Measuring Bubbles via Put-Call Disparity: A Model-Free Approach
Robert A. Jarrow (Cornell U.) and Simon Kwok (U. of Sydney)
May 2026
This paper introduces simple, model-free lower and upper bounds for measuring the size of asset price bubbles. Assuming only that the market satisfies no-free-lunch-with-vanishing-risk and that all trading strategies are admissible, our framework avoids restrictive parametric models and the no-dominance assumption. We demonstrate that put-call disparity provides an observable lower bound, and is economically justified by short-sale constraints. Additionally, the lowest price of an out-of-the-money (OTM) call option determines the upper bound. To ensure empirical reliability, we modify these bounds using data-driven regularization and bootstrap methods to disentangle genuine bubble signals from market microstructure noise and to reduce reliance on thinly traded deep OTM options. Using S&P 500 index option prices from 1996 to 2025, we document a sustained bubble during the COVID-19 era and capture market exuberance preceding the 2000 dot-com and 2008 financial crashes. In addition, the empirical study suggests that the market violates no-dominance and is incomplete.