Research Review | 5 June 2026 | Risk Management

Key Takeaways

• Put‑call disparity yields observable lower bound for bubbles
• Out‑of‑the‑money call price sets upper bubble bound
• COVID‑19 era showed sustained S&P 500 bubble
• Results suggest market violates no‑dominance, is incomplete

Pulse Analysis

Measuring asset‑price bubbles has long been hampered by reliance on parametric models that assume specific dynamics for volatility, drift, or investor behavior. Traditional approaches often require calibrating stochastic processes, which can be fragile when markets experience structural breaks or extreme events. By contrast, the put‑call disparity method leverages a fundamental arbitrage relationship: the price difference between out‑of‑the‑money puts and calls reflects the cost of carrying a position under short‑sale constraints. This simple, model‑free insight provides a direct, observable lower bound on bubble magnitude, sidestepping many of the estimation pitfalls that plague conventional techniques.

The authors construct both lower and upper bounds using only the no‑free‑lunch‑with‑vanishing‑risk condition and admissible trading strategies. The lower bound emerges from the put‑call spread, while the upper bound is anchored by the cheapest OTM call price. To enhance empirical reliability, they apply data‑driven regularization and bootstrap resampling, filtering out microstructure noise and mitigating the thin‑trading problem of deep OTM options. This methodological rigor allows the framework to be deployed on real‑world option data without heavy modeling assumptions, making it attractive for risk managers seeking timely bubble diagnostics.

Applying the technique to three decades of S&P 500 index options reveals a sustained bubble throughout the COVID‑19 pandemic, as well as early warning signals before the dot‑com bust and the 2008 financial crisis. These results suggest that markets may routinely violate the no‑dominance condition and operate in an incomplete setting, challenging standard asset‑pricing theory. For policymakers and institutional investors, the ability to flag bubble formation with transparent, observable metrics could inform macro‑prudential interventions and portfolio hedging strategies, while also opening new research avenues into the interaction between market frictions and price anomalies.