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(在險價值)和CVaR(條件風(fēng)險價值)理論是當(dāng)今社會上在識別、度量和分析風(fēng)險領(lǐng)域發(fā)展得比較成熟的理論,在世界范圍內(nèi)都得到了廣泛的運用。但Artzner指出VaR不滿足次可加性,不是一致風(fēng)險估計量,且對風(fēng)險變量尾部損失的測量不夠充分,這導(dǎo)致它往往忽略了對超出閾值的實際發(fā)生值的分析。從統(tǒng)計學(xué)的角度看,VaR只是一個對應(yīng)于某置信水平的分位數(shù),沒有考察分位點下方的信息,無法精確的刻畫出風(fēng)險。而CVaR滿足次可加性,是一致性風(fēng)險度量,比VaR能更全面地刻畫損失分布的特征,對于VaR模型存在的兩個缺陷CVaR模型都一一克服了。但Heyde等研究者指出CVaR的這個優(yōu)點也導(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)勢互補。 為了提高VaR與CVaR模型度量風(fēng)險的準(zhǔn)確性,國內(nèi)外眾多研究者都圍繞著未來金融市場變量的分布、波動率的估計、模型的計算方法等方面進(jìn)行了大量的研究。在金融市場變量的分布方面,研究者們提出了用幾何布朗運動、ARMA模型、廣義誤差分布、偏斜T分布等來擬合變量的變動過程；在波動率的估計的估計方面,一些研究者發(fā)展了ARCH模型、GARCH模型以及ARMA-GARCH模型來捕捉波動信息,解決波動的集聚性問題；在模型的計算方法上,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。然而金融市場風(fēng)險特別是金融危機的發(fā)生是一種稀有事件,要對稀有事件進(jìn)行計算需要大量的樣本量作為保證,這就增加了問題的復(fù)雜程度,但上述三種方法都沒能解決估計稀有事件存在的問題,這就有待研究者們進(jìn)一步的修正和改進(jìn)。相對于傳統(tǒng)方法,重要抽樣法能夠在抽樣時分配給引起事件發(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)而能提高估計效率。因此,重要抽樣技術(shù)可以很好的解決這一問題。本文嘗試將這種方差縮減技術(shù)——重要抽樣運用到蒙特卡洛法中,通過指數(shù)變換來改變變量的概率測度,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過程,再根據(jù)歷史數(shù)據(jù)(或初始值)利用計算機來模擬生成目標(biāo)時刻的隨機數(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)位級別】：碩士
【學(xué)位授予年份】：2014
【分類號】：F830.91;O212.2

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