Time-Varying Crash Risk Embedded in Index Options: The Role of Stock Market Liquidity*

Abstract We estimate a continuous-time model for the stock market index where the stochastic volatility and crash probability depend on the realized spot variance and the stock market illiquidity. We find that market illiquidity is a useful economic covariate in the modeling of time-varying stock market crash risk embedded in index options. The relative contribution of spot variance in the time-varying crash risk is weakened once the market illiquidity variable is added to the model, and out-of-sample option pricing error also improves. Examining the relationship between market illiquidity and option-implied crash risk, we find that the availability of arbitrage capital and adverse selection facing liquidity providers are potential economic links. Our study highlights the benefits of adding a market illiquidity measure to index return models with time-varying crash risk.