This paper constructs a call pressure index (CP) from China's SSE 50 ETF option market and finds a robust U-shaped nonlinear predictability for directional option returns as measured by log returns. The effect reflects that extreme call pressures—whether unusually low (reversal) or high (momentum)—contain information, while moderate levels are dominated by noise trading. Robustness checks using delta-hedged returns confirm that predictability stems primarily from directional exposure rather than volatility dynamics. The predictability is stronger in high-volatility and down-market states and survives controlling for implied skewness, variance risk premium, and other common predictors. A simple timing strategy based on rolling-window forecasts achieves a Sharpe ratio of 0.97, which further increases to 2.43 after applying a prediction threshold. A parsimonious volume-based indicator captures unique predictive information beyond complex proxies, offering a feasible path for emerging markets lacking proprietary order flow data.

In this paper, we extend the long-run risks model of Bansal and Yaron (BY, 2004) to allow both a long- and a short-run volatility component in consumption growth, long-run risks, and dividend growth. Our two volatility model better captures macroeconomic volatility than a single volatility model, and can reconcile simultaneously the large negative market variance risk premium, di?ering predictability in excess returns, consumption, dividends, and stock market volatility, all of which are di±cult to explain previously by the BY model.

In this paper, we derive the corresponding implied VIX formulas under the locally riskneutral valuation relationship proposed by Duan (1995) when various forms of GARCH model are proposed for S&P 500 index. The empirical study shows that the GARCH implied VIX is consistently and significantly lower than the CBOE VIX for all kinds of GARCH model investigated. Moreover, the magnitude of the difference suggests that the GARCH option pricing model is not capable of capturing the variance premium, which indicates the incompleteness of the GARCH option pricing under the locally risk-neutral valuation relationship. The source of this kind of incompleteness is then theoretically analyzed. It is shown that the framework of GARCH option pricing model fails to incorporate the price of volatility risk or variance premium.