發(fā)布時(shí)間：2018-03-01 04:26

  本文關(guān)鍵詞： VaR CVaR ARMA模型 Monte Carlo模擬 方差縮減技術(shù) 重要抽樣法　出處：《廣西師范大學(xué)》2014年碩士論文　論文類型：學(xué)位論文

【摘要】：VaR(在險(xiǎn)價(jià)值)和CVaR(條件風(fēng)險(xiǎn)價(jià)值)理論是當(dāng)今社會(huì)上在識(shí)別、度量和分析風(fēng)險(xiǎn)領(lǐng)域發(fā)展得比較成熟的理論,在世界范圍內(nèi)都得到了廣泛的運(yùn)用。但Artzner指出VaR不滿足次可加性,不是一致風(fēng)險(xiǎn)估計(jì)量,且對(duì)風(fēng)險(xiǎn)變量尾部損失的測(cè)量不夠充分,這導(dǎo)致它往往忽略了對(duì)超出閾值的實(shí)際發(fā)生值的分析。從統(tǒng)計(jì)學(xué)的角度看,VaR只是一個(gè)對(duì)應(yīng)于某置信水平的分位數(shù),沒(méi)有考察分位點(diǎn)下方的信息,無(wú)法精確的刻畫(huà)出風(fēng)險(xiǎn)。而CVaR滿足次可加性,是一致性風(fēng)險(xiǎn)度量,比VaR能更全面地刻畫(huà)損失分布的特征,對(duì)于VaR模型存在的兩個(gè)缺陷CVaR模型都一一克服了。但Heyde等研究者指出CVaR的這個(gè)優(yōu)點(diǎn)也導(dǎo)致了模型缺乏穩(wěn)健性。故本文將兩者綜合在一起分析以促進(jìn)優(yōu)勢(shì)互補(bǔ)。 為了提高VaR與CVaR模型度量風(fēng)險(xiǎn)的準(zhǔn)確性,國(guó)內(nèi)外眾多研究者都圍繞著未來(lái)金融市場(chǎng)變量的分布、波動(dòng)率的估計(jì)、模型的計(jì)算方法等方面進(jìn)行了大量的研究。在金融市場(chǎng)變量的分布方面,研究者們提出了用幾何布朗運(yùn)動(dòng)、ARMA模型、廣義誤差分布、偏斜T分布等來(lái)擬合變量的變動(dòng)過(guò)程；在波動(dòng)率的估計(jì)的估計(jì)方面,一些研究者發(fā)展了ARCH模型、GARCH模型以及ARMA-GARCH模型來(lái)捕捉波動(dòng)信息,解決波動(dòng)的集聚性問(wèn)題；在模型的計(jì)算方法上,研究者的研究方法主要有：分析法、歷史模擬法、蒙特卡洛模擬法等等。然而金融市場(chǎng)風(fēng)險(xiǎn)特別是金融危機(jī)的發(fā)生是一種稀有事件,要對(duì)稀有事件進(jìn)行計(jì)算需要大量的樣本量作為保證,這就增加了問(wèn)題的復(fù)雜程度,但上述三種方法都沒(méi)能解決估計(jì)稀有事件存在的問(wèn)題,這就有待研究者們進(jìn)一步的修正和改進(jìn)。相對(duì)于傳統(tǒng)方法,重要抽樣法能夠在抽樣時(shí)分配給引起事件發(fā)生的主要原因更大的權(quán)重,更利于捕捉稀有事件的發(fā)生,進(jìn)而能提高估計(jì)效率。因此,重要抽樣技術(shù)可以很好的解決這一問(wèn)題。本文嘗試將這種方差縮減技術(shù)——重要抽樣運(yùn)用到蒙特卡洛法中,通過(guò)指數(shù)變換來(lái)改變變量的概率測(cè)度,使得小概率內(nèi)包含更多的有效樣本以提高模擬效率。 本文我們選擇ARMA模型作為擬合股票組合日收益率的隨機(jī)過(guò)程,再根據(jù)歷史數(shù)據(jù)(或初始值)利用計(jì)算機(jī)來(lái)模擬生成目標(biāo)時(shí)刻的隨機(jī)數(shù),然后分別采用傳統(tǒng)的蒙特卡洛模擬法與基于重要抽樣的蒙特卡洛模擬法求得股票組合的VaR與CVaR值,并將計(jì)算結(jié)果作比較,發(fā)現(xiàn)隨著置信水平的增大,改進(jìn)后的蒙特卡洛模擬法的計(jì)算結(jié)果比傳統(tǒng)的蒙特卡洛模擬法的結(jié)果更接近于真值,顯示出重要抽樣法估計(jì)稀有事件的有效性。
[Abstract]:The theory of VaR and Cvar (conditional risk value) is a mature theory in the field of identifying, measuring and analyzing risks, which has been widely used all over the world. But Artzner points out that VaR is not satisfied with subadditivity. Not consistent risk estimates, and inadequate measurement of tail loss of risk variables, From a statistical point of view, VaR is just a quantile corresponding to a certain confidence level, without looking at the information below the locus. CVaR satisfies subadditivity, which is a consistent risk measure, which can describe the characteristics of loss distribution more comprehensively than VaR. For the two defects of VaR model, the CVaR model has been overcome one by one. However, Heyde et al. pointed out that this advantage of CVaR also leads to the lack of robustness of the model. Therefore, this paper combines the two models together to promote the complementary advantages. In order to improve the accuracy of risk measurement by VaR and CVaR models, many researchers at home and abroad are focusing on the distribution of variables and the estimation of volatility in the future financial markets. In the aspect of the distribution of financial market variables, the researchers put forward the geometric Brownian motion ARMA model, generalized error distribution and skew T distribution to fit the variation process of the variables. In the estimation of volatility, some researchers have developed ARCH model and ARMA-GARCH model to capture fluctuation information and solve the problem of volatility agglomeration. Historical simulation, Monte Carlo simulation and so on. However, financial market risk, especially the occurrence of financial crisis, is a rare event, to calculate rare events needs a large number of samples as a guarantee. This adds to the complexity of the problem, but none of these three methods can solve the problem of estimating rare events, which requires further revision and improvement by researchers. The important sampling method can assign more weight to the main cause of the event, which is more favorable to capture the rare events, and thus improve the efficiency of estimation. The important sampling technique can solve this problem very well. This paper tries to apply this variance reduction technique to Monte Carlo method to change the probability measure of variables by exponential transformation. Make small probability contain more valid samples to improve the efficiency of simulation. In this paper, we choose ARMA model as a stochastic process to fit the daily return rate of stock portfolio, and then use computer to simulate and generate random number of target time according to historical data (or initial value). Then, the traditional Monte Carlo simulation method and the Monte Carlo simulation method based on important sampling are used to obtain the VaR and CVaR values of the stock combination, and the calculated results are compared, and it is found that with the increase of confidence level, The result of the improved Monte Carlo simulation method is closer to the true value than that of the traditional Monte Carlo simulation method, which shows the effectiveness of the important sampling method in estimating rare events.
【學(xué)位授予單位】：廣西師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：F830.91;O212.2

