Master thesis – Business Economics: Finance
The Circuit Breaker in Chinese Stock Market:
The Impact on Option Price Volatility
Student Name: Qinyuan Pei
Student Number: 10435948
Thesis supervisor: Dr. P.J.P.M. (Philippe) Versijp
July 2016
1
Statement of Originality
This document is written by Student Qinyuan Pei who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it.
The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
2
PREFACE AND ACKNOWLEDGEMENTS
The motivation for me to write this thesis was the sudden termination of circuit breaker in Chinese stock market. This regulatory instrument was implemented in China for the first time; many scholars have conducted studies on foreign mature markets, such as the U.S and Japan. This fresh news raised my interests to mimic a study on Chinese security market. The learning process of writing a Master level thesis has proven to be valuable for me. I would like to thank both the university as well as my supervisor who taught me how to properly conduct academic research and think critically. I will always be ready to learn new skills with a critical mind; the same applies for life outside of academics. Thank you all for your guidance and assistance over the past one year.
3
Content
1. Introduction ... 5 2. Literature Review ... .. 8 2.1 Circuit Breakers ... 8 2.2 Price Limits... 122.3 Stock Index Options... 13
2.4 “T+1” Trading Restriction ... 14
2.5 Black Sholes Pricing Model ... 15
3. Methodology ... 17 3.1 Historical Volatility ... 17 3.2 Regression Models ... 18 4. Data ... 21 4.1 Option Data ... 21 4.2 Stock Data ... 22
5. Regression results and Interpretations ... 23
6. Conclusion ... 38
Bibliography ...40
4
Abstract
From the perspective of electrical engineering, a “circuit breaker” is a tool to shut down electricity when it exceeds the capacity; in other words, a circuit breaker is a switching button to control the maximum volume of electrical activity. On the financial market, circuit breakers are designed to moderate market volatility by halting trading when a big price swing occurs. The breakers are triggered when prices reach certain pre-established thresholds and the market will halt trading automatically for a short period of time. Numerous countries adopt this regulatory instrument to address market imperfection. The attractiveness of circuit breakers motivated the research carried out in this paper.
Following the stock market crash in 1987, various countries imposed circuit breakers on their financial markets, with the intention to protect the market from speculation behaviors. Rapidly falling prices may raise panic amongst market participants and create execution uncertainty. A circuit breaker provides a cooling-off time for investors to re-evaluate market information and reformulate investment strategies. However, no theoretical or empirical studies have concluded that circuit breakers have the desired effect on lowering market volatility. In fact, the effectiveness of the instrument is disputed by researchers. In September 7th 2015, the China Securities Regulatory Commission (CSRC) announced that circuit breakers would be imposed on China’s A-stock market, starting from January 1st 2016. However, the instrument was suspended after four trading days. The usefulness of circuit breakers on China’s stock market was doubted by many. Using data from China’s stock and option markets, this paper extends existing literature in two ways. First, it was the first time to impose circuit breakers on China’s stock market; very few researches have studied circuit breaker effectiveness on the Chinese market. Second, most papers intend to examine the impact of circuit breakers on stock market volatility, while this paper will approach the issue differently, namely on option market volatility. Thus, we attempt to provide two empirical evidences: a) circuit breakers have a positive effect on reducing option volatility; b) the affection of circuit breakers differs between options.
5
1. Introduction
Circuit breakers, a tool to shut down security transactions in financial market, are designed to moderate market volatility by halting trading when a big price fluctuation occurs. Two pre-determined thresholds function as switching buttons to control the maximum or minimum trading prices. When breakers are triggered, trading automatically stops for a short period of time. Market participants will make use of this time period to re-evaluate their strategies.
Following the 1987 stock market crash, committees aiming to reduce volatility and stabilize the market adopted several circuit breakers. Numerous countries have adopted the instrument to address market imperfection. However, the effectiveness of circuit breakers is disputed. Some argue that circuit breakers offer cooling-off time for investors to respond during huge price fluctuations on a stock market. Others suggest that circuit breakers bring panic to a market. Many academics hold that circuit breakers are guilty until proven innocent (Pagan, 1990).
From Bruce and Jeremy (1991)’s point of view, value buyers are the ones who could avoid market falling because they only chase attractive and worthy opportunities. When the market prices start to become unstable, value buyers may hesitate to place orders because of the transactional risk; they won’t have any idea about the prices at which their order will be executed. Their paper argues why the stock market needs circuit breakers: because market shocks will aggravate panic for investors, both psychologically and behaviorally. To prevent markets from overreacting to fluctuations, a circuit breaker will provide a cooling-off time for investors to re-consider. According to Bruce and Jeremy (1991), circuit breakers are not intended to prevent a rapid, fundamental price adjustment, but rather to facilitate the price by reducing transactional risks and thereby encouraging value buyers to bring their demands back to the market.
The Chinese stock market has seen an incredible growth during the last five years. On the 1st of January 2016, a circuit breaker was applied for the first time on the A-share market. After Chinese A-stock price triggered the 7 percent threshold two times in four trading days, circuit breaker rule was suspended by the CSRC. The China Securities Regulatory Commission
6 (CSRC) announced that the circuit breaker would be suspended from the 8th of January 2016. Most of the economics experts have suggested that the threshold values (5 percent and 7 percent) need to be renegotiated. It is noteworthy that there was a so-called 10 percent price limit for all stocks on the A-Share market. However, foreign stock markets such as the United States do not have this threshold for protection. Moreover, the U.S. stock market provides the most effective delisting mechanism.
Great attention has been given to the effectiveness of circuit breakers. The termination shocked investors and raised panic among stock market participants. Circuit breakers are implemented directly on China’s A-share stock market; the affection of it on the stock market is certain, whether positive or negative. Considering the interrelation of the stock market and option market, we would like to examine whether there is a positive / negative impact on option volatility.
Among the existing studies on the performance of market-wide circuit breakers, the common barrier was the lack of a dataset. For example, since the implementation of circuit breakers on the New York Stock Exchange (NYSE), it was triggered only once in history. Trading data on that single day was not sufficient to examine the performance of circuit breakers. The same issue arises in this paper. Since the circuit breaker mechanism was imposed only during four trading days, the data set of four days will necessarily limit our investigation. Thus, the pre-announcement and post-announcement trading data will also be included in this paper.
In this case, the examined subject will be 162 trading days instead of four. The time period will be divided into three sub-periods: (1) Pre-announcement, starting July 23rd 2015 and ending September 6th 2015. (2) Post-announcement and post-implementation, starting September 7th 2015 and ending January 8th 2016. (3) Post-termination, starting January 9th 2016 and ending March 23rd 2016.
According to a study from Yizhou and Zhenlong (2009), based on Hang Seng Index (HIS) options, it can be concluded that the larger the trading volume of options, the more information implied volatilities will contain, and the stronger prediction power does implied volatility have. However, Santoni and Liu (1993), who have tested the volatility changes
7 following the adjustments in circuit breaker rules, suggest that the imposition of circuit breakers does not have a significant impact on volatility.
