電機資訊學院: 資訊工程學研究所指導教授: 呂育道蔡芸琤Tsai, Yun-ChengYun-ChengTsai2017-03-032018-07-052017-03-032018-07-052016http://ntur.lib.ntu.edu.tw//handle/246246/275595市場價格以及市場的連續二次變率（continuous quadratic variation）在高頻交易（high-frequency trading）中扮演著關鍵角色。然而，微結構雜訊（microstructure noise）的存在使得無法觀察到市場真實價格（true price）及造成連續二次變率的估計誤差。我們根據Zhou 的設定，假設可觀察到的市場價格是由無法觀察到的市場真實價格加上微結構雜訊所組成。並假設微結構雜訊為獨立同分佈（independent and identically distributed）且獨立於無法觀察到的市場真實價格。2005年，Zhang et al. 提出用於含有微結構雜訊之高頻資料的連續二次變率批次估計法（two-scales realized variance）。此估計法只能在所有採樣資料全都收集到後才能進行運算。本論文提出此估計法的遞迴版本（recursive two-scales realized variance），這個方法在每一筆採樣資料收集到後就能運算出當下的二次變率估計值。經實際市場期貨資料以及模擬資料的實驗結果證實，這個遞迴版本能夠在所有採樣資料全部收集到前，就能得到正確的估計值。 當無法觀察到的市場真實價格採樣來自於幾何布朗運動過程（geometric Brownian motion process）並與微結構雜訊組成可觀察到的市場價格時，卡爾曼濾波器（Kalman filter）能從可觀察到的市場價格估計出最佳的市場真實價格。然而，在實際運作中，使用卡爾曼濾波器時，必須估計或取得真實的微結構雜訊及市場真實價格的斜方差矩陣（covariance matrix）。但通常這兩個斜方差矩陣都是未知的且必須被估計。因此，對於含有微結構雜訊之高頻資料，本論文提出一個穩定的卡爾曼濾波器（robust Kalman filter）來估計無法觀察到的市場真實價格。本論文提出的方法，不需要事先取得這兩個斜方差矩陣便能進行市場真實價格的估計。經模擬資料的實驗結果證實，本論文提出的方法可以獲得和卡爾曼濾波器相似的市場真實價格估計值，且這些實驗中的卡爾曼濾波器是可取得真實的微結構雜訊及市場真實價格的斜方差矩陣。The market prices and the continuous quadratic variation play critical roles in high-frequency trading. However, the microstructure noise could make the observed prices differ from the true prices and hence bias the estimates of continuous quadratic variation. Following Zhou, we assume the observed prices are the result of adding microstructure noise to the true but hidden prices. Microstructure noise is assumed to be independent and identically distributed (i.i.d.); it is also independent of true prices. Zhang et al. propose a batch estimator for the continuous quadratic variation of high-frequency data in the presence of microstructure noise. It gives the estimates after all the data arrive. This thesis proposes a recursive version of their estimator that outputs variation estimates as the data arrive. The recursive version estimator gives excellent estimates well before all the data arrive. Both real high-frequency futures data and simulation data confirm the performance of recursive estimator. When prices are sampled from a geometric Brownian motion process, the Kalman filter can produce optimal estimates of true prices from the observed prices. However, the covariance matrix of microstructure noise and that of true prices must be known for this claim to hold. In practice, neither covariance matrix is known so they must be estimated. This thesis presents a robust Kalman filter (RKF) to estimate the true prices when microstructure noise is present. The RKF does not need the aforesaid covariance matrices as inputs. Simulation results show that the RKF gives essentially identical estimates to the Kalman filter, which has access to the two above mentioned covariance matrices.1214192 bytesapplication/pdf論文公開時間: 2016/7/26論文使用權限: 同意有償授權(權利金給回饋學校)高頻交易微結構雜訊二次變率批次估計法卡爾曼濾波器high-frequency tradingmicrostructure noisetwo-scales realized varianceKalman filterthesis10.6342/NTU201600797http://ntur.lib.ntu.edu.tw/bitstream/246246/275595/1/ntu-105-D98922012-1.pdf