Predicting Stock Market Crises Using Stock Index Derivatives: Evidence from China

ABSTRACT The article offers a comprehensive analysis of the early warning capability of China’s stock index derivatives for the first time. A rolling window logit model is employed to predict stock market crises using data from CSI 300 index futures and SSE 50 ETF options. The findings demonstrate that (1) stock index derivatives play a vital role in predicting stock market crises; (2) short-term forecasts are better predicted by near-month derivatives contracts, whereas for long-term warnings, far-month contracts tend to perform better; and (3) in-the-money calls and out-of-the-money puts are superior to at-the-money options in predicting stock market crises. The insights provided by this article can assist emerging countries in establishing and utilizing derivatives markets more efficiently.


Introduction
The stock market crisis is an extreme event that poses a significant threat to the stability of capital markets and the wealth of investors.China's stock market, as an emerging market, is largely dominated by inexperienced individual investors. 1This makes it particularly vulnerable to crises, as these investors are unable to protect themselves from a stock market crisis due to their lack of knowledge and resources.Moreover, restrictions on short selling 2 and barriers to derivatives trading 3 further limit their ability to mitigate losses through hedging strategies.It is important to address these issues to ensure the stability of the market.One effective way is to gather information from the derivatives markets, which are primarily dominated by well-informed institutional investors.These investors have an information advantage and strong research capabilities, that enable them to detect market risks more sensitively and take measures to mitigate stock market crises ahead of time.As a result, the derivatives market, with its unique structure of investors and inherent abilities for price discovery and risk hedging, contains significant information related to the potential stock market crises.
The main objective of this research is to investigate whether the index derivatives market serves as an early warning system for the stock market crisis.Here are some more specific issues to consider: which type of warning is more efficient, short-term or long-term?Which derivatives contract, among those with various maturities and different levels of moneyness, has the best early warning capability?This paper intends to address these concerns by using data from China's index derivative market, which is preferred over developed countries for two reasons.First, as an emerging market, China's index derivatives market may still be immature compared to developed financial markets.Consequently, it remains uncertain whether China's index derivatives market offers opportunities for hedging or merely provokes speculation, with hedgers alert to the impending crisis while speculators are solely interested in financial gain.Second, in contrast to developed markets, China's stock market is dominated by individual investors who are viewed as uninformed or driven by sentiment and behavioral biases (Huang, Chiu, and Lin 2022;Ma et al. 2022;Xu et al. 2022).However, the index derivatives market is dominated by well-informed institutional investors. 4These characteristics may pose a challenge to the established role of index derivatives as documented by research in developed financial markets regarding their informational value.
This paper chooses Chinese Security Index 300 (CSI 300) index futures and Shanghai Stock Exchange (SSE) 50 exchange-traded fund (ETF) options in the analysis to investigate the effectiveness of China's index derivatives in providing early warnings for stock market crises. 5A rolling window logit model is employed to predict stock market crises.This model takes into account various factors including index derivatives return, trading volume, open interest, and the volatility index (VIX).To effectively analyze the numerous indicators, this paper adopts the widely used principal components analysis (PCA) method in prediction literature.This method is utilized to extract useful information and obtain the common components within variables. 6In order to implement short-, medium-, and long-term predictions of stock market crises, the data is processed into daily, weekly, and monthly frequencies.The study examines index derivatives with various maturities separately, and additionally compares index options with different levels of moneyness.The findings indicate that: (1) the inclusion of index derivatives indicators considerably improves the model's predictive power when compared to traditional models that only take macroeconomic and stock market variables into account; (2) derivatives contracts of different maturities are indicative of anticipated crises occurring at different periods in the future.In terms of short-term predictions, near-month contracts tend to be more accurate than far-month contracts.However, with regard to long-term predictions, far-month contracts are superior to near-month contracts; (3) As the degree of crisis-related information varies across option moneyness, in-the-money index calls and out-of-the-money index puts tend to outperform at-the-money option contracts.
This paper contributes to the literature in three ways.First, to the best of our knowledge, this is the first empirical work to systematically examine China's index futures and options markets.This paper analyzes both the index futures and options markets in China, in contrast to previous literature that investigates only one of the two derivatives markets.The sample covers the period since the introduction of index derivatives in China, which enables a comprehensive evaluation of the functioning of China's index derivatives market.Second, this paper enriches the literature on index derivatives markets in emerging nations.In contrast to developed markets, China's financial system heavily relies on debt financing, and the stock market is dominated by individual investors, suggesting that its capital market is still in the process of maturing.Comprehending the role of index derivatives in such a market can provide a great reference for emerging countries that have newly established stock markets and aspire to establish sustainable derivatives markets.Third, this paper adds to the literature on stock market crisis warnings by further exploring forecasts with various time horizons.In comparison to most previous research that focuses solely on long-term forecasts, this paper investigates both short-term and longterm forecasts, providing a more comprehensive analysis.The selection of a forecast horizon involves balancing two opposite considerations.On the one hand, the index derivatives market may reflect more relevant information as a stock market crisis approaches, making warning signals closer to the crisis more reliable; on the other hand, identifying a potential crisis as early as possible allows investors to take prevention actions.The combination of short-term and long-term forecasts enables investors to respond quickly to an imminent crisis and prepare in advance for potential risks in the long term.
The remainder of the paper is organized as follows.Section 2 reviews the literature; Section 3 describes the data and methodologies; Section 4 discusses the empirical results and tests the robustness of estimations; and Section 5 concludes.

