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.

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指数期权中嵌入的时变崩盘风险：股票市场流动性的作用

我们估计股票市场指数的连续时间模型，其中随机波动率和崩盘概率取决于已实现的现货方差和股票市场流动性不足。我们发现，在指数期权中随时间变化的股市崩盘风险建模中，市场流动性不足是一个有用的经济协变量。一旦将市场非流动性变量加入模型，现货方差对时变崩盘风险的相对贡献就会减弱，样本外期权定价误差也有所改善。检查市场流动性不足与期权隐含崩盘风险之间的关系，我们发现套利资本的可用性和流动性提供者面临的逆向选择是潜在的经济联系。