本文關(guān)鍵詞： 復(fù)雜性 金融網(wǎng)絡(luò) 金融物理 相關(guān)系數(shù)　出處：《華東理工大學(xué)》2013年博士論文　論文類(lèi)型：學(xué)位論文

【摘要】：金融市場(chǎng)是一個(gè)受到大量不同對(duì)象相互作用和相互影響,從而表現(xiàn)出各種復(fù)雜多變現(xiàn)象的復(fù)雜系統(tǒng)。伴隨著金融物理學(xué)等新興交叉性學(xué)科的出現(xiàn),數(shù)學(xué)、統(tǒng)計(jì)物理、幾何學(xué)等方法和思想被運(yùn)用到金融市場(chǎng)中。本文從兩類(lèi)復(fù)雜網(wǎng)絡(luò)入手,進(jìn)而將重心轉(zhuǎn)向時(shí)間序列相關(guān)性,對(duì)不同規(guī)模、不同對(duì)象的金融市場(chǎng)分別進(jìn)行分析和探討。 首先,我們研究了全世界上百個(gè)經(jīng)濟(jì)體的相互投資行為,以2001年到2006年的投資行為為樣本,構(gòu)造了30個(gè)復(fù)雜網(wǎng)絡(luò)。通過(guò)分析世界投資網(wǎng)絡(luò)的統(tǒng)計(jì)性質(zhì),發(fā)現(xiàn)世界的投資行為正在日益全球化。另外,我們也發(fā)現(xiàn)世界投資網(wǎng)絡(luò)是無(wú)標(biāo)度的,并具有小世界的特性。世界投資網(wǎng)絡(luò)的邊權(quán)重服從Weibull分布,節(jié)點(diǎn)強(qiáng)度服從冪律分布。世界投資網(wǎng)絡(luò)也表現(xiàn)出了一定的富人俱樂(lè)部特性以及異配性。異速生長(zhǎng)標(biāo)度指數(shù)是η=1.17±0.02,異速生長(zhǎng)流標(biāo)度指數(shù)是ζ=1.03±0.01。 其次,我們以世界57個(gè)國(guó)家和地區(qū)的股票指數(shù)的日度收益率為研究對(duì)象,用日度收益率時(shí)間序列的相關(guān)系數(shù)來(lái)構(gòu)建復(fù)雜網(wǎng)絡(luò),通過(guò)計(jì)算復(fù)雜網(wǎng)絡(luò)的最大平面圖以及最大平面圖的社團(tuán)結(jié)構(gòu),我們發(fā)現(xiàn)這些指數(shù)能夠按照地域性被較好劃分開(kāi)來(lái)。復(fù)雜網(wǎng)絡(luò)邊權(quán)重的均值的快速動(dòng)態(tài)演化較好的對(duì)應(yīng)一些歷史上的重要金融危機(jī)。我們證明3個(gè)月長(zhǎng)度的時(shí)間窗口能較好的用于研究,最大平面圖的互信息變換、最大平面圖的節(jié)點(diǎn)度數(shù)以及相關(guān)系數(shù)矩陣的第一、第二特征值和第一、第二特征向量都顯示出相應(yīng)的信息。我們將相關(guān)系數(shù)轉(zhuǎn)變成對(duì)應(yīng)節(jié)點(diǎn)之間的距離之后,通過(guò)距離構(gòu)建最小生成樹(shù),并分析最小生成樹(shù)的標(biāo)準(zhǔn)化樹(shù)長(zhǎng)、單步保有率和異速生長(zhǎng),發(fā)現(xiàn)在那些金融危機(jī)的時(shí)間點(diǎn),最小生成樹(shù)的標(biāo)準(zhǔn)化樹(shù)長(zhǎng)發(fā)生較大的變化,同時(shí)邊發(fā)生了大量的替換,而在傳輸效率方面,結(jié)構(gòu)變得更加高效。 接著,我們針對(duì)上海證券交易所的255只股票進(jìn)行相關(guān)系數(shù)和偏相關(guān)系數(shù)的分析和對(duì)比。收益率在相關(guān)系數(shù)和偏相關(guān)系數(shù)的第一特征向量上投影的和上證指數(shù)的收益率具有很好的線性關(guān)系。我們分離相關(guān)系數(shù)矩陣和偏相關(guān)系數(shù)矩陣,并對(duì)分離出來(lái)的對(duì)象進(jìn)行Block的分塊研究,并且發(fā)現(xiàn)偏相關(guān)系數(shù)能比相關(guān)系數(shù)更好的進(jìn)行分塊。 然后,我們引入了Hayashi和Y'oshida提出的異步相關(guān)系數(shù)算法。對(duì)于歐洲6個(gè)證券交易所的活躍股票,分別計(jì)算不同時(shí)間間隔的皮爾遜相關(guān)系數(shù)以及異步相關(guān)系數(shù)。發(fā)現(xiàn)1分鐘時(shí)間間隔的時(shí)間相關(guān)系數(shù)對(duì)于異步相關(guān)系數(shù)有一個(gè)“向下”的偏移現(xiàn)象。在通過(guò)對(duì)比基于皮爾遜相關(guān)系數(shù)的最小生成樹(shù)和用異步相關(guān)系數(shù)修正過(guò)的最小生成樹(shù),發(fā)現(xiàn)在阿姆斯特丹、倫敦、布魯塞爾和馬德里這4個(gè)證券交易所的股票之間存在較多的由于皮爾遜相關(guān)系數(shù)的“向下”偏移而導(dǎo)致的結(jié)構(gòu)變化,同時(shí)發(fā)現(xiàn)這四個(gè)證券交易所中股票的連續(xù)買(mǎi)賣(mài)交易之間間隔的平均時(shí)間都近似或者大于1分鐘。這些最小生成樹(shù)和基于異步相關(guān)系數(shù)的最小生成樹(shù)都以各自的證券交易所而聚成一類(lèi),而不同的證券交易所之間也會(huì)以相同的行業(yè)進(jìn)行相連。 最后,我們使用之前引入的異步相關(guān)系數(shù)對(duì)寶鋼股份和寶鋼JTB1的持倉(cāng)變化量進(jìn)行分析。相關(guān)系數(shù)的分布都在一定范圍內(nèi)服從指數(shù)分布,而在0的附近則主要服從冪律分布。分析寶鋼JTB1的異步相關(guān)系數(shù)矩陣的特征值和特征向量,發(fā)現(xiàn)持倉(cāng)變化量在異步相關(guān)系數(shù)的第一特征向量上的投影,隨著時(shí)間一分為二,收益率與持倉(cāng)變化量投影之間在前后兩端有著不同的線性關(guān)系,前后斜率相差將近3倍。第二特征向量分量為負(fù)時(shí),在我們定義的收益率之下,對(duì)應(yīng)投資者的收益率多數(shù)為正,為正時(shí)則相反,在靠近0處,收益率正負(fù)性則不是很清晰。隨著第二特征向量分量從小到大,投資者1分鐘后的盈利情況成上升趨勢(shì)。另外,投資者以短期投資為主要獲利手段,而在這些短期投資中,主動(dòng)成交要比被動(dòng)成交更能獲得收益。