Literature Review
A lot of studies focusing on Chinese stock market crises have examined a variety of potential signals derived from the macro economy and the stock market (Fu et al. 2020;Lu, Liu, and Chen 2021;Song et al. 2023;Wang, Zong, and Ma 2020;Xu et al. 2019;Zhang, Xian, and Fang 2019).Xu et al. (2019) propose a model with mixed frequency investor sentiment for predicting stock market volatility.They collect the investor sentiment features from internal and external aspects of the financial market, such as trading volume, relative strength index (RSI), and psychological line index (PSY).Zhang, Xian, and Fang (2019) predict the stock market crisis based on the perspective of behavioral finance.According to the results, the impact of investor sentiment on the stock market crisis is more significant than that of macroeconomic variables, with a notable positive effect.Fu et al. (2020) use principal components analysis to develop a comprehensive index that effectively captures both stock market valuation and investor sentiment.Subsequently, they propose an early warning system based on the comprehensive index.Wang, Zong, and Ma (2020) construct an integrated early warning system to predict stock market turbulence with stock market variables, such as the close price, log return and realized volatility of stock index.Lu, Liu, and Chen (2021) introduce an early warning system that utilizes market indicators and mixed frequency investor sentiments to predict stock market crises with greater accuracy and efficiency.Song et al. (2023) create an investor sentiment indicator to predict Chinese stock market volatility.This indicator is generated by several sentiment proxies, such as share turnover and consumer confidence index.In contrast to the majority of previous literature, the current paper utilizes data from index derivatives markets to predict stock market crises over various forecasting horizons.To provide a rationale for the selection of derivative variables in this paper, a brief review of the literature on the relationships between spot and index derivative markets will be presented.
Trading in stock index futures and options facilitates price discovery and risk management, which as a result enhances the predictability of spot market prices and volatility.The relationships between index derivative prices and the underlying equity prices are examined extensively in the literature.For example, Xu and Wan (2015) find that the index futures market takes the lead over the stock market in China, which is in line with the majority of previous studies conducted on developed economies.According to Liu et al. (2019), SSE 50 ETF options contain information about future return of the underlying assets and contribute to the price discovery process.These discoveries are consistent with the transaction cost hypothesis, which posits that price discovery should occur first in the market with lower transaction costs.
The informational role of futures and option volume and open interest is also researched in previous literature.Chen et al. (2013) document that index futures trading significantly reduces the volatility of the Chinese stock market.The impact of SSE 50 ETF index options on stock market volatility is examined by Wu, Liu, and Feng (2022).The empirical evidence reveals that the introduction of index options lead to an increase in trading volume and open interest, which in turn reduces the volatility of index returns.This confirms that futures and options trading not only improves the quality and speed of information flows, but also expands the range of feasible risk management tools available to investors, and thus reduces spot market volatility.Additional literature explores the relationship between option implied volatility and stock market volatility.The volatility index (VIX), built on option implied volatility, represents one measure of investors' expectations on stock market volatility and is often referred to as the "fear index".According to Wang (2019), the VIX and its component have a statistically significant effect on stock market volatility.Pan et al. (2019) demonstrate that the VIX can improve volatility prediction.
Although these studies document that index derivatives perform a chief role in price discovery and risk management for hedgers, they do not directly utilize index futures or options variables to predict stock market crises.This research focuses on the prediction of stock market crises by analyzing the information from China's index derivatives market, including both index futures and option markets, during the period since the market's inception.In addition, the research incorporates investor sentiment and macroeconomic variables, building upon previous studies in this area.

Definition of Stock Market Crises
It is important to be clear exactly how a stock market crisis is defined.To identify the periods of significant price declines in the histories, we use the ratio of the current index level at time t to the maximum index level over k rolling periods before time t, and convert index level series to the ML sequence: where P t is the closing price of the stock index at time t, and we set one year as a rolling period in calculating this ratio.Our study differs from much previous research in two ways.We not only focus on the predictability of crises, but also compare the efficiencies under different frequencies of daily, weekly, and monthly.Specifically, P t is the index level on day t in the daily prediction, or the index level on the last trading day of week t (month t) in the weekly (monthly) prediction.The corresponding rolling periods mentioned above are 250 trading days, 52 weeks and 12 months, respectively.
The ratio of 100% indicates that the index level at time t rises to the maximum value in the rolling one-year period.A low value of ML indicates a significant price decline in the index level over the last year.The more stock index falls, the closer ML gets to zero.The natural question is, to what extent can a stock index drop be considered a crisis?We translate ML to a binary crisis indicator CC to answer this question.The binary crisis variable is constructed based on a sequence of cutoff values, which requires taking the moving averages of the ratio minus a factor of moving standard deviations.Following previous studies (Coudert and Gex 2008;Fu et al. 2020;Li, Chen, and French 2015), a crisis is identified if ML is less than two and a half standard deviations below its mean value, 7 CC is defined as: where ML t is the mean value of ML from time t-k to t-1, and σ t is the standard deviation over the last year.For example, we calculate the mean value and the standard deviation of ML for the first 250 trading days, then subtract the first day of this sample and add an additional day at a time in calculating these two statistics in each of the following days, the historical trends are shown in Figure 1 as follows.
Figure 1 displays the ML ratio over the sample period from April 2010 to December 2022.The periods shaded gray in Figure 1 represent several crisis events in the sample period.

Derivatives Market Indicators
Derivatives market indicators include return, trading volume, open interest, trading amount, and the VIX.In addition, the average effective spread and the futures arbitrage basis which reveal information about crises are also considered in this paper (Fung 2007;Li, Chen, and French 2015).The key variables at time t are defined in Table 1.

Control Variables
In addition to the futures and option indicators mentioned earlier, various factor such as micro and macro-investor sentiment, liquidity of the stock market, short-selling activity, turnover ratio, and treasury term spread are taken into account to accurately predict stock market crises.The definitions of these control variables are as follows.

Psychological line index (PLI).
The psychological line index is the ratio of the number of trading days when the stock index rises to the total number of trading days. 8Before a crisis, there is usually a moderate increase in trading volume for the index, while the index price may increase slightly or remain stagnant.These trends indicate a potential impending downturn in the market.A lower PLI value is often indicative of a higher probability of a crisis occurring.

