Why are quadratic normal volatility models analytically tractable?

TL;DR

This paper explains why Quadratic Normal Volatility models are analytically tractable by characterizing them as transformations of stopped Brownian motion, which accounts for their explicit option pricing formulas.

Contribution

It provides a characterization of Quadratic Normal Volatility models as transformations of stopped Brownian motion with a measure change depending on the terminal value.

Findings

Explicit formulas for option prices in these models.

Connection between model construction and Brownian motion transformations.

Clarification of the models' analytic tractability.

Abstract

We discuss the class of "Quadratic Normal Volatility" models, which have drawn much attention in the financial industry due to their analytic tractability and flexibility. We characterize these models as the ones that can be obtained from stopped Brownian motion by a simple transformation and a change of measure that only depends on the terminal value of the stopped Brownian motion. This explains the existence of explicit analytic formulas for option prices within Quadratic Normal Volatility models in the academic literature.