.0360、ξ=0.530、ρ=-0.329。二次漂移证伪在93%的零假设模拟中选出虚假项，表明该方法在指定Heston库内的系数估计可靠，但不适用于无限制的模型发现。
英文摘要
Estimating the coupled drift, diffusion, and leverage structure of a stochastic-volatility model directly from a price path is an unresolved inverse problem: Kramers--Moyal increment estimators amplify sampling noise as the step shrinks, weak-form SINDy has not been extended to coupled two-dimensional diffusions or to the return--variance cross-variation producing leverage, and Heston calibration typically relies on option-implied surfaces rather than the physical-measure path. We extend the spatial weak-form Galerkin framework to the Heston model: variance increments, squared variance increments, squared price increments, and their cross-product are projected onto shared Gaussian kernels in variance space, giving one LASSO regression that jointly recovers mean reversion $κ$, long-run variance $θ$, vol-of-vol $ξ$, and leverage correlation $ρ$, with a drift-informed bias correction analogous to scalar-SDE diffusion debiasing. Across 30 daily-observed Heston simulations, $ξ$, $ρ$, and $ρξ$ are recovered with median errors under 2\%. Applied to S\&P 500 data spanning the 2007--2010 crisis, the method recovers negative leverage consistent with the documented equity leverage effect, and a 50-stock Indian panel shows the same sign under several independent variance proxies.
Comments18 pages, 13 figures