Relative intensity index (RSI).
The relative intensity index compares the rise and falls of index over a period. 9The index typically experiences a gradual increase before a crisis, reaching its peak before a potential downturn.Consequently, a lower RSI value indicates a higher likelihood of price drops.Note: ML is the ratio of the current index level at time t to the maximum index level over k rolling periods before time t.A crisis is identified (i.e., CC = 1) if ML is less than two and a half standard deviations below its mean value.The solid line represents ML sequence; the dashed line represents the difference between the moving average and 2.5 times the moving standard deviation of ML.The periods shaded gray mark the time when the solid line falls below the dashed line, representing the crisis periods.The difference between the closing price of put options and the listing base price on trading day t (in week t, in month t).
Note: Short-term predictions are made using daily data.To facilitate the analysis of medium-and long-term predictions, daily data is aggregated into weekly or monthly data.The above indicators can be extended to four types: current-month, next-month, quarterly-month and next quarterly-month.Options indicators can be extended to three types: in-the-money (ITM), at-the-money (ATM), and out-of-the-money (OTM).The current-month and next-month contracts are referred to as the near-month contracts, while the quarterly-month and next quarterly-month contracts are referred to as the far-month contracts.

Investor confidence index (ICI).
The investor confidence index is based on the investor's optimistic/pessimistic view about the investment prospects and typically experiences a notable decline prior to a crisis.This paper uses the investor confidence index compiled by the China Securities Protection Fund Corporation to predict stock market crises.

Index trading amount (ITA)
. Yang and Zhou (2015) document that ITA depicts investors' panic behavior during a crisis.ITA rises steadily before the crisis, once panic spreads, investors rush to sell, leading to a surge in trading volume and a simultaneous drop in prices.Therefore, it is reasonable to use ITA for crises predictions.

Margin balance ratio (MR).
Short traders are bearish traders in the market (Liu, Luo, and Zhao 2020).The risk of crisis increases as the balance becomes shorter.To accurately assess the margin balance, it is essential to consider the trading amount of index.Therefore, we calculate the MR indicator by dividing the margin balance by the trading amount of the A-share market.

Turnover ratio (TR).
Stock market crises are usually manifested as liquidity exhaustion, therefore, liquidity has a high correlation with crises.For simplification, liquidity should be expressed by turnover ratio, which is the ratio of index trading volume to the total number of outstanding shares.

Treasury term spread (TS).
The spread between the long-term and short-term treasury bond rates is usually higher before the crisis than during or after it because central banks generally cut shortterm interest rates during crises.According to Li, Chen, and French (2015), a stock market crisis forecast with the addition of treasury term spread is better than a prediction without that.Therefore, the difference between the yield of the 10-year treasury bond and the 3-month treasury bond is also under control.

Data
The sample period commences from April 16, 2010, which is the birth of China's first index futures, the CSI 300 index futures.Since the analysis needs to cover stock market crises in 2015 and 2018, the sample period is from April 2010 to December 2022.The sample of futures data contains 11,451 daily observations.The SSE 50 ETF option was not listed until February 9, 2015, therefore, its sample range spans from February 2015 to December 2022.The sample of options data consists of 238,738 daily observations, 120,033 of which are call options, while 118,705 of which are put options.The CSI 300 index options was created in December 2019, following several major crises.As a result, there has been no opportunity to test its effectiveness as a crisis warning mechanism.The data is filtered by excluding the abnormal data of the whole market circuit breaker on January 4 and 7, 2016.The sample periods and data sources are presented in Table 2. Before turning to regression analysis, we first estimate the relationship between the log returns of CSI 300 index and CSI 300 index futures, as shown in Figure 2.
Figure 2 shows that CSI 300 index had several significant declines in February 2012 and August 2015, and the return of index futures decreased during the months preceding the crises, such as in December 2011 and July 2015.These observations suggest that the peak of index futures return contains information of expectations on impending falls.Conversely, the bottom of index futures return indicates a potential recovery of the spot market.For example, index futures return declined thrice in 2017 and reached the bottom in 2018 before the recovery.This paper also examines the movement of index options return before the stock market crisis, as shown in Figure 3.
Figure 3 shows that put options return was significantly higher than call options before the crisis in April 2018 and October 2019, indicating that the anticipation of a stock market crisis could have more demands for put options than call options, consequently leads to put options being priced higher than call options.The reason may be that investors can benefit from falling prices by selling call options or buying put options.

Methodologies
In order to summarize the information implied by so many variables, a principal components analysis (PCA) method is used to lower the dimensions of the original data, and construct new independent variables, which are linear combinations of the original variables.The principal components analysis method constructs principal components in three steps as follows: Step 1.Given standardized data of derivatives and control variables to be elements of PCA, obtain a sequence of eigenvalues and corresponding eigenvectors based on the covariance matrix of centralized data.Specifically, the eigenvalue is the variance of each principal component, and the eigenvector is a vector containing the transformation coefficients of each principal component.Due to the mixed frequency of control variables, PLI and RSI are only considered for the weekly (monthly) prediction, and ICI is only included in the monthly prediction.The other control variables are all selected as PCA elements cross different frequencies.
Step 2. Calculate the percentage of the total variance explained by each principal component, called contribution rate, and choose the number of components (n) for which their cumulative contribution rate is more than 85%.
Step 3. Multiply the original standardized data with the matrix of transformation coefficients, and take the first n columns as the principal components (X PCA ) to predict stock market crises.
The following logit model is constructed to test what extent these principal components can predict the crisis coefficient: where X PCA tÀ 1 is a vector of principal components at time t-1.We carry out this logit model using the maximum likelihood method as Equation (4) and extrapolate CC tþ1 with the steps detailed in Section 3.5.
It's hard to believe that a crisis could arise from a low predicted value of CC.Then what level of the predicted CC value can be considered a definite signal of a crisis?We must establish a threshold for determining when a predicted value indicates a definite signal of an impending crisis.This paper sets the threshold level to 25%, following Zhang, Xian, and Fang (2019).