This paper has a contrary hypothesis compared to the study above. By calculating the standard deviation (a proxy of volatility) of stock and option prices; running panel regressions between option volatility and CB dummies with other relevant factors and fixed effects; adopting data from the CSI 3001 Index stock market and stock index option market. We intend to estimate two hypotheses: a) circuit breakers have a positive effect on reducing option volatility; b) the affection of circuit breakers differs between options.
The main hypothesis in this paper is that circuit breakers can moderate option market volatility. We add a CB dummy variable in the regression, in which the dummy equals 1 from September 7th 2015 until January 8th 2016, and 0 otherwise. We assume that when the dummy equals 1, the coefficient is negative. That means the existence of circuit breakers decreases market volatility. The regression results show significant evidence that circuit breakers help to decrease option volatility, which is consistent with this hypothesis. The additional hypothesis is that the affection of circuit breakers varies between options, ceteris paribus. Thus, our option datasets include five options with the same time to maturity but different strike prices. Ultimately, we have failed to provide enough evidence for this hypothesis; the regression results show that it is hard to capture a relationship between option volatility and option strike prices in this paper.
The structure of this paper will be organized as follows: Section 2 will discuss relevant papers and research from various perspectives, as well as instructions of background knowledges. Section 3 will introduce the methodology in this paper and section 4 will show datasets. In section 5, panel regression results and analysis will be included, while the conclusions will be in section 6.
1 The CSI 300 is a capitalization-weighted stock market index designed to replicate the performance of 300 stocks traded in the Shanghai and Shenzhen stock exchanges.
8
2. Literature review
2.1 Circuit BreakersOn the financial market, circuit breakers are designed to moderate market volatility by halting trading when a big price swings occurs. The fundamental purpose of a circuit breaker is to re-inform participants by providing a breathing time. Large price swings may result when heavy volume is accumulated; the paperwork required to execute trades will rapidly increase. Circuit breakers allow the market to absorb heavy trading volume and offer a period of time for regulators to bring the market back to order.
The purpose of setting the circuit breaker mechanism is to reduce “waterfall risk”. Once a deduction starts more will follow, just like a waterfall. The “waterfall risk” is caused by unexpected market risks or other accidental factors that lead to a price move. During a period of time the market is likely to enlarge the risk inertia and volatility; price changes will inevitably bring higher risks to the market and psychological panic to investors. Circuit breakers ensure that when the threshold is reached, price fluctuations will slow down and prices halt automatically; in this case, information can be fully and timely delivered, the reaction time will be sufficient for regulators to stabilize the market. From the perspective of investors, they will have the chance to re-evaluate their investment decisions, in order to reduce their losses to a minimum.
Various controversies are vehemently discussed among circuit breakers researchers. Opinions from previous studies demonstrate the potential benefits of circuit breakers. Research from Christie, Corwin and Harris (2002) found that circuit breakers might improve the efficiency of information transmission and reduce information asymmetry. Kodres and O’Brien (1994) argue that informed traders are more likely to withdraw their capital when noise trades cause price swings, because market price execution uncertainty has increased in this case. They also found that circuit breakers can promote trading on markets. Before the movements of prices, investors can execute desired trades. Westerhoff (2003) argued that circuit breakers may have a beneficial effect on reducing price deviations if traders prefer to chase trends. Therefore, setting up price thresholds may protect markets from speculation. Market participants will acquire time and information to perform a re-evaluation.
9 Circuit breakers improve market efficiency and performance by providing re-evaluation time for participants. Consequently, they moderate market volatility and provide an orderly market. Other theoretical researches have also provided evidence that circuit breakers can positively affect market price movements. For example, Greenwald and Stein (1991) suggest that a trading pause can play a decisive role in reducing panic and transaction risk. Panic and risk are certain to rise, since the execution price is not predictable and uncertain. They have also concluded that the role of a circuit breaker is to balance the relationship between trade and information disclosure, as well as to reduce transaction risk. As they note: “the basic purpose of any circuit breaker should be to reduce transactional risk in an effort to stimulate value-buyer responsiveness” (1991, p. 458). When a heavy volume shock occurs, transaction risk and market panic increase rapidly and prices will fail to reflect information as they should.
Numerous countries have adopted circuit breakers in the past decades; their attractiveness and effectiveness are disputed continuously. Regulators of worldwide financial markets aim to promote the perfection of markets. In the United States, the motto of the Securities and Exchange Commission (SEC) is to provide market participants a fair, orderly and efficient market and, as a consequence, a developed and healthy worldwide economy. Market efficiency has two perspectives according to the SEC. First, if trading can be transacted at a low cost, with fast speed and minimum error probability, a market can be marked as operationally efficient. Second, a market is informationally efficient if information can be delivered quickly and accurately. When investors are fully informed they will be able to allocate capital rationally and efficiently on a fair market.
Alternatively, Kim and Sweeney (2002) concluded that circuit breakers may set barriers and hinder market efficiency. Opponents also suggest that circuit breakers fail to achieve the objective; they introduce unnecessary and artificial barriers. As a matter of fact, asset prices information content include all publicly available data, therefore, any artificial movements may have impact on market prices. Circuit breakers may also have an impact on ex ante investment decisions of market participants and, as a consequence, market price volatility. When panic is raised among investors, people may mimic others’ trading decisions, which will increase uncertainty on the market. In terms of this phenomenon, Subrahmanyam (1994) described it as “magnet effect”. Thus, when the price rises or drops near to the
10 thresholds, agents are forced to execute transactions in advance before trading halts, which will lead to an increase of market volatility. Furthermore, informed traders may reduce their expectations when circuit breakers are triggered, leading to higher transaction costs for uninformed investors.
The report from Ackert, Church, and Jayaraman suggests that the movements of future prices are not fully affected by the existence of circuit breakers; information content on the market will determine the price movements. They concluded that circuit breakers accelerate trade while setting up boundaries to price discovery, because market regulators always want to guide trades before circuit breakers are triggered.
On October 19th 1987, Wall Street’s stock market crashed. The Dow Jones Industrial Average (DJIA) dropped sharply by hundreds of points after opening in the morning; until the end of the trading day the Dow Jones Industrial Average (DJIA) was subject to a decrease of 554 points (7.2 percent). The aggregate loss of market value that day amounted to $503 billion. Soon afterwards, the crash raised panic throughout the whole market. Investors tried to get rid of stocks on hand as fast as possible, a selling frenzy that formed the direct cause of the paralysis of the technology trading system. Thus, a global stock market crisis was triggered. In 1987, the Brady Commission report was introduced. In the report, portfolio insurance and index arbitrage were defined as the causes of the crash and the adaptation of circuit breakers was considered as one of the most efficient methods to ease market fluctuations as much as possible. At the first anniversary of the stock market crash, on October the 19th 1988, the New York Stock Exchange introduced circuit breakers. The current circuit breaker rule set up the thresholds based on the Dow Jones Industrial Average (DJIA), a computation based on Standard and Poor’s 500 stock index (S&P 500). The S&P 500 is widely used as a benchmark in derivative markets.
