The Study Of Realized Volatility Under High Frequency Finance Data

In finance field, uncertain risk, the volatility of assets returns process, is the origin of chasing benefits in the market, is also the base of active financial market; Assets returns process affected by many factors in market environment is objectively forming the uncertain fluctuation. Whatever for chasing benefits or assets value-keeping purpose people always hope being able to forecast the best results to the upcoming fluctuation. Relying on advanced computer and data storing technology it is more and more easy to gain high frequency finance data. People hopes make the much better forecasting to volatility by the high frequency finance data that is depicted more exquisite to market details. So, the study of assets price fluctuation under high frequency finance data is more and more concerned.Realized volatility brought by Andersen & Bollerslev etc is a kind of effective method to estimate volatility. But the high frequency finance data has also expanded the affection of market microstructure noise to the data while it brings a lot of effective information. It makes that the bias is coming when estimating latent true integrated volatility by realized volatility. What we will do in this article is going a further step study exactly to the question above. First of all, we infer out the calculating method of realized volatility theoretically and gain the limit property of realized volatility. This is the important theory base we start to study; And later, we study the magnanimity method of market microstructure noise under high frequency finance data. We gain two kinds of calculating method about high frequency data market microstructure noise error. And we compare the two methods by Monte-Carlo simulation later. By so, we discuss the optimal sampling frequency; Subsequently, we make a adjusting to realized volatility brought by Andersen etc and get a method so-called adjusted realized volatility ARV_t, which is able todecrease the effect of measurement error to high frequency data; Next, we begin to think about the effect due to market microstructure noise. The noise effect due to low frequency data is less than that due to high frequency data, so it is nature to think of adopting the optimal sub-sampling. We set a rule for optimal sub-sampling. Under the rule we get a new calculating method so-called optimal sub-sampling adjusted realized volatility OARV_t. This new method is effectively able to decrease the estimating bias; Then, We propose an unbiased estimation that is bias correction realized volatility BCRV_t. Finally, we use Monte-Carlo random simulation to get a lot of simulated data. The results are good proof of that bias correction realized volatility BCRV_t is a better approach to estimate latent true integrated volatilitythan others above under high frequency finance data. And by so, we are going a further step to discuss the question about the frequency of optimal sub-sampling.