【參考文獻(xiàn)】

相關(guān)期刊論文 前10條

1 田新時(shí),劉漢中,李耀;基于DeltaGamma正態(tài)模型的VaR計(jì)算[J];系統(tǒng)工程;2002年05期

2 余為麗;;VaR估計(jì)的非參數(shù)模型——?dú)v史模擬法[J];消費(fèi)導(dǎo)刊;2008年20期

3 李志海;葉建萍;楊善朝;;基于ARMA-GARCH模型的風(fēng)險(xiǎn)價(jià)值與條件風(fēng)險(xiǎn)價(jià)值計(jì)算[J];廣西科學(xué);2009年04期

4 劉小茂,田立;VaR與CVaR的對(duì)比研究及實(shí)證分析[J];華中科技大學(xué)學(xué)報(bào)(自然科學(xué)版);2005年10期

5 謝非;陳利軍;秦建成;;蒙特卡羅模擬法與歷史模擬法度量匯率風(fēng)險(xiǎn)比較研究[J];經(jīng)濟(jì)師;2011年10期

6 李忠民;張靜;;歐式敲入期權(quán)的蒙特卡洛定價(jià)法改進(jìn)——蒙特卡洛重要抽樣法[J];科學(xué)技術(shù)與工程;2011年05期

7 禾祺夫;董立娟;;基于蒙特卡羅模擬的VaR對(duì)香港恒生指數(shù)期貨的實(shí)證研究[J];內(nèi)蒙古科技與經(jīng)濟(jì);2010年01期

8 龔樸;鄧洋;胡祖輝;;銀行信用組合風(fēng)險(xiǎn)多成分重要性抽樣算法研究[J];管理科學(xué)學(xué)報(bào);2012年11期

9 付秀艷;黃文禮;陶祥興;姚艷杰;;基于CVaR技術(shù)在中國(guó)股指期貨中的應(yīng)用[J];寧波大學(xué)學(xué)報(bào)(理工版);2013年04期

10 孫曉冬;趙斐;;VaR與CVaR在投資組合中的應(yīng)用及對(duì)比分析[J];北京市財(cái)貿(mào)管理干部學(xué)院學(xué)報(bào);2007年02期

相關(guān)博士學(xué)位論文 前1條

1 蘇濤;金融市場(chǎng)風(fēng)險(xiǎn)VaR度量方法的改進(jìn)研究[D];天津大學(xué);2007年

，

本文編號(hào)：1550379