Prediction Steps
Take the daily prediction as an example.We set k trading days as the rolling period in calculating the predicted probability of a crisis using the logit model.The estimation steps are as follows: Step 1.Given the derivatives and control variables from day t-k to t-1, construct the principal components X PCA tÀ 1 by applying the PCA method.
Step 2. Estimate the coefficient β tÀ 1 of this sample, with CC from day t-k+1 to t. β tÀ 1 can be obtained from Equation (3).
Step 3. Calculate the crisis coefficient on day t+1 ( c CC tþ1 ).Multiply the principal components on day t (X PCA t ) with the coefficients on day t (β t ^¼ β tÀ 1 ), and yield c CC tþ1 .

Summary Statistics
Table 3 reports the descriptive statistics of the main variables for the sample periods.The mean values of crisis periods and normal periods are presented respectively, furthermore, the differences and p-stats are shown in the last column in Table 3.
The last column of Table 3 reports that there are statistically significant differences in the mean values of main variables between normal periods and crisis periods.Most futures and options indicators during crisis periods exhibit significant differences compared to normal periods, indicating that these variables reveal valuable information of the stock market crisis.The stationary test results show that most variables are stationary sequences.

Empirical Results: An Example
To demonstrate the process of a rolling window regression and prediction in detail, this paper takes the daily prediction of the futures model as an example.We set 250 trading days as the rolling period, so the first sample period is from April 16, 2010, to April 29, 2011 (250 trading days after the birth of index futures), and CC is from April 19, 2010, to May 3, 2011.Given the sample data of explanatory variables and control variables, we take the KMO test.The overall KMO value is 0.6018, suggesting that these variables are available for the principal components analysis.Then, we obtain the principal components by performing the PCA method.Table 4 presents the eigenvalues and their contribution rates.To avoid losing too much information, we choose the first six principal components, i.e., X PCA 1 , the subscript denotes the first regression sample.The cumulative contribution rate of the first six principal components is 89.3703%, more than 85%.Each of the first four components explains more than 10% of the sample variance, well capturing the co-movement of individual proxies, representing the trend of index futures return and trading before a stock market crisis properly.The coefficients for each principal component are shown in Table 5.
Table 5 presents the coefficient of each principal component, and we label the first three largest (absolute) values for each component in bold font.For example, column (1) shows that the first principal component places importance on the returns of current-month, next-month, and quarterly-month contracts, all of which have the expected sign, confirming their positive impact on the probability of a crisis.Column (2) shows that the second component emphasizes the trading volumes of quarterly-month and next quarterly-month contracts, revealing the positive relationship of far-month contracts trading with crisis probability.The third component in column (3) also emphasizes the positive relationship of futures returns and crisis signals.Both the second and third components support the importance of treasury term spread.Column (4) stresses the increase in  Note: Superscript m1, m2, s1 and s2 are for current-month, next-month, quarterly-month and next quarterly-month contracts, respectively.The current-month and next-month contracts are referred to as the near-month contracts, while the quarterly-month and next quarterly-month contracts are referred to as the far-month contracts.
arbitrage basis of near-month contracts and the increment of index trading amount before the outbreak of a crisis.Column (5) stresses the positive relationship of current-month contracts' trading volume with the crisis again; it also shows that the turnover ratio will increase before a crisis.Column (6) underlines the significant impacts of arbitrage basis on crises, and reveals that the treasury term spread will increase before a crisis, as we expected in the above analysis.
With the results in Table 5, we convert explanatory and control variables into the sequence of principal components, plug them into Equation (3) and estimate the regression coefficients on April 29, 2011.By multiplying the regression coefficients with the principal components on May 3, 2011, we obtain the probability of a crisis on May 4, 2011, which completes the first forecast of a stock market crisis.In the same way, with the sample of 250 trading days from April 19, 2010, to May 3, 2011, the coefficients of Equation (3) can be estimated; multiply the coefficients with the principal components on May 4, 2011, we can obtain the forecast value of the crisis coefficient on May 5, 2011.The KMO values, R 2 values, and forecast values of CC in each of the following days could be calculated by rolling the window.Due to limited space, part of these sequences are shown in Table 6.In the same way, we conduct weekly and monthly predictions with data from the same period.
Table 6 reports the predicted values of CC based on the daily data of futures and control variables.The first day (May 4, 2011) and the last three days (December 28-December 30, 2022) are normal periods, and the predicted values of CC are either zero or close to zero, indicating that the model does not send a warning signal.The middle three days (April 12-April 16, 2018) experienced a crisis with actual values of CC equaling one, and the predicted values of CC are much higher than 25%, indicating that futures contracts are effective in predicting stock market crises.Similarly, the forecast results can be obtained with weekly and monthly data.Due to space limitations, they will not be repeated here.The forecast results (local) of SSE 50 ETF options are reported in Table 7.
Since SSE 50 ETF options were listed on February 9, 2015, the first sample period is from February 9, 2015, to February 25, 2016, and CC is from February 10, 2015, to February 26, 2016.The first predicted value of CC on February 29, 2016, is zero.During the middle three days, the predicted values of CC are almost equal to one and predicted values for the last three days are all about zero, which indicates that options are efficient in forecasting stock market crises.According to the actual and predicted values of CC in Tables 6 and 7, the futures and options models' predictive performances are presented in Figures 4 and 5, respectively.
Figure 4 presents the predicted values of CC based on daily data of CSI 300 index futures.The predicted values rose steeply to a significant 0.9 during the outbreak of stock market crises in June 2015 and February 2018, which illustrates the predictive power of the index futures model.The predictive performance of the index options model is shown in Figure 5.
Figure 5 presents that the predicted values of CC skyrocket over periods shaded gray, issuing clear signals during the outbreak of crises.Overall, Figures 4 and 5 show that both the index futures and options have excellent early warning capabilities.