The effectiveness of circuit breaker rules varies from country to country and from market to market, and it reflects the rational decision of market regulators. The Chinese economy has grown significantly with the beginning of reform and opening up in China. The international status of China has evolved during the last decades. Chinese governors intend to sustainably develop the financial market, establishing a fair and favorable field for investors. Most of the participants on China’s security market are small investors.
11 Circuit breakers are one of the trading curbs that the China Securities Regulatory Commission (CSRC) uses to curb the effects of overreaction from market participants. A circuit breaker was first known as a switch that shuts down electrical liquidity when it reaches a system’s capacity in electrical engineering. After going through the stock market crash in 1987, Brady (1988) suggested a circuit breaker to prevent market fluctuation.
According to relevant provisions, the circuit breaker mechanism uses the Shanghai and Shenzhen 300 index (CSI 300) as a benchmark, and set ±5% and ±7% as two fusing thresholds. Thresholds determine fusing time. When the 5% threshold is triggered, trading will be paused for 30 minutes, after which it will resume; when the 5% threshold is triggered after 14:30 and the 7% threshold at any time of the day, trading will be suspended until the market closes. Table1 shows a comparison between the U.S. and China, the regulation in the U.S. security market is loose compared to China. The threshold for closing the market is 20% in the U.S., which is much higher than 7% in China. However, circuit breakers only control intraday drop in the U.S., while in the Chinese system circuit breakers control both increase and decrease in intraday prices.
Table1. Market-wide Circuit breakers in the U.S. and China Circuit breakers in U.S., calculation based on S&P’s 500
7% intraday drop Trading halts for 15 minutes before 15:25, after that time the market closes. (once a day)
13% intraday drop Trading halts for 15 minutes before 15:25, after that time the market closes. (once a day)
20% intraday drop The market closes within the trading day. Circuit breakers in China, calculation based on the CSI 300 Index
5% intraday increase/decrease Trading halts for 30 minutes before 14:30, after that time the market closes. (once a day)
12
2.2 Price Limits
Circuit breakers are one of the regulatory instruments on China’s security market; another one is so-called “price limits”. Price limits are restrictions to prices, requiring trade prices to be within a certain range. When traders are unwilling to negotiate and their expected prices are beyond the range, trading will stop immediately. Trading can resume at any time once the agreed price is within the limited range.
In December 1996, the China Securities Regulatory Commission (CSRC) introduced Price Limits with a 10% threshold, intended to suppress irrational speculation behaviors. Heated debates have been fought out by domestic and foreign academic researchers for decades; they keep questioning whether price limits have practical effects on market stability. Supporters argue that price limits can stabilize the market by reducing price fluctuations and curb irrational investments on the stock market, thus contributing to the healthy development of the market.
A number of researchers hold the point of view that when sharp fluctuations occur in the market, this artificial price limit may destroy the market mechanism. In this case, market prices cannot reflect traders’ willingness on time, nor reduce price volatility. Papers from Greety and Mulherin (1992) suggest that circuit breakers cannot perform the role of stabilizing the market; they may increase market volatility somehow. Similar research conclusions also arose with Lee, Ready and Seguin (1994), Subrahmanyam (1994), and Goldstein and Kavajecz (2000).
When dramatic changes occur in the market, such as when contract prices decrease or increase by more than 10% in a very short period of time, and when the markets only rely on price limits, it will easily result in big losses and respective settlement risk, since investors do not have enough time reaction. The 10% threshold of price limits will alert investors about the risks before prices spin out of control. This mechanism can rationally evaluate market trends and potential systemic risks in order to provide enough time and information for market regulators and participants to react.
Opponents believe that the information can only be spread widely and divergently when there is a continuous trading. Therefore, price limits do not reduce information asymmetry,
13 but instead hinder the diffusion line information. Price limits will lead to an increase in information asymmetry and noise transactions. Peiyuan and Donghui (2001) analyzed the impact of price limits on volatility, using the daily data from the Shanghai and Shenzhen stock market, and concluded that price limits did not contribute to help reducing price volatility nor excessive behavior from investors. On the contrary, price limits draw a negative impact on normal trading activities. Xiaofeng, Xiaoguang and Cunzhi (2001) found that when the market is relatively small, price limits may help to reduce market price movements; but when the market size is getting larger, price limits will exacerbate the instability of the market instead of reducing fluctuations.
2.3 Stock Index Options
A stock index option (abbreviated as option in following texts) is a type of financial derivative that is more flexible, compared to other securities. It allows investors to buy or sell a certain amount of assets at a certain price in a certain time in the future. In other words, option contracts give rights to buyers buying or selling the underlying asset at an exercise price in the future. The option buyers can choose whether or not to exercise their rights in the option contract time, while the sellers of the option only have two rights: to receive payment from the sale of the option and to accept the obligation to exercise assigned at the expiration date of the option.
Option contracts can be divided into call option contracts and put option contracts. A call option is an agreement that gives an investor the right to buy an instrument at a pre-determined price within a pre-pre-determined time period. A put option is a contract that gives investors the right to sell an underlying security at a determined price within a pre-determined time period.
According to partitioning of the exercise time range, option contracts can also be divided into European option contracts and American option contracts. European options only allow exercising of the option at the maturity date. American options allow the buyer to exercise at maturity or any trading day prior to maturity. In order to simplify the investigation, only European call options will be considered in this paper. From the index options listed on the Chicago Stock Exchange (CBOE) there are two main forms: one is the American option with ETF as the underlying asset and T+3 ETF delivery; the other one is based on the stock index
14 known as European options, using T+0 cash instant delivery. After the 2008 economic crisis, global ETF trading volume increased significantly. ETF possesses characteristics from stock options and index options, and is welcomed by different types of investors and, as a consequence, its market size has grown rapidly.
There are three types of option varieties on the Chinese options market. While on some mature option markets abroad, such as the ones in the United States, Japan, the UK and other European countries, they have richer species and advanced systems. Options as a financial derivative play an important role in hedging risks. At present, around 51 species are launched on the Shanghai Stock Exchange, 34 on the Shenzhen Stock Exchange. The Shanghai and Shenzhen Exchange (SSE) 50 Index exchange-traded fund reflected the overall situation on the Shanghai stock market comprehensively: it contains 50 stocks with the best mobility.
