Is the minimum value of an option on variance generated by local volatility?

TL;DR

This paper investigates whether the minimum value of a variance option can be derived from local volatility models, providing insights into model-free bounds on volatility derivatives and challenging existing conjectures.

Contribution

It offers a counter-example to a common conjecture, enhancing understanding of the relationship between local volatility and variance options.

Findings

Counter-example to the widespread conjecture

Insights into model-free bounds on volatility derivatives

Analysis of local volatility models' implications

Abstract

We discuss the possibility of obtaining model-free bounds on volatility derivatives, given present market data in the form of a calibrated local volatility model. A counter-example to a wide-spread conjecture is given.