Crash Risk Matters: An Option‐Implied Approach to the Expected Market Return

Qiang Chen and Xinyi Song

Journal of Futures Markets, 2026, vol. 46, issue 3, 511-528

Abstract: This study introduces a lower bound that integrates the market's simple return risk‐neutral variance ( SVI X t 2) and a combination of log‐return moments ( VI X t 2) to predict market log returns. A distinctive feature of the model is that the ratio of VI X t 2 to SVI X t 2 captures crash risk, and the lower bound of log returns depends on the joint effect of crash risk and risk‐neutral variance. Our in‐sample analysis shows that crash risk exhibits significant predictive power for market returns, and its marginal effect differs markedly between crisis and noncrisis periods. In out‐of‐sample testing, we argue that crash risk outperforms several benchmarks in return prediction, while the joint effects of crash risk and variance risk achieves higher accuracy in forecasting crash events. We further demonstrate that our model delivers superior performance when the risk aversion is high, particularly during periods of crises.

Date: 2026
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