2.4 “T+1” Trading Restriction
There are two organized stock exchanges located in Shanghai and Shenzhen. Most of the large and state-owned companies are listed on the Shanghai Securities Exchange (SSE), while small joint ventures and export-oriented companies are listed on the Shenzhen Securities Exchange (SZSE). According to C.K. Xu (2000)’s study on the microstructure of China’s stock market, only two types of orders exist: market orders and limit orders, both valid for one day. The trading floor is 100 shares per unit. Since there are brokers standing between traders, the (T+1) model was installed on China’s stock market that is contrary with the (T+0) model on the United States stock market, and there is no market maker to supervise stock prices by trading for his own account. “T+1” is a trading restriction on the Chinese stock market; it requires traders to wait at least until the next trading day to sell their stocks. “T” refers to the buy transaction date, “1” refers to the next trading day. At present, the “T+1” trading system was installed on China’s Shanghai Stock Exchange (SSE) and the Shenzhen Stock Exchange (SZSE). However, differently from China other major capital markets such as the U.S. adopt the T+0 trading system. The “T+0” system allows an investor to buy and sell a stock within one trading day. Hence, it is also known as the “day trading” system.
According to Kyle (1985), the “T+1” trading system reduces the liquidity of the assets. In Amihud and Mendelson (1986)’s study, illiquid stocks lead to increased transition costs; they
15 must have a higher expected return in order to attract investors. Chinese researchers Chung and Wei (2005) empirically tested Amihud and Mendelson (1986)’s theory on China’s A-share market and drew a consistent conclusion. Di and Wu (2008) compared the “T+1” trading system in China and the “T+0” system in capital markets abroad in their papers. They found that “T+0” improves the liquidity of the market, but does not have significant impact on reducing market volatility. However, Jie (2013) studied the same topic as Di and Wu (2008), but her subject is China’s stock index options listed on the Shanghai Stock Exchange (SSE) and the Shenzhen Stock Exchange (SZSE). She concluded that the “T+0” trading system improves the yield and significantly reduces the systemic risk and, as a consequence, moderates market volatility from a long term perspective. Yong (2009) included the GARCH model in his empirical research and in a different conclusion proved that stock market volatility tends to decrease when the “T+1” trading system is implemented on stock markets. Although “T+0” is welcomed by international countries it benefits security markets in increasing market liquidity. It has the constraint that the major participants on stock markets need to be institutions instead of individual investors. When one considers the current Chinese stock market structure most of the investors are individuals. In that case, if “T+0” is adopted on the Chinese stock market it will result in serious speculations and price manipulation phonemes, which is not conducive to the sustainable development of China’s stock market.
2.5 Black Sholes Pricing Model
Since the first options contract was listed in 1973, options are welcomed by investors as derivatives of speculation and a risk aversion tool. As the broad application of options, researchers have put effort in exploring option pricing models, producing a series of option pricing theories. Among those theories the most influential one was introduced by Fisher Black and Myron Scholes in 1997, called the Black-Scholes Pricing Model. This model has been agreed to be the most successful model in the field of applied economics and has won Scholes the 1997 Nobel Prize in Economics.
The ideas behind the Black Scholes Pricing Model assume that stock prices follow the Geometric Brownian Motion (GBM) and stock option prices at maturity logarithm obey normal distribution. On the basis of a series of assumptions, an investment portfolio
16 including stocks and its derivatives is constructed in the Black Scholes Pricing Model. In the combination, the gains of two positions are highly negatively correlated; in any short period of time, profit (loss) of stocks offsets the loss (profit) of derivatives. Since the portfolio is a risk free combination, the yield of the portfolio in a short time interval is equal to the risk-free interest rate, without risk-risk-free arbitrage. The Black Sholes Pricing Model Formula shows as follows: 𝐂 = 𝐒𝐍 (𝐝𝟏) − 𝑲𝒆−𝒓(𝑻−𝒕)𝑵(𝐝𝟐)（1） 𝐝𝟏 = 𝒍𝒏(𝑺/𝑲) + (𝒓 + 𝝈 𝟐 𝟐 ⁄ )(𝑻 − 𝒕) 𝝈√𝑻 − 𝒕 𝐝𝟐 = 𝐝 𝟏− 𝝈√𝑻 − 𝒕
C represents call the option price at time t, S represents the stock price at time t, K is the strike price, T is the expiration day, r is the risk-free interest rate from time 𝒕 until maturity, 𝝈 represents the volatility of option returns and N means that the model follows normal distribution. (1) is the Black Scholes Option Pricing Model (BS Model).
The Black Sholes Model shows that an option price at time t is a function about𝐒𝑡,𝑲, 𝒓, 𝑻
and 𝝈. Where𝐒𝑡,𝑲, 𝒓 and 𝑻 are known, when the market price of an option is given, the
underlying asset’s volatility can be estimated based on the option price. The estimated value, then, is the implied volatility. Black Sholes Model proves the rationality of the second hypothesis in this paper, that, options with different strike price may have different option volatility.
17
3. Methodology
According to the study of Theodore and Craig (1992), it has been concluded that there is an interrelation between ex ante estimation of future market volatility and prices of call options on the Standard and Poor’s Index. Black Fisher‘s study also shows stock returns are negatively related to unexpected increase in volatility in 1976. This paper will mimic Theodore and Craig (1992)’s idea, examine the interrelation between circuit breaker and stock market volatility.
3.1 Historical volatility
In this paper, the historical volatility will be adopted instead of implied volatility. We are aiming at detecting the impact of circuit breaker in a passing time period instead of estimating the volatility of options in some point of future. Financial experts find the standard deviation efficient because it shows the potential possibility that extreme value of return occurs, the probability of large positive or negative return increases along with standard deviation. Hence, standard deviations of stock and option daily returns are used as the proxy of historical volatilities. The calculation formula reads as follows:
(𝜎̂)𝑡+1 2 = 1 𝑛 − 1 ∑ (𝑅𝑡− 𝑅)2 𝑡 𝑖=𝑡−𝑛 𝑅𝑖 = ln (𝑆𝑖⁄𝑆𝑖−1) 𝑅 = 1 𝑛 ∑ 𝑅𝑖 𝑡 𝑖=𝑡−𝑛 𝜎 = 𝜎̂√𝑡𝑟𝑎𝑑𝑖𝑛𝑔 𝑑𝑎𝑦𝑠 𝑖𝑛 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑦𝑒𝑎𝑟
𝑅𝑡 signifies the daily rate of return, 𝑆𝑖 the daily closing prices, n the number of trading days
18
3.2 Regression Models
3.2.1 Panel Regression Model 1
Yit = β0+ γ1CB + β1X1,it+ β2X2,it+ uit (1)
Yit- (Dependent variable) option volatility
CB- (Independent variable) Dummy variable equals 1 if trading date is between 7th of September 2015 to 8th of January 2016 and 0 otherwise.