Evaluating the Performance of Prediction
To evaluate the performance of our models, we adopt two types of measurement: the goodness-of-fit, such as accuracy and F2 value; and credit-score calibrations, such as the area under the curve (AUC) and quadratic probability score (QPS) value.These evaluation measures are calculated as follows.First of all, combining the predicted and actual values of CC, there are four performance situations known as the confusion matrix, which is shown in Table 8.
The values of TP, TN, FN and FP reported in Table 8 can  Compared with the precision value, we pay more attention to the sensitivity value because it is the lesser of two evils considering the massive losses of crises.Therefore we select a more comprehensive measure, i.e., F2 value, which is calculated as follows: Higher accuracy and higher F2 values demonstrate better predictions.The area under the curve (AUC) is obtained in the following three steps.
First, we match every element of the samples with crises to every element without crises, and obtain ðTP þ FNÞ � ðFP þ TNÞ pairs of samples.
Second, c CC crisis is the predicted value of the element from crisis samples, c CC normal is the predicted value of the element from normal samples, and the indicator function I defined on the two sets of samples is as follows: Third, area under the curve (AUC) is calculated as follows: Generally, the value of AUC is between 0.5 and 1.0, and a perfectly informative signal would trigger AUC = 1.The quadratic probability score is calculated as follows: QPS ranges from 0 to 2, with a zero for a perfect forecast.

Out-Of-Sample Performance of Early Warning Models
The early warning model attempts to predict a crisis in the coming days, weeks, or months.We estimate the model with different rolling periods of one to three years and select the best result based on the AUC value.To distinguish the predictive power of derivatives variables from control variables, we construct a traditional model considering only the macroeconomic and stock market variables.In addition, the results for the traditional model and derivatives models are presented in Table 9.Table 9 presents the performance of the traditional model utilizing macroeconomic and stock market variables, alongside the performance of derivatives models incorporating stock index futures and options data.The "Futures+Options" model combines index futures and options variables through the PCA method; its accuracy rate is 96.18% in daily predictions, indicating that 96.18% of the observations are correctly estimated.From the perspective of daily predictions, the F2, accuracy and AUC values of the traditional model are lower than that of the "Futures+Options" model, meaning it is inferior to the derivatives model in predicting stock market crises; a higher QPS value indicates its weaker performance as well.The "Options" model encompasses all the information implied by the index options market, and its performance surpasses that of considering call or put options alone.The "Futures+Calls" model and the "Futures+Puts" model incorporate more information than considering futures and options separately.Overall, the incorporation of derivatives variables results in a noteworthy enhancement in the overall performance of the traditional model, which is verified in weekly and monthly predictions as well.identified; F2 is a comprehensive measure giving more weight to sensitivity than precision.AUC is between 0.5 and 1.0, and a perfectly informative signal would trigger AUC = 1.QPS ranges from 0 to 2, with a zero for a perfect forecast.
Although the F2 and AUC values of the "Options" model are higher than that of the "Futures" model, we cannot conclude that options are superior to futures given the following three reasons: (1) Hedgers can either short a futures contract or buy a put option, but the latter involves a much higher cost due to the option premium.Futures sellers are required to sell assets at a predetermined price, protecting against a decline in stock price, but they can not benefit from a rise in stock price.By purchasing put options, the buyer can secure a minimum sale price for their stock if its market value dips below the specified strike price.Conversely, if the stock price rises, the buyer may still reap the benefits of the stock's earnings without any obligation to sell.In essence, while purchasing put options may offer more robust protection compared to selling futures, the associated cost is comparatively higher.Therefore, it would be inaccurate to assert that options are a superior choice over futures.(2) Given the unique characteristics of China's capital market, CSI 300 index futures are settled in cash without transferring the underlying asset, while SSE 50 ETF options involve physical delivery.The buyer of puts must prepare spot 50 ETF for delivery upon expiration, which is equivalent to paying 100% margin.In contrast, futures only require a 10% margin.Consequently, it is not intuitively to conclude that put options are superior to futures.(3) CSI 300 index consists of the top 300 largest and most liquid stocks listed on both the Shanghai and Shenzhen Stock Exchanges.SSE 50 ETF is an open-end fund which tracks the 50 largest and most liquid stocks traded on the Shanghai Stock Exchange.As a result, CSI 300 index futures can provide hedging for a wider range of stocks compared to SSE 50 ETF index options.In addition, since the Shanghai and Shenzhen stock markets are actually not synchronized, investors who hold stocks in the Shenzhen stock market would prefer index futures to options.
Derivatives contracts with different maturities reflect expectations for crises occurring at different periods in the future, this paper examines the predictive performance of current-month, next-month, quarterly-month, and next quarterly-month contracts separately.The results are presented in Table 10.
Table 10 reports the forecast performance of index futures contracts with different maturities.From the perspective of daily predictions, near-month contracts exhibit higher F2, accuracy and AUC values compared to far-month contracts, indicating that near-month contracts incorporate more short-term information.Besides, the QPS values of near-month contracts are lower than that of far-month contracts; in other words, near-month contracts are more efficient in extracting daily information.Regarding the weekly prediction, the F2, accuracy and AUC values of far-month contracts are greater than those of near-month contracts, demonstrating that far-month contracts have comparative advantages in the medium-term prediction.In terms of monthly prediction, it is hard to tell if nearmonth or far-month contracts are superior in forecasting due to the limitation of sample size.F2 is a comprehensive measure giving more weight to sensitivity than precision.AUC is between 0.5 and 1.0, and a perfectly informative signal would trigger AUC = 1.QPS ranges from 0 to 2, with a zero for a perfect forecast.
Additionally, it has been observed that the effectiveness of warnings deteriorates as the frequency decreases, indicating that the performance of a short-term warning is better than that of a long-term warning.
Although it may be obvious that near-month contracts outperform far-month contracts in shortterm predictions, this finding has a significant implication for enhancing crisis early warning capabilities.For a more effective short-term warning, it is recommended to focus solely on current-month contracts, rather than consider the various futures contracts of varying maturities.From the perspective of daily prediction, the AUC value of current-month contracts model is higher than that of the composite futures model, which is 84.35% and 83.60%, respectively.Similarly, in the long-term warning, it is better to focus only on far-month contracts compared to considering all these futures contracts.Taking monthly prediction as an example, the AUC value of quarterly-month contracts model is higher than that of the comprehensive futures model, which is 63.54% and 60.70%, respectively.These conclusions are tenable for options contracts in the long-term prediction, as shown in Table 11.
Table 11 reports that when compared to far-month contracts, near-month contracts obviously have better predictive capabilities given the higher F2, and AUC values in daily prediction.While from the perspective of weekly and monthly prediction, far-month contracts are superior to near-month contracts.In addition, options contracts tend to perform better in short-term warnings compared to long-term warnings.Overall, both near-month futures and options contracts are more efficient in extracting crisis-related information for short-term warnings.However, when it comes to long-term warning, far-month contracts tend to be more superior.To examine the forecast performance of options contracts with different moneyness, which are different in risk characteristics and the amount of information, we consider in-the-money (ITM), at-the-money (ATM), and out-of-the-money options (OTM) separately in Table 12 as follows.
Table 12 shows a comparison of the prediction performance based on the daily data of SSE 50 ETF options, categorized by different moneyness levels.From the perspective of call options, it is clear that ITM contracts exhibit stronger performance, given their highest F2 and AUC values, indicating that ITM calls possess better predictive capabilities.One possible explanation could be that ITM call options and OTM put options tend to be priced higher and expect more significant price fluctuations.As equity prices move down, volatilities tend to move up (Cao, Chen, and Hull 2020).It means that the F2 is a comprehensive measure giving more weight to sensitivity than precision.AUC is between 0.5 and 1.0, and a perfectly informative signal would trigger AUC = 1.QPS ranges from 0 to 2, with a zero for a perfect forecast.
stock index declines are accompanied by increases in volatility, making even greater declines possible.This corresponds to the heavier left tail of the implied distribution than the lognormal distribution.Consider a deep OTM put option with a low strike price of K (K/S 0 well below 1.0), this option pays off only if the stock index falls below K.The heavy left tail shows that the probability of this is higher than we expect, therefore leads to a higher price and implied volatility for the option, which indicates a more pessimistic attitude toward the future stock market.As a result, these options may contain more information about a potential decline in the stock market.Moreover, both ITM calls and OTM puts can outperform a comprehensive options model that includes various index options contracts.

