发表机构
Imperial College London（伦敦帝国理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过比较ρ=-1的Heston模型与校准至相同欧式期权价格的一维局部波动率模型的积分方差，为J. Gatheral的凸序不等式猜想提供了Heston模型反例
AI 中文摘要
我们将Heston模型（ρ=-1）与校准至相同欧式期权价格的一维局部波动率模型进行比较，证明对每个固定到期日T>0，其积分方差满足I_T^H ≺_{cx} I_T^{LV}，该严格排序为J. Gatheral猜想的凸序不等式提供了Heston模型反例
英文摘要
We consider the Heston model with perfect negative spot--variance correlation and its one-dimensional local-volatility projection. Let $I_T^{\mathrm H}$ and $I_T^{\mathrm{LV}}$ denote their respective integrated variances over $[0,T]$. We establish the inequality \[ \mathbb{E}\bigl[(I_T^{\mathrm H}-K)^+\bigr] < \mathbb{E}\bigl[(I_T^{\mathrm{LV}}-K)^+\bigr] \] for every maturity $T>0$ and every strike $K>0$. Consequently, Heston integrated variance is strictly smaller in convex order than the integrated variance of the calibrated local-volatility model. This strict ordering gives a Heston-model counterexample to the convex-order inequality conjectured by J. Gatheral.
