Measuring Bubbles via Put‐Call Disparity: A Model‐Free Approach

This paper uses violations of put‐call parity to provide simple lower and upper bounds for measuring the size of asset price bubbles. Assuming only no‐arbitrage, this bubble detection approach avoids restrictive parametric model assumptions. We show that put‐call disparity provides a bubble's lower bound, and the lowest price of an out‐of‐the‐money call option determines the bubble's upper bound. To enhance precision in the presence of market frictions, we implement data‐driven regularization and bootstrap. 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. The evidence also supports the assertion that stock markets are incomplete and often violates no‐dominance.