An Alternative Definition of Stock Market Crises
To test the robustness of estimates to an alternative definition of a stock market crisis.We select an aggregate index, which is calculated as the weighted average of the CSI 300 index and the SSE 50 index, using trading volume as the weight, construct another crisis coefficient following the steps in Section 3.1, and estimate all models in Table 9.The results of the traditional and derivatives models are presented in Table 13.Table 13 reports the prediction performance to an alternative calculation of the crises coefficient.From the perspective of daily prediction, derivatives models have distinct advantages over the traditional model in extracting crisis-related information.In terms of weekly and monthly prediction, although all performances have been weakened, the "Futures+Options" model is still superior to the traditional model with a significant advantage.Overall, derivatives variables remarkably enhance the performance of crisis early warning relative to the traditional system.

Divide the Sample into Pre-Restriction and Post-Restriction Periods
In late August 2015, under intensified social pressure, the China Financial Futures Exchange (CFFEX) adopted restrictions on index futures trading in China.Mutual funds and hedge funds, registered as "speculators" are applied to restrictions on futures trading, and these institutional investors are suddenly exposed to huge systematic risks (Han and Liang 2017).As the futures market shifts from a well-functioning state to a nearly complete stop, we reexamine the predictive power of index futures trading by dividing the sample into pre-restriction and post-restriction periods; the results are shown in Table 14.
Table 14 presents the performance of futures model based on pre-restriction and post-restriction samples, respectively.Compared with the evaluation results using data before the restriction, the policy has a significant impact on the F2, accuracy, and AUC values, thus impairing their role in the early warning of stock market crises.Additionally, the QPS value has increased, indicating a decrease AUC is between 0.5 and 1.0, and a perfectly informative signal would trigger AUC = 1.QPS ranges from 0 to 2, with a zero for a perfect forecast.
in the efficiency of the early warning system.The index-arbitrage theory can explain the results: restrictions on index futures trading impose a high cost to index hedging, preventing informed traders from using index futures to implement insurance strategies or manage systematic risks.

Employ Machine Learning Techniques to Predict Stock Market Crises
The discussion about predicting crises and turbulence has remained a constant topic, especially when it comes to comparing the efficiency of traditional regression models and machine learning F2 is a comprehensive measure giving more weight to sensitivity than precision.AUC is between 0.5 and 1.0, and a perfectly informative signal would trigger AUC = 1.QPS ranges from 0 to 2, with a zero for a perfect forecast.F2 is a comprehensive measure giving more weight to sensitivity than precision.AUC is between 0.5 and 1.0, and a perfectly informative signal would trigger AUC = 1.QPS ranges from 0 to 2, with a zero for a perfect forecast.
techniques.As a robustness check, we estimated all models in Table 9, employing the machine learning technique of support vector machine (SVM) to predict stock market crises, as reported in Table 15.
Table 15 shows that including derivatives variables again significantly improves the accuracy of predictions compared with the traditional model.In terms of daily, weekly, or monthly prediction, most derivatives models outperform the traditional model due to their higher F2, accuracy, AUC values, as well as lower QPS values.In addition, compared with the results in Table 9, the traditional regression model is superior to machine learning techniques in crisis prediction, supporting the view that the conventional logit model is relatively efficient for crisis prediction (Beutel, List, and von Schweinitz 2019).