X1,it- (Control variable) stock volatility X2,it- (Control variable) option volume
1) Dependent variable (Yit): index option price historical volatility. We use standard
deviation of daily rate of return as the proxy of index option price historical volatility, calculate as the square root of (daily return-mean of return) ^2. Daily index option price is daily closing price, which is the final price of a stock was traded on previous trading day. The closing price represents the most up-to-date valuation of a stock until trading commences again on the next trading day. Daily rate of return is overnight return measures the return generated by an option when the market is closed, based on its price change from the close of one trading day to the opening of the next trading day. 2) Independent variable:
1> Dummy variable (CB, abbreviation of circuit breaker), we define this dummy variable as the first independent variable in this model because of the hypothesis mentioned in the beginning of this paper: circuit breaker has a positive impact on index option (historical) volatility, circuit breaker indeed helps to moderate volatility in option market. In other words, dummy variable CB is also a control variable on time series. Time periods was split into three sub-periods in this paper: sub-periods (1) pre-announcement: starting July 23rd 2015 ending September 6th 2015. (2) Post-announcement and post-implementation: Starting September 7th 2015 ending January 8th 2016. (3) Post-termination: starting January 9th 2016 ending March 23rd 2016. In this case, dummy variable 𝐶𝐵 equals to 1 if trading date is between 7th of
19 September 2015 to 8th of January 2016 (option market was under the “protection” of circuit breakers), and 0 otherwise.
3) Control variables
1> Stock volatility (X1,it), we use standard deviation of stock daily return as the proxy of
stock historical volatility. Raw data of CSI 300 index stock trading information has the same periods as option from 23rd July 2015 to 23rd March 2016. Daily stock price rate of return is overnight return generated by a stock when the market is closed, based on its price change from the end of one trading day to the starting of the next trading day. We also use daily closing price of CSI 300 index stock to receive daily rate of return and its’ standard deviation is calculate as the square root of (daily rate of return-mean of return) ^2.
2> Option volume (X2,it), option daily trading volume is another potential factor that is
assumed to have influence on index option price (historical) volatility. Daily trading volume is the number of transactions of an option during the previous trading day. The unit of option daily trading volume is 1000 per unit.
4) Entity term (i), based on the original purpose, I would like to include strike price of option as another potential factor that will affect index option price volatility. So five options were picked up from raw data, these five options have same time to maturity but different strike prices. Moreover, five options increased the number of observations in the regression.
3.2.2 Panel Regression Model 2
Thus far we assumed that the effects for the CB dummy variable are equal for all data. However, the dataset in this paper consist five options; there are reasons to believe that the effects for the dummy variables vary for different options. In model2, we add four additional dummy variables and four interaction terms. We intended to examine whether the affection of circuit breaker varies between each option. Equation (2) as follow:
20 Yit = α1β2CB + β3X1,it+ β4X2,it+ α2d2+ α3d3+ α4d4 + α5d5
+γ1d6+ γ2d7+ γ3d8+ γ4d9+ uit (2) Yit - (Dependent variable) option volatility
CB - (Independent variable) Dummy variable equals 1 if trading date is between 7th of September 2015 to 8th of January 2016 and 0 otherwise.
X1,it- (Control variable) stock volatility
X2,it- (Control variable) option volume
d2 - (Dummy variable) Option_dummy2 equals to 1 if data belongs to option2 and 0
otherwise.
d3 - (Dummy variable) Option_dummy2 equals to 1 if data belongs to option3 and 0
otherwise.
d4 - (Dummy variable) Option_dummy2 equals to 1 if data belongs to option4 and 0
otherwise.
d5 - (Dummy variable) Option_dummy2 equals to 1 if data belongs to option5 and 0
otherwise.
d6 - (Interaction term CB * Option_dummy2) between CB and Option_dummy2 d7 - (Interaction term CB * Option_dummy3) between CB and Option_dummy3 d8 - (Interaction term CB * Option_dummy4) between CB and Option_dummy4 d9 - (Interaction term CB * Option_dummy5) between CB and Option_dummy5
21
4. Data
From previous academic study on circuit breaker, the common barrier for the data analysis was the lack of a dataset. For example, since the implementation of circuit breakers on the New York Stock Exchange (NYSE), it was triggered only once in history. Trading data on that single day was not sufficient enough to examine the performance of circuit breakers. The same issue arises in this paper. If a circuit breaker was suspended after four trading days the dataset would be too meagre for estimation. Because of this, the study in this paper will examine the impact of circuit breakers on option volatility, starting from the day it was announced. History data was collected from Shanghai Exchange, selecting trading data from 23rd of July 2015 to 23rd March 2016. Statistical description summary of the dataset can be found in the Appendix.
4.1 Option Data
This paper performs a selection of European call (stock index) option data. According to the Black Sholes model mentioned in the previous part, the strike price and time to maturity have potential influence on option volatility. The time to maturity will not be considered in this paper, since time periods are unchangeable in this paper because of the circuit breaker rule. In order to receive stronger proof for the investigation, five sets of European call (stock index) option data 2with same time of maturity but different strike prices3 were picked up from the dataset. Each dataset has 162 observations from 23rd of July 2015 to 23rd March 2016, including basic daily trading information: date, opening price, closing price, highest and lowest price, trading volume, Vega etc. Thus, in total, the observation of option data is 810. The standard deviation of daily rate of return is used to measure the historical option volatility, calculated as the square root of (daily return-mean of return) ^2.
Option trading volume is the number of transactions of an option during the previous trading day. Some studies conclude that trading volume has a direct impact on volatility, and that trading volume increases as the market becomes more efficient. Valued buyers and sellers
2
The five index option codes are 10000287, 10000288, 10000289, 10000290, and 10000291, their strike pieces are 2.65, 2.7, 2.75, 2.8 and 2.85. They are listed on Shanghai Exchange from 23rd of July 2015 to 23rd March 2016.
3 The index options strike price is the price at which a contract can be exercised; it is fixed in the contract. For call options; the strike price is the case when the option can be bought until the expiration date.
22 bring demands to an efficient market. In this paper, option volume is set as one of the variables that are assumed to have effect on option price volatility.
4.2 Stock Data
There are 162 observations in the stock dataset from 23rd of July 2015 to 23rd March 2016. The information includes the daily closing price, which is the final price of a stock that was traded on the previous trading day. It represents the most up-to-date valuation of a stock until trading commences again on the next trading day. The daily stock return is the overnight return generated by a stock when the market is closed, based on its price change from the end of one trading day to the start of the next trading day. The trading volume is the number of transactions of a stock during the previous trading day. The highest and the lowest price each day are included in the dataset as well. The standard deviation of daily stock return is used to measure the stock price volatility, calculated as the square root of (daily return-mean of return) ^2.
23
5. Regression results and Interpretations
5.1 Panel Regression Model 1Yit = β0+ γ1CB + β1X1,it+ β2X2,it+ uit (1) Yit- (Dependent variable) option volatility
CB- (Independent variable) Dummy variable equals 1 if the trading date is between 7th of September 2015 and 8th of January 2016 and 0 otherwise.
