Volitilty Index: Theory, Method And Application In China

The difficulty of measuring market behavior is obvious, there are thousands of market index represents each country, assets and investment style you can think of. On the one hand, explosive growth of index shows the attention to achievements and process of the quantitative investment, but it also shows the powerful of the index and deeply influence on the investment market. The Volatility Index, VIX, introduced by the Chicago Board Options Exchange(CBOE) is a successful model among these. VIX reflects the consensus expection of the future volatility of the market in order to preventing risk and guiding trade.Based on the world-widely recognized of theⅥⅩindex, introduced by Chicago Board Options Exchange, and in order to provide a index to measure our current market volatility and reveal the investors' expectation of future market risk, we construct a China Volatility Index CV. In this thesis, all of the studies are focused on the methodology of the Volatility Index CV and the statistical characteristics as well as market functions.The key points and main achievements of the thesis are listed as follows:1.We proposed China Volatility index construction plan, based on detailed intrepreation of the Chicago Board Options Exchange volatility index VIX. We used the average of bid and ask price of each trade to calculate the 20-day realized volatility of the stock index futures contracts. Furthermore, we used the Exponential Moving Average method to eliminate the micro-structure noise in the series of the realized volatility. And finally we calculated China Volatility index by weighted average of 20-day adjusted realized volatility of the near-term stock index futures contract and thd the next-term stock index futures contract. Although we can not prove the China Volatility index based on the adjusted realized volatility is the best forecast of future market volatility, but we can prove that the index is a relatively objective outcome.2.To capture the long-memory in the volatility index, we resort to the heterogeneous autoregressive(HAR) model(Corsi,2004). We analysis heterogenous in the market caused by three main volatility components, intraday(60 minutes), short-term(1 day)and mid-term(5 days or 1 week). Furthermore, we developed the HAR model on time and space in order to describe the volatility and changes of the heterogeneous in the market. We find that the HAR model performs very well in fitting the volatility index, and the MS-HAR model are the best of them, through the analysising the forecast effect of the models. The empirical results show that the volatility index has significant long memory and first-order autocorrelation. And there are significant different among 3 kinds of main components of volatility, and the intraday volatility components has the most powerful influence on the volatility index, as well as the short-term and mid-term volatility components has limited influence on the volatility index.Overall, we described the market heterogenous in the volatility index based on the HAR model and its extended. That is, there are short-term and mid-term investors in the market, and most of them are the short-term investors. This is one of the reasons for severely volatility in our current financial market. Notable is, from the analysis of chapter 3 we also confirmed the long-term fluctuation components(10-day and 20-day) have no significant effect on the volatility index, possibly because of the long-term investment philosophy has not yet formed in the curren financial market in China, is also possible that the longer volatility component did not include in our model, so that which can not reflect the long-term volatility components on the volatility index.3.Copula model is introduced into analysis of the function of the volatility index to avoid defects of linear correlation coefficient and classical analysis methods. Based on fully understanding of copula theory, we systemic studied the relationship between volatility index and the comtempory H&S stock index return as well as future index return. The result shows that, the relationships between volatility index and stock index return series are better fitted by t-Copula model, and there are negative correlations among different time periods of volatility component with corresponding stock index returns to a certain extent. Moreover, there are also negative correlations among the volatility index with expection future stock index returns, and the correlationship is symmetrical. Further, the empirical analysis also indicated that, it can help to make investment decisions based on those correlationship:the high volatility index can be seen as a sell signal, while low volatility index can be seen as a buy signal. It is important that, any prediction is based on the uncertainly factors, the conclusion drawn from our empirical analysis have some reference value on investment descion only in the 10-day or 20-day's investment periods, the available evidence is unable to confirm the volatility index have prediction ability in the intraday or beyond 20-day.4.In order to futher study the dynamic change correlationship between volatility index and stock index returns we introduced a time-varying condtional Copula model, and focused on the contrast in fitting volatility index and stock index returns based on the static Copula model and time-varying condtional Copula model, and the advantages in estimating the Value at Risk(VaR) of the stock index returns. The results showed, the time-varying condtional Copula model had better fitting effect than static Copula. In addition, based on the time-varying correlation patterns, and using Monte Carlo simulation method to estimate the expected future stock index returns risk value had better conclusion than the traditional normal method and fixed relative mode.