[Abstract]:The financial market is a complex system which is influenced by a lot of different objects , thus exhibiting various complex and changeable phenomena . With the emergence of emerging cross disciplines such as finance physics , the methods and ideas of mathematics , statistical physics and geometry are applied to financial markets . This paper starts with two types of complex networks , and further analyzes and discusses the financial markets of different scales and objects . First , we have studied the mutual investment behavior of hundreds of economies around the world . By analyzing the statistical nature of the world ' s investment network , we have found that the world ' s investment behavior is increasingly globalized . In addition , we find that the world investment network is not scale and has the characteristics of small world . Secondly , based on the daily return of stock index of 57 countries and regions of the world , we construct a complex network by using the correlation coefficient of daily return time series . We find that these indexes can be divided better according to the regional characteristics . We prove that the time windows of 3 months length can be better used in the research , the maximum plan view mutual information transformation , the node degree of the maximum plan view and the first and second characteristic vectors of the correlation coefficient matrix show the corresponding information . We find that the minimum spanning tree has a great change in the time point of the financial crisis , and the structure becomes more efficient in terms of transmission efficiency . Secondly , we analyze and compare the correlation coefficient and the partial correlation coefficient of 255 stocks in Shanghai Stock Exchange . The yield has a good linear relationship with the yield of Shanghai Stock Exchange on the first feature vector of correlation coefficient and partial correlation coefficient . We separate the correlation coefficient matrix and the partial correlation coefficient matrix , and block the isolated objects , and find that the partial correlation coefficient can be better than the correlation coefficient . We have introduced Hayashi and Y ' oshida ' s asynchronous correlation coefficient algorithm . For the active stocks of six European stock exchanges , Pearson correlation coefficient and asynchronous correlation coefficient of different time intervals are calculated . In the end , we analyze the change of positions of Baosteel ' s shares and Baosteel ' s JTBs by using the asynchronous correlation coefficient introduced before we use them . The distributions of correlation coefficient are subject to exponential distribution within a certain range , while at 0 it is mainly subject to power law distribution . When the component of the second feature vector is negative , the profit of the corresponding investor is upward trend with the second characteristic vector component from small to large . In addition , the investor takes short - term investment as the main profit means , and in these short - term investments , the active transaction is more profitable than the passive transaction .

【學(xué)位授予單位】：華東理工大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2013
【分類(lèi)號(hào)】：F830.9;O157.5

【參考文獻(xiàn)】

相關(guān)期刊論文 前4條

1 汪秉宏;周濤;王文旭;楊會(huì)杰;劉建國(guó);趙明;殷傳洋;韓筱璞;謝彥波;;當(dāng)前復(fù)雜系統(tǒng)研究的幾個(gè)方向[J];復(fù)雜系統(tǒng)與復(fù)雜性科學(xué);2008年04期

2 崔海蓉;何建敏;;基于復(fù)雜網(wǎng)絡(luò)理論的銀行系統(tǒng)性風(fēng)險(xiǎn)研究評(píng)述[J];西安電子科技大學(xué)學(xué)報(bào)(社會(huì)科學(xué)版);2009年04期

3 戴汝為;系統(tǒng)科學(xué)及系統(tǒng)復(fù)雜性研究[J];系統(tǒng)仿真學(xué)報(bào);2002年11期

4 戴汝為;復(fù)雜巨系統(tǒng)科學(xué)——一門(mén)21世紀(jì)的科學(xué)[J];自然雜志;1997年04期

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