X1,it- (Control variable) stock volatility
X2,it- (Control variable) option volume
Table2-1 shows the regression analysis controlled by date and option fixed effects, aiming to estimate the relation between option volatility and circuit breakers affection during the time period from 23rd July 2015 to 23rd March 2016. The dataset is based on daily data of stock index option data and daily CSI 300 Index data. The dependent variable is option volatility, which is defined as the standard deviation of option daily rate of
Table 2-1 (1) (2) (3) (4) CB -5.7*** -2 -1.3 -1.5 (-6.4) (-.4) (-.27) (-.31) Stock volatility 4.5 4.5 (1.2) (1.2) Option volume . 00033 (.21) _constant 14*** 6.2* -1.4 -1.3 (22) (1.8) (-.31) (-.31) Fixed effects
Date fixed effects No Yes Yes Yes
Option fixed effects
No Yes Yes Yes
Observations 810 810 810 810
R-square 0.0483 0.7159 0.7159 0.7159
24 return. The independent variable is CB (dummy variable) which equals 1 if the trading date is between 7th of September 2015 and 8th of January 2016, and 0 otherwise. Control variables are stock volatility and option volume. Standard deviation of daily rate of return is considered as the proxy of stock volatility in this paper. Statistical significance at the 10%, 5% and 1% levels is indicated by *, ** and *** respectively.
Model1 represents a multiple regression model with option stock volatility, option volume and dummy variable CB. We present the regression in two ways: Table 2-1 shows results with both date and option fixed effects, Table 2-2 shows results only controlled by option fixed effects.
In Model 1 we present a model in which we test whether: a) circuit breakers have a positive effect on reducing option volatility. We estimate all parameters simultaneously because that leads to us the ‘controlled’ effects. With both date and option fixed effects controlled, Table 2-1 shows the fact that option volatility increases as the level of stock volatility is higher. Furthermore, we found that circuit breakers have a positive effect on volatility, which is consistent with the hypothesis. The coefficients of dummy variable (CB) are negative in all circumstances. This means that when the dummy variable equals one, the dependent variable option volatility decreases.
The outcomes of Equation (1) are presented in Table 2-1. As expected, option volatility is somewhat lower now, after taking into account other relevant factors, of which a circuit breaker is the most important. After controlling, a circuit breaker has a negative coefficient of -2 points, which is much lower than -5.7. Concerning the interpretation of the parameters for the dummy variable in Table 2-1, one could argue that they always reflect the deviation from the reference category of the original variable, after controlling for relevant other variables. Hence, we conclude that fixed effects have effective impact on the regression. The coefficients of a circuit breaker become lower after taking into account the relevant other factors. Table 2-1 ends with the value for a constant (also called ‘intercept’ in the literature), which takes the value 14 under the circumstance of no fixed effects, while tabling the value 1.3 under the control of fixed effects.
Column (1) begins with the basic regression between option volatility (dependent variable) and a circuit breaker (dummy variable), without controlling fixed effects. The coefficient is -5.7, which means that, when the dummy variable equals 1, the volatility of option in the same time period will be 5.7 units lower. The table shows that the result is significant at the
25 1 percent confidence level. From Column (1) we can conclude that circuit breakers have a positive effect on option volatility or, in other words, circuit breaker moderate option volatility.
In Column (2) date and option fixed effects are added to the regression. The coefficient of the dummy variable decreases to -2 and is no longer statistically significant, meaning that, when the dummy variable equals 1, the dependent variable (option volatility) deceases by 2 units. The constant deceases from 14 to 6.2, the same as the significant level.
In Column (3) stock volatility is added to control the regression. The coefficient of stock volatility is 4.5. This means that stock volatility and option volatility are positively correlated. When stock volatility is increased by 1 unit option volatility will increase by 4.5 units. Unfortunately, the result is not significant enough to prove the hypothesis.
In Column (4) all relevant factors are included in the regression. Option volume seems to have an ignorable impact on option volatility. None of the results are significant anymore. From Table 2-1, we can conclude that option volatility and circuit breakers are strongly correlated in a negative way. One of the possible explanations is that circuit breakers indeed moderate option volatility. However, the coefficient is not significant enough to prove this explanation in this table. The economic effect of option volume is positive but very small. Option volatility is also positively correlated with stock volatility. In any case, the overall coefficient of determination(R-square) does not change much, which means results are not ideal and persuasive enough to prove the hypothesis.
26 Table 2-2 (1) (2) (3) (4) CB -5.7*** -5.7*** -4.9*** -5.3*** (-6.4) (-6.4) (-5.5) (-6) Stock volatility 2.4*** 2.2*** (6.7) (6) Option volume .0051*** (3.4) _constant 14*** 14*** 10*** 10*** (22) (13) (8.8) (8.6) Fixed effects
Date fixed effects No No No No
Option fixed effects No Yes Yes Yes
Observations 810 810 810 810
R-square 0.0483 0.0515 0.1017 0.1148
Table2-2 shows the regression analysis controlled by option fixed effects, aiming to estimate the relation between option volatility and circuit breakers affection during the time period from 23rd July 2015 to 23rd March 2016. The dataset is based on daily data of stock index option data and daily CSI 300 Index data. The dependent variable is option volatility, which is defined as the standard deviation of option daily rate of return. The independent variable is CB (dummy variable) which equals 1 if the trading date is between 7th of September 2015 and 8th of January 2016, and 0 otherwise. Control variables are stock volatility and option volume. Standard deviation of daily rate of return is considered as the proxy of stock volatility in this paper. Statistical significance at the 10%, 5% and 1% levels is indicated by *, ** and *** respectively.
Table 2-2 shows the results with option fixed effects only. We estimate all parameters simultaneously without date fixed effects. Table 2-2 shows the fact that option volatility increases as the level of stock volatility is higher. The coefficients of the dummy variable (CB) are negative in all circumstances, which means when the dummy variable equals one, the dependent variable option volatility decreases. Furthermore, we found that option volatility and the dummy variable are negatively correlated, meaning circuit breakers have a positive effect on volatility. This is in compliance with the hypothesis.
The outcomes of Equation (1) without date fixed effects are presented in Table 2-2. As expected, option volatility is somewhat lower now after taking into account other relevant factors, of which the circuit breaker is the most important. After controlling, the circuit
27 breaker has a stable negative coefficient. Concerning the interpretation of the parameters for the dummy variable in Table 2-2, one could remark that they always reflect the deviation from the reference category of the original variable, after controlling for relevant other variables. Hence, we conclude that option fixed effects have effective impact on the regression. The coefficients of the circuit breaker stay relatively the same after taking into account the relevant other factors. Table 2-2 ends with the value for a constant (also called ‘intercept’ in the literature) that takes the value of 14 under the circumstance of no fixed effects, while taking the value of 10 under the control of option fixed effects. R-square value increases as by adding up other relevant control variables, meaning that the explanation level of this model increases significantly.