Conclusions
As a conclusion, this paper reveals that China's index derivatives market performs a vital role in predicting stock market crises and stabilizing the capital market.The index derivatives markets are expected to incorporate crisis-related information more efficiently compared to the spot market, owing to their distinct investor structures.The spot market is typically dominated by individual investors, whereas index derivatives markets are predominantly influenced by institutional investors.In the finance literature, institutions are usually presumed to be well-informed rational investors with the motivation and capability to recognize risks and implement appropriate hedging strategies, whereas individuals are viewed as uninformed or driven by sentiment and behavioral biases, lacking the necessary knowledge and resources to engage in derivatives hedging (Bohl, Salm, and Schuppli 2011).As a result, the derivatives market can offer valuable indications about upcoming stock market F2 is a comprehensive measure giving more weight to sensitivity than precision.AUC is between 0.5 and 1.0, and a perfectly informative signal would trigger AUC = 1.QPS ranges from 0 to 2, with a zero for a perfect forecast.
crises because of the information disparity and capability gap that exists between investors in the derivative market and those in the spot market.To the best of our knowledge, this is the first study to comprehensively examine the early warning function of China's index derivatives market.Conclusions are summarized as follows.
(1) The addition of index futures or option indicators significantly improves the performance of the traditional model, which solely incorporates factors from the macro economy and the stock market.The model that combines futures and options variables has the best performance.
(2) In short-term forecasts, near-month contracts outperform far-month contracts, furthermore, it is better to focus solely on near-month contracts rather than considering all of these derivative contracts.Similarly, in the long-term warning, far-month contracts are superior to near-month contracts, it is better to focus only on far-month contracts compared to considering multiple contracts.
(3) In-the-money calls and out-of-the-money puts have the best warning capabilities among index options, even outperform the comprehensive options model that includes various options contracts.The reason may be that in-the-money calls closely resemble direct investments in the underlying asset, and out-of-the-money puts exhibit higher levels of leverage and a greater demand for risk hedging, therefore they are more likely to reflect crisis-related information.
Based on the findings of this research, we make the following suggestions: (1) Safeguarding the interests of small and medium-sized investors forms the bedrock of securities market legislation.
To ensure their protection, timely provision of warning information regarding stock market crises is of paramount importance.This measure helps address the information asymmetry between individuals and institutions, while establishing a fair and equitable mechanism for information sharing, thus ensuring investors have equal access to opportunities and resources.
(2) The hedging function of financial derivatives is fundamental in predicting stock market crises.Actively encouraging and guiding investors to utilize the financial derivatives market for risk management is crucial for the healthy development of the stock market.By employing hedging strategies, investors can effectively manage systematic risks in the stock market and gain valuable insights into stock market crises.This, in turn, enhances the accuracy and timeliness of predicting stock market crises.
(3) For policymakers in emerging markets who are responsible for decisions regarding the establishment and expansion of index derivatives markets, this research offers a valuable insight into how abnormal fluctuations in these markets can serve as an indicator of potential crises.Such findings are instrumental in enhancing market stability and overall efficiency, ultimately creating a safer and more dependable investment environment for investors.

Notes
1.According to a report released by the China Securities Investor Protection Fund Corporation, as of December 31, 2019, the total number of stock investors in China reached 159.7524 million, of which individual investors accounted for 99.76%.According to the 2020 Market Quality Reports of the Shanghai Stock Exchange (SSE), the orders submitted by individual investor accounted for 65.01% of the total market orders.2. Short-selling was prohibited in China until 2010 and has been underutilized for many years.According to statistics from the CSMAR database, by the end of our sample period (December 30, 2022), the trading amount of shorting-sell accounts for 6% of the Chinese A-share market.While short sellers are often sophisticated investors with private information and play a disciplinary role in the stock market (Boehmer, Jones, and Zhang 2008;Jiang, Habib, and Hasan 2022;Li, Zhu, and Pontiff 2022;Wang et al. 2022).3.According to the Regulations of the China Securities Regulatory Commission, the following requirements must be satisfied by individual investors applying to trade stock index futures or index options: (1) The available fund balance of the margin account for 5 consecutive trading days before applying for account opening shall not be less than RMB 500,000; (2) Have basic knowledge of stock index futures or options and pass the relevant tests; and so forth.4. For example, according to the 2021 Market Quality Reports of the Shanghai Stock Exchange (SSE), institutional investors account for 60.68% of the trading volume of the options market.5. CSI 300 index futures, created in 2010, is China's first stock index derivatives, its underlying asset is CSI 300 which consists of the top 300 largest and most liquid stocks listed on both the Shanghai and Shenzhen Stock Exchanges.SSE 50 ETF option was issued in 2015 and is the first financial option in China, its underlying asset is SSE 50 ETF.SSE 50 ETF is an open-end fund which tracks the 50 largest and most liquid stocks traded on the Shanghai Stock Exchange.CSI 300 index futures and SSE 50 ETF options are China's first financial futures and options, respectively, and their underlying assets represent the performance of the top A-share companies, therefore, we use CSI 300 index futures and SSE 50 ETF options in our analysis.6. Please see, Han and Li (2017); Fu et al. (2020); Zhang, Ma, and Liao (2020); Song et al. (2023); Zhang, Wahab, and Wang (2022); Zhang and Wang (2022).7.As a robustness check, we set the threshold value to two and three standard deviations below the mean of ML respectively.Due to space limitation, the results are not reported because they are similar to the main findings.These results are available upon request.8. PLI ¼ Tu T :T u the number of trading days when the closing price of the stock index is higher than the previous trading day, and T is the total number of trading days over a while.9. RSI t ¼ 100 , P t is the closing price of the index at time t.
10.The mean value of futures closing price on trading day t is an arithmetical mean of futures contracts across all exercise prices.The mean value of futures closing price in week (month) t is an arithmetical mean of closing prices for all trading days in week (month) t.The conclusions are stable if the closing price is calculated as a weighted average with trading volume as the weight.
11. VIX t ¼ 100 ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi where σ 1 and σ 2 are the implied volatility of a nearmonth and a far-month option contracts, respectively.The most recently expiry contract over seven days is a near-month contract, and a second-near-expiry contract is a far-month contract.T 1 and T 2 are the remaining days of a near-month contract and a far-month contract, NT 1 and NT 2 are the remaining expiration time (in minutes) of a near-month contract and a far-month contract, NT 30 ¼ 30 � 1440 and NT 365 ¼ 365 � 1440 .12. CSPD t ¼ P T tÀ 1 Cprc t À Bprc t � � � � =T:Cprc t is the average closing price, and Bprc t is the average listing base price of option contracts, which is determined by the exchange, using the options pricing formula to calculate the benchmark price of options.T is the number of trading days.

