Sentiment-based Stock Index Futures Pricing

Futures pricing theory in traditional finance suggests that rational arbitrage necessarily brings futures prices close to spot price. But a number of studies find that the stock index futures prices deviate from the spot price in China. Futures pricing theory in traditional finance cannot offer a perfect explanation. In recent years, more and more behavior finance researches present that stock index futures sentiment and stock index sentiment play systematic roles in stock index futures pricing. Hence, it would be important to incorporating stock index futures sentiment and stock index sentiment in stock index futures pricing model, and help to improve our understanding of the behavior of stock index futures prices.In this paper, we find that stock index futures sentiment and stock index sentiment have both an important impact on stock index futures returns in our empirical results. We build stock index futures pricing models and do researches on the influence mechanism of stock index futures sentiment and stock index sentiment through numerical simulations, and offer some explanations of financial anomalies: stock index futures mispricing, the level of inefficiency, option bubble and option smile.First, the section 3 sets up stock index futures sentiment at day/week/month frequencies, and examine stock index futures sentimental effect. We consider four separate proxies, such as interest opening, volume, BSI index and PSY index and construct a composite stock index futures sentiment. We test the stock index futures sentimental effect by OLS models and panel data models. The empirical results show that the stock index futures sentimental effect is statistically significant day/week/month frequencies. The term structure character of the stock index futures sentimental effect is a monotonous decreasing function of the time term. Moreover, mixed-frequency stock index futures sentiment is more important than the low-frequency one. We add to stock index futures sentiment in TGARCH-M model. Specifically, stock index futures sentiment has an asymmetric effect on stock index futures returns and volatility.Second, the section 4 sets up stock index sentiment at day/week/month frequencies, and examine stock index sentimental effect. We consider four separate proxies: volume, adjusting turnover rate, BSI index and PSY index, and construct a composite stock index sentiment. The effects of stock index sentiment on the stock index futures returns are significant at day/week/month frequencies, but the effect of stock index sentiment is less than the effect of stock index futures sentiment on the stock index futures returns. The empirical results also show that the term structure character of stock index sentiment is a monotonous decreasing function of the time term. Mixed-frequency stock index sentiment is also more important than the low-frequency one.Third, the section 5 derives a closed-form expression for the stock index futures price in static environment, and it can describe investors’ myopic behavior and short-term trading behavior in stock index futures market. It could explain the mechanism about how stock index futures sentiment and the margin level affect price and trading volume. It could give some explanations of financial anomalies: mispricing and excess volume and measure the level of inefficiency in stock index futures market.Fourth, for illustrating the impact from dynamic sentiment, this section presents a dynamic stock index futures pricing model based on long-term sentiment investor, short-term sentiment investor, and arbitrageurs. The section 6 uses market clearing method to deduce dynamic model of stock index futures, and analyze the changes of stock index futures prices with the change of long-term investors, short-term sentiment investor sentiment and wealth. The model offers explanations for the arbitrage limited in stock index futures market.Fifth, for illustrating the effect of stock index futures sentiment and stock index sentiment, the section 7 presents a continuous stock index futures pricing model. The model shows that stock index futures sentiment and stock index sentiment play important roles on the equilibrium stock index futures price with no-arbitrage equilibrium method. This section explains the futures and spot markets sentiment power make stock index futures prices deviating from the stock index price.Sixth, the section 8 uses sentiment pricing method in the stock option pricing. Under a continuous economic environment, this section develops stock option pricing formula with options sentiment and the underlying stock sentiment with no-arbitrage equilibrium method. This model can explain the options market bubble and option smile.Finally, this paper makes some empirical researches to analyze the effect of sentiment factor, construct stock index futures pricing model with sentiment. Further, this paper carries out the corresponding simulation analyses, these results show that sentiment factor plays a systematic and important role in stock index futures pricing. Hence, our researches would help to improve our understanding the behavior of derivatives prices and avoid investing risk.