| Nowadays, financial derivatives, which can be trade with leverage and can be used for risk hedging, have become a very important instrument for financial investment and speculation. As a result, for a country or a region, the efficiency of its financial derivatives market has also become a critical aspect to judge whether its overall financial market is well developed. As international financial derivatives markets grow bigger and better regulated, financial derivatives are being more and more prevalent. And as one of the most important financial derivatives, options can perfectly satisfy the requirement of investors for investment, arbitrage, and hedge etc., with its special payoff structure, leverage effect, and flexible design.The Chinese option market is still in the primary stage, so its market efficiency and regulatory system have yet to be well developed. And the market trade volume is also relatively small. From Feb 9th 2015. the Shanghai Stock Exchange started to issue options of SSE50 ETF, which is the first set of option product traded on-exchange in China. In the next year after this event, the Chinese stock market built a short-lived bubble and subsequently experienced a sharp dropping. During this period, if stock investors could properly use this kind of new option products to hedge their positions, they could have avoid most of the loss caused by share price dropping. Therefore, investors are paying more attention to options after this crisis, and the demand of these options is hiking. However, for Chinese capital market has many special characteristics, such as high policy risk and high individual investor ratio, we need to strictly control the risk in order to let this option market develop smoothly. In this case, the regulator set a very high threshold for investors and classified them for easy supervision. Besides, they also set position limit for investors:each new-enter investor's holding position is strictly limited, and can be gradually loosened after the investor grows more experienced and qualified. Although the regulator had already done this, the Chinese option market had severely fluctuated result from the pessimistic emotion caused by bubble burst from June 15th 2015. The government had practiced many temporary market-saving policies in this crisis, including further restricting the option market. Therefore, in this market environment, the Chinese option market is mostly used for hedging and speculating, but rarely used for arbitrage, not to mention the stable and profitable quantitative option-investment strategies.This paper research arbitrage strategies of options, based on option volatility model,combined with comparative study of volatility model and options investment to provide reference ideas about options investment for investors.This paper mainly used relevant research reference, theoretical comparison, and empirical data analysis methods to analyze volatility-prediction models (Historical Volatility Models, GARCH-family Models, and Implied Volatility Models). The proper volatility-prediction models were chosen for predicting near the exercise day (in this paper the strategy-running day was 5 days before exercise day). As the predicted volatility was obtained, this paper estimated the confidence interval of the underlying asset (SSE50 ETF) price in exercise day under 90% confidence level, then use the combination of options to construct option strategy (after comparison, this paper used short-sell strangle strategy), in order to realize stable investment returns. Through comparing different out-of sample option strategy test, which based on different volatility-prediction models, this paper analyzed and evaluated the efficiency and accuracy of each volatility-prediction model and corresponding strategy.There are many kinds of GARCH models in GARCH-family, such as classical GARCH model, EGARCH model, and GJR-GARCH model etc. But this paper only chose GARCH model, EGARCH model, and GJR-GARCH model under normal distribution and student (T) distribution assumption. This paper used static and dynamic methods to regress GARCH models. The static model means building different kinds of GARCH-family models at the first predicting day, then picking the best kind of GARCH model, considering the significances of regression coefficient and AIC measures. After static model once chosen, it was constantly used for whole strategy period. Although its regression coefficient changed each time the data rotated, the model type never changed. On the contrary, the dynamic model did the model picking at every predicting day, so the dynamic method used mixed prediction series from different models.For doing the in-sample theoretical comparison, this paper chose the daily close price of SSE50 ETF from Sep 22th 2009 to Jan 31th 2015 to build the model, and predicted its volatility of exponential return from Feb 1st 2010 to Feb 1st 2015. The prediction happened once a month, and the prediction length was 5 trading days. At the prediction day of each month, the static models regressed with past 120days'data 250days'data and past500 days'data when the dynamic ones used the same data. By using the outcome of these two methods to regress against the realized volatility, it showed