Figure 1 .
Figure 1.The ratio of CSI 300 index levels over rolling one-year maximum levels (ML): 2010-2022.Note: ML is the ratio of the current index level at time t to the maximum index level over k rolling periods before time t.A crisis is identified (i.e., CC = 1) if ML is less than two and a half standard deviations below its mean value.The solid line represents ML sequence; the dashed line represents the difference between the moving average and 2.5 times the moving standard deviation of ML.The periods shaded gray mark the time when the solid line falls below the dashed line, representing the crisis periods.
Excluding the abnormal data of the whole market circuit breaker on January 4 and 7, 2016.

Figure 2 .
Figure 2. Returns on CSI 300 index and CSI 300 index futures (current-month contracts).Note: The solid line represents the return on CSI 300 index; the dashed line represents the return on CSI 300 index futures, which is the log return of current-month contracts based on the average closing price.

Figure 3 .
Figure 3. Returns on CSI 300 index and SSE 50 ETF options (current-month contracts).Note: The solid line represents the return on CSI 300 index; the dashed line represents the return on SSE 50 ETF put options, which is the log return of current-month puts based on the average closing price; the dotted line represents the return on SSE 50 ETF call options, which is the log return of current-month calls based on the average closing price.

Figure 4 .
Figure 4. CSI 300 index level and the predicted values of CC (i.e., b CC) based on daily index futures data.Note: The solid line represents the closing price of the CSI 300 index.The dashed line represents the predicted value of CC, meaning the estimated probability of a crisis.The periods shaded gray represent the crisis periods (i.e., CC = 1).

Figure 5 .
Figure 5. CSI 300 index level and the predicted values of CC (i.e., b CC) based on daily call options data.Note: The solid line represents the closing price of the CSI 300 index.The dashed line represents the predicted value of CC, meaning the estimated probability of a crisis.The periods shaded gray represent the crisis periods (i.e., CC = 1).
be further associated: accuracy = (TP + TN)/(TP + FP + FN + TN); precision = TP/(TP + FP); sensitivity = TP/(TP + FN).Accuracy measures what percentage of the observations are correctly estimated; precision measures what percentage of crisis signals are correct; sensitivity determines what percentage of crises have been correctly identified.

Table 1 .
Explanatory variables.ΔlnðFCLS t Þ Log-return of the futures contracts on trading day t based on the average closing price (in week t, in month t). 10 Open interest of futures lnðFOI t Þ Log of the total open interest of the futures contracts on trading day t (at the end of week t, at the end of month t).Trading volume of futures lnðFVOL t Þ Log of the total trading volume of the futures contracts on trading day t (in week t, in month t).Trading amount of futures lnðFAMT t Þ Log of the total trading amount of the futures contracts on trading day t (in week t, in month t).Futures arbitrage basis ðBASIS t Þ Difference between the futures contracts' closing price and the stock index closing price on trading day t (in week t, in month t).Volatility indexðVIX t ÞWeighted average of the options implied volatility on trading day t (in week t, in month t). 11Return of calls ΔlnðCCLS t Þ Log-return of the call option contracts on trading day t based on the average closing price (in week t, in month t).

Open interest of calls lnðCOI t Þ Log of the total open interest of the call option contracts on trading day t (at the end of week t, at the end of month t). Trading volume of calls lnðCVOL t Þ Log of the total trading volume of the call option contracts on trading day t (in week t, in month t). Trading amount of calls lnðCAMT t Þ Log of the total trading amount of the call option contracts on trading day t (in week t, in month t). Effective spread of calls ðCSPD t Þ The difference between the closing price of call options and the listing base price on
trading day t (in week t, in month t).12Return of puts ΔlnðPCLS t Þ Log-return of the put option contracts on trading day t based on the average closing price (in week t, in month t).Open interest pf puts lnðPOI t Þ Log of the total open interest of the put option contracts on trading day t (at the end of week t, at the end of month t).Trading volume of puts lnðPVOL t Þ Log of the total trading volume of the put option contracts on trading day t (in week t, in month t).Trading amount of puts lnðPAMT t Þ Log of the total trading amount of the put option contracts on trading day t (in week t, in month t).Effective spread of puts ðPSPD t Þ

Table 2 .
Sample periods and data sources.

Table 3 .
Descriptive statistics of the main variables.

Table 4 .
Principal component eigenvalues and contribution rates based on daily data of CSI 300 index futures (local: April 16, 2010-April 29, 2011).

Table 6 .
Predicted values of CC based on daily data of CSI 300 index futures (local).

Table 7 .
Predicted values of CC based on daily data of SSE 50 ETF call options (local).

Table 8 .
The confusion matrix.

Table 9 .
Compare the predictive power of derivatives models and the traditional model.To evaluate the performance of our models, we adopt two types of measurement: the goodness-of-fit, such as accuracy and F2 value; and credit-score calibrations, such as the area under the curve (AUC) and quadratic probability score (QPS) value.Accuracy = (TP + TN) / (TP + FP + FN + TN); precision = TP / (TP + FP); sensitivity = TP / (TP + FN); F2 = (2 × 2 + 1) × precision × sensitivity / (2 × 2 × precision + sensitivity).Accuracy measures what percentage of the observations are correctly estimated; precision measures what percentage of crisis signals are correct; sensitivity determines what percentage of crises have been correctly

Table 10 .
The predictive power of CSI 300 index futures contracts with different maturities.

Table 11 .
The predictive power of SSE 50 ETF options contracts with different maturities.

Table 12 .
The predictive power of SSE 50 ETF options contracts with different moneyness.

Table 13 .
An alternative definition of stock market crises.Accuracy measures what percentage of the observations are correctly estimated; precision measures what percentage of crisis signals are correct; sensitivity determines what percentage of crises have been correctly identified;

Table 14 .
The performance of futures model based on pre-restriction and post-restriction samples.

Table 15 .
Employ machine learning techniques to predict stock market crises.