本文選題：Copula + GARCH��； 參考：《中國科學(xué)技術(shù)大學(xué)》2017年碩士論文

【摘要】：對資產(chǎn)組合的風(fēng)險(xiǎn)描述方法,在最初馬科維茨(Markowitz)提出的M-V模型中用資產(chǎn)收益率的方差來描述風(fēng)險(xiǎn)。方差作為描述隨機(jī)變量離散水平的統(tǒng)計(jì)量,包含了隨機(jī)變量在均值周圍的向上和向下波動。后來,研究者提出了 VaR(Value at Risk,在險(xiǎn)價(jià)值)這一衡量指標(biāo)。VaR表示資產(chǎn)組合在一定置信水平下,將來一定時(shí)間段中可能產(chǎn)生的最大損失值。因此相比較方差而言,VaR更偏重下行風(fēng)險(xiǎn)。但在VaR的計(jì)算中,一般情況下會假設(shè)資產(chǎn)的收益率分布服從正態(tài)分布,這與實(shí)際情況有較大差別。因此,運(yùn)用Copula來描述資產(chǎn)收益率之間的相依關(guān)系并找到他們的聯(lián)合分布是一個(gè)很好的方法。在金融資產(chǎn)的配置和資產(chǎn)組合的研究中我們會用到隨機(jī)優(yōu)化模型作為分析工具,隨機(jī)優(yōu)化模型的整體分析思路是模擬生成資產(chǎn)收益率的情景,同時(shí)根據(jù)生成的情景構(gòu)造情景樹,將生成的情景樹代入模型求解,由此得到優(yōu)化結(jié)果。傳統(tǒng)的K-means聚類分析產(chǎn)生收益率的情景在初始需要根據(jù)經(jīng)驗(yàn)人為設(shè)定分類的個(gè)數(shù)K,具有主觀性和不確定性,基于對上述K-means聚類分析方法的改進(jìn),本文選擇使用Copula來描述資產(chǎn)收益率之間的相依關(guān)系并得到聯(lián)合分布,同時(shí)用基于Copula的情景生成方法生成的情景構(gòu)造情景樹,并將得到的結(jié)果代入模型,得到最優(yōu)的投資組合。依據(jù)上面的思路,本文先介紹了 Copula以及相應(yīng)的邊緣分布建模方法,并介紹了 VaR和CVaR模型來描述風(fēng)險(xiǎn)。隨后本文通過GARCH模型對資產(chǎn)收益率的邊緣分布建模,并使用