that the dynamic model contents more information than static model when it comes to volatility prediction. When using historical volatility for analysis, this paper also used statistical regression to compare and find out what time-span of historical volatility could give the best prediction. Therefore the best time-span historical volatility was used for historical method prediction. When calculating the implied volatility, the reference options were the most frequently traded at-the-money call option. In order to perform reliable comparison, all the methods above predicted once a month at the same day, and the prediction lengths were the same — 5 days.For dong the out-of-sample test, this paper chose the daily data,1 minute high-frequency data from Feb 9th 2015 to Feb 29th 2016. The test showed that the dynamic GARCH model performed much better than the static one:static GARCH model method got negative returns more frequently, compare the predicton intervals based on two models,it shows that the prediction intervals are the same in most cases.but the option strategies based on static model appear a loss when they are differient. This showed that in out-of-sample test, dynamic GARCH model contents more information than static one. in other words, dynamic GARCH model is more predictive. This conclusion was the same as the one in in-sample test. On the other hand, the statistical comparison among dynamic GARCH, historical volatility, and implied volatility showed that the historical volatility method is the most unreliable one:its prediction had the smallest mean value and median value, but its maximum and minimum value were more extreme, which suggested that historical volatility method underestimates the volatility and has unstable prediction. As a result, its empirical test had the most frequent trade as well as the most frequent stop-loss. The prediction of implied volatility was much bigger than the other two, which was consistent with the phenomenon that the implied volatility in Chinese option market is always overvalued. As a result, the empirical test based on implied volatility prediction rarely had a trade, thus had small returns. So this strategy was neither practicable nor efficient. Dynamic GARCH prediction values were just in the middle of the other two, and these predictions were statistically more reasonable. The empirical test also showed that the trade frequency based on dynamic GARCH was high enough, and it had relatively fewer stop-loss times and highest accumulated return. According to overall comparison, in short-term volatility prediction, dynamic GARCH contented the most information as well as had the best predicting power.Although out-of-sample test suggest that dynamic GARCH strategy generated rational return and was practicable, it could turn out to be big failure and cause a huge loss if the market trend sharply change, together with the liquidity distress and option trade become infrequent. Considering about this, this paper chose 4 kinds of open-close timing, which was "open the position at the beginning/ending of the day" and "close the position at the beginning/ending of the day", except stop-loss activated. The comparison of out-of sample test in these 4 scenarios suggested that different timing had significant influence on strategy returns. As the empirical statistic showed, "begin-open, end-close" strategy had similar return to "begin-open, begin-close" strategy, and "end-open, end-close" strategy was similar to "end-open, begin-close" strategy, but the former two were much higher than the latter two. In other words, regardless close timing, the begin-open strategies had significant higher returns than end-open strategies.All the tests in this paper had assumed that market had no friction (no liquidity problem, no market impact, etc.), but there was little trade volume near the beginning and ending of the trading time in real world, which might affect the strategy.since the accuracy of prediction of GARCH model improve with the reduction of the forecast period,so in practice,consider building positions on the E-1 day,on the E-2 day and on the E-3 day.Besides, a strangle strategy includes two position, so whatever one wants to open it or close it, these two position should move at the same time, otherwise investor will face very huge risk exposure which might end up affecting the strategy return. Furthermore, Chinese option market had only a short history that was less than 2 years, so there was quite a small data for out-of sample test. However, the Chinese stock market had an extraordinary fluctuation during sample period, but the strategy could still achieve 15.28% accumulated return, that could be the evidence of the stability of this strategy. But the efficiency of this strategy still needed more data and time to support.Because of the limit of data, this paper didn't run regression to evaluate the implied volatilities'information content, and didn't try mixed prediction, which could be weighted average prediction of historical volatility, GARCH-family, and implied volatility. These researches could be helpful after the Chinese option market had grown more sophisticated and had longer history. |
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