Gatheral's Conjecture Revisited

2026-09-04

AI Summary

本文通过比较Heston模型与一维局部波动率模型，证明了Gatheral猜想中的凸序不等式在Heston模型下不成立。

Abstract

We compare the Heston model with $ρ=-1$ to the one-dimensional local-volatility model calibrated to the same European option prices. We show that, for each fixed expiry $T>0$, their integrated variances satisfy \[ I_T^{\mathrm H}\prec_{\mathrm{cx}} I_T^{\mathrm{LV}}. \] This strict ordering gives a Heston-model counterexample to the convex-order inequality conjectured by J.\ Gatheral

Problem

• Gatheral's Conjecture
• Heston Model
• Local Volatility Model
• Convex Order

Innovation

• Heston model
• local-volatility model
• convex order
• integrated variance