Column (1) begins with the basic regression between option volatility (dependent variable) and the circuit breaker (dummy variable), without controlling fixed effects. The coefficient is -5.7, which means that, when the dummy variable equals 1, option volatility in the same time period will be 5.7 units lower. The table shows that the result is significant at the 1 percent confidence level. From Column (1) we can conclude that circuit breakers have a positive effect on option volatility, in other words, circuit breaker moderate option volatility. In Column (2) option fixed effects are added to the regression. The coefficient of the dummy variable stays the same and is still statistically significant at the 1 percent confidence level. Comparing this to Table 2-1, while taking the date fixed effect out of consideration; the regression result seems more significant and efficient in explaining hypothesis.
In Column (3) stock volatility is added to control the regression. The coefficient of stock volatility is 2.4 and significant at the 1 percent confidence level. This means that stock volatility and option volatility are positively correlated: when stock volatility is increased by 1 unit option volatility will increase by 2.4 units. Both independent variables and constant are significant in Column (3) without the control of a date fixed effect.
In Column (4) all relevant factors are included in the regression. Option volume seems to have small impact on option volatility, because the coefficient is 0.0051 compared to other control variables. However, the coefficient of option volume is significant at the 1 percent confidence level. The impact of option volume on option volatility is small but cannot be ignored.
28 From Table 2-2 we can find that option volatility and circuit breaker are strongly correlated in a negative way. The economic effect of option volume is positive but very small. Option volatility is positively correlated with stock volatility as well. The overall significant level of results in Table 2-2 is much higher than in Table 2-1. The difference between them is whether or not we choose to control the date fixed effect, meaning that the change of time series has influence on control variables in this model.
5.2 Panel regression model 2
Yit = α1β2CB + β3X1,it+ β4X2,it+ α2d2+ α3d3+ α4d4 + α5d5
+γ1d6+ γ2d7+ γ3d8+ γ4d9+ uit (2)
Yit- (Dependent variable) option volatility
CB- (Independent variable) Dummy variable equals 1 if the trading date is between 7th of September 2015 to 8th of January 2016 and 0 otherwise.
X1,it- (Control variable) stock volatility
X2,it- (Control variable) option volume
d2 - (Dummy variable) Option_dummy2 equals to 1 if data belongs to option2 and 0
otherwise.
d3 - (Dummy variable) Option_dummy2 equals to 1 if data belongs to option3 and 0 otherwise.
d4 - (Dummy variable) Option_dummy2 equals to 1 if data belongs to option4 and 0 otherwise.
d5 - (Dummy variable) Option_dummy2 equals to 1 if data belongs to option5 and 0 otherwise.
d6 - (Interaction term CB * Option_dummy2) between CB and Option_dummy2 d7 - (Interaction term CB * Option_dummy3) between CB and Option_dummy3
29 d8 - (Interaction term CB * Option_dummy4) between CB and Option_dummy4
d9 - (Interaction term CB * Option_dummy5) between CB and Option_dummy5
Table 3-1 coefficients Standard error t-value p-value (2-tailed) Main effects _constant 9.87 1.49 6.61 0.000 Option_dummy1 Reference Option_dummy2(𝑑2) .428 1.97 0.22 0.82 Option_dummy3(𝑑3) -1.03 1.97 -0.52 0.602 Option_dummy4(𝑑4) 2.41 1.97 1.22 0.222 Option_dummy5(𝑑5) 1.54 1.97 0.78 0.434 CB (𝑑1) -4.81 1.94 -2.48 0.013 Stock volatility (𝑋1) 2.16 .36 6.00 0.000 Option volume(𝑋2) .005 .0015 3.49 0.001 Interaction effects CB (𝑑1)* Option1 Reference CB (𝑑1)* Option2(𝑑6) -.809 2.75 -0.29 0.768 CB (𝑑1)* Option3(𝑑7) 1.258 2.74 0.46 0.647 CB (𝑑1)* Option4(𝑑8) -2.21 2.75 -0.80 0.421 CB (𝑑1)* Option5(𝑑9) -.917 2.75 -0.33 0.739
Thus far, we assumed that the effects for the dummy variables are equal for all data. However, the dataset in this paper consist of five options; there are reasons to believe that the effects on the dummy variables vary for different options. In this paper we use interaction to represent categories when effects differ across groups. In Table 2-1 and Table 2-2 we present the outcomes of two separate regression analyses: one in which both date and option fixed effects were controlled, while the other only had option fixed effects included. As a result, we get estimates for the effects of circuit breakers on options. In order to estimate if circuit breakers have different impact on each option, we will generate
30 interaction terms to represent the affection later in this section. Table 3-1, therefore, serves mainly as a didactical tool to show the interactions.
In Equation (2) the first line is a combination of Model 1. The second line holds the so-called ‘interactions’ and consist of multiplications of the dummy variables. Different than with Model 1 we treat the five options as five individuals instead of one combined subject. In the dummy variable d2 the code 1 stands for option2 while for other options the code is 0; in
variable d3 the code 1 stands for option3, while for other options the code is 0; in variable d4
the code 1 stands for option4, while for other options the code is 0; in variable d5 the code 1
stands for option5, while for other options the code is 0. Option1 is treated as the reference and is not included in the regression model. It is noteworthy that in Equation (2) there are interaction terms. We generate them in order to estimate the effect of circuit breakers on each option. For instance, d6 represents the interaction between a circuit breaker and
option2; d7 represents the interaction between a circuit breaker and option3; d8 represents
the interaction between a circuit breaker and option4; d9 represents the interaction
between a circuit breaker and option5. Once more, the interaction between the circuit breaker and option1 is treated as the reference and is not included in the regression model.
Table 3-2 (1) (2) (3) (4) (5) (6) Main effects CB (𝑑1) -5.7*** -2 -1.3 -1.5 -1.5 -1.6 (-6.4) (-.4) (-.27) (-.31) (-.31) (-.33) Stock volatility (𝑋1) 4.5 4.5 4.5 4.5 (1.2) (1.2) (1.2) (1.2) Option volume(𝑋2) .00033 .00033 .0005 (.21) (.21) (.31) Option_dummy2(𝑑2) .33 .43 (.38) (.34) Option_dummy3(𝑑3) -.37 -1.2 (-.43) (-.99) Option_dummy4(𝑑4) 1.4 2.2* (1.6) (1.7) Option_dummy5(𝑑5) 1.4 1.5 (1.6) (1.2)
31 Table3-2 shows the regression analysis controlled by date and option fixed effects, aiming to estimate the relation between option volatility and circuit breakers affection during the time period from 23rd July 2015 to 23rd March 2016. In this table, additional dummy variables are generated to examine interaction effects between a circuit breaker and options. The dataset is based on daily data of stock index option data and daily CSI 300 Index data. The dependent variable is option volatility, which is defined as the standard deviation of option daily rate of return. The independent variable is CB (dummy variable) which equals 1 if the trading date is between 7th of September 2015 and 8th of January 2016, and 0 otherwise. Control variables are stock volatility and option volume. Standard deviation of daily rate of return is considered as the proxy of stock volatility in this paper. Statistical significance at the 10%, 5% and 1% levels is indicated by *, ** and *** respectively.
The same as in Model1 we present Model2 in two ways: one is controlled by both date and option fixed effects, with regression results shown in Table 3-2; the other one will be controlled by option fixed effects only. We will find out the efficiency of date fixed effects by comparing these two tables.
In this model we test whether: a) circuit breakers have a positive effect on reducing option volatility; b) does the impact of a circuit breaker differ between options. Both of these two hypotheses are controlled by date and option fixed effects. As we can see from Table 3-2 all the coefficients of the dummy variable (circuit breaker) are negative, although they are not significant enough. Nevertheless, it means that, when the dummy variable equals 1 option volatility decreases. The results for interaction terms give the answer to the second
Interaction effects CB (𝑑1)* Option2(𝑑6) -.22 (-.12) CB (𝑑1)* Option3(𝑑7) 1.7 (.96) CB (𝑑1)* Option4(𝑑8) -1.5 (-.87) CB (𝑑1)* Option5(𝑑9) -.15 (-.088) _constant 14*** 6.2* -1.4 -1.3 -1.3 -1.4 (22) (1.8) (-.31) (-.31) (-.31) (-.31) Fixed effects
Date fixed effects No Yes Yes Yes Yes Yes
Option fixed effects No Yes Yes Yes Yes Yes
Observations 810 810 810 810 810 810
32 hypothesis: the impact of circuit breakers differ between options. According to the results, there is not enough evidence to support this hypothesis. Because the coefficients of each interaction term are similar, adding them does not change other relevant factors such as stock volatility and option volume much. In any case, they are not significant enough at a certain confidence level, while controlled by date and option fixed effects.
Column (1) begins with the basic regression between option volatility (dependent variable) and a circuit breaker (dummy variable), without controlling fixed effects. The coefficient is -5.7, which means that, when the dummy variable equals 1, the option volatility of option in the same time period will be 5.7 units lower. The table shows that the result is significant at the 1 percent confidence level. From Column (1) we can conclude that circuit breakers have a positive effect on option volatility in this regression model as well. In other words, circuit breakers moderate option volatility.
In Column (2) date and option fixed effects are added to the regression. The coefficient of the dummy variable is decreased to -2 and not significant at any certain confidence level any more, meaning that if the dummy variable equals 1, the dependent variable (option volatility) decreases by 2 units. The constant decreases from 14 to 6.2, as does the significant level.
In Column (3) stock volatility is added to control the regression. The coefficient of stock volatility is 4.5. This means that stock volatility and option volatility are positively correlated. When stock volatility is increased by 1 unit, option volatility will increase by 4.5 units. Unfortunately, the result is not significant enough to prove our hypothesis.
In Column (4) option volume is included in the regression. It seems to have ignorable impact on option volatility because its coefficient is relatively small and not significant enough at a certain confidence level.
In Column (5) four dummy variables are included in the regression: Option_dummy2 (d2)
equals to 1 if the data belongs to option 2; Option_dummy3 (d3) equals to 1 if the data
belongs to option 3; Option_dummy4 (d4) equals to 1 if the data belongs to option 4;
Option_dummy5 (d5) equals to 1 if the data belongs to option 5. Once more, option 5 was
33 variables we would like to separate each option, instead of treating them as a combined dataset. According to the results in Table 3-2, all the coefficients of relevant factors stay unchanged compared to Column (4). The significant level in Column (5) still stays undetectable for all variables.
In Column (6) another four variables are added to the regression in our final stage. They are interaction terms intended to examine whether the effect of a circuit breaker differs between the five options. In order to determine the impact of a circuit breaker on each option, we generate interaction terms to see if there are interaction effects between the circuit breaker and each option data set. They are CB (d1)* Option2 (d6) equals to 1 if there
is interaction between a circuit breaker and option2; CB (d1)* Option2 (d7) equals to 1 if
there is interaction between a circuit breaker and option3; CB (d1)* Option4 (d8) equals to 1
if there is interaction between a circuit breaker and option4; CB (d1)* Option5 (d9) equals to
1 if there is interaction between a circuit breaker and option2. The interaction term of option1 and a circuit breaker was treated as the reference and was not included in the regression model. By adding these dummy variables we can see that the coefficients of other variables do not change much. Most of them stay the same, nor is the significant level of variables in this column undetectable.
To summarize, according to Table 3-2, we tested a) whether circuit breakers have a positive effect on reducing option volatility; b) does the affection of a circuit breaker differ between options. Based on the negative coefficients of the CB dummy variable (circuit breaker), we can conclude that option volatility and circuit breakers are strongly correlated in a negative way. In other words, circuit breakers indeed help to moderate option volatility. The results that are not controlled by any fixed effect are more significant than those controlled by date and option fixed effects, which means fixed effect controllership has an essential impact on our regression. Because of the lack of effectiveness and a significant level of interaction terms, we have to conclude that we failed to prove the second hypothesis in this model. This means that there is not enough evidence to prove that the affection of a circuit breaker differs between each option. Furthermore, the overall coefficient of determination(R-square) does not change much, which means results are not ideal and persuasive enough to comply with the hypothesis.
34 Table3-3 shows the regression analysis controlled by option fixed effects, aiming to estimate the relation between option volatility and circuit breakers affection during the time period from 23rd July 2015 to 23rd March 2016. In this table, additional dummy variables are generated to examine interaction effects between a circuit breaker and options. The dataset is based on daily data of stock index option data and daily CSI 300 Index data. The dependent variable is option volatility, which is defined as the standard deviation of option Table 3-3 (1) (2) (3) (4) (5) (6) Main effects CB (𝑑1) -5.7*** -5.7*** -4.9*** -5.3*** -5.3*** -4.8** (-6.4) (-6.4) (-5.5) (-6) (-6) (-2.5) Stock volatility (𝑋1) 2.4*** 2.2*** 2.2*** 2.2*** (6.7) (6) (6) (6) Option volume(𝑋2) .0051*** .0051*** .0052*** (3.4) (3.4) (3.5) Option_dummy2(𝑑2) .016 .43 (.011) (.22) Option_dummy3(𝑑3) -.38 -1 (-.28) (-.52) Option_dummy4(𝑑4) 1.3 2.4 (.93) (1.2) Option_dummy5(𝑑5) 1.1 1.5 (.78) (.78) Interaction effects CB (𝑑1)* Option2(𝑑6) -.81 (-.29) CB (𝑑1)* Option3(𝑑7) 1.3 (.46) CB (𝑑1)* Option4(𝑑8) -2.2 (-.8) CB (𝑑1)* Option5(𝑑9) -.92 (-.33) _constant 14.4*** 13.8*** 10*** 10*** 10*** 9.9*** (22) (13) (8.8) (8.6) (8.6) (6.6) Fixed effects
Date fixed effects No No No No No No
Option fixed effects No Yes Yes Yes Yes Yes
Observations 810 810 810 810 810 810
