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Gatheral's Conjecture Revisited

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  • Vladimir Lucic

Abstract

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] 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.

Suggested Citation

  • Vladimir Lucic, 2026. "Gatheral's Conjecture Revisited," Papers 2609.05047, arXiv.org, revised Oct 2026.
    • Handle: RePEc:arx:papers:2609.05047
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    References listed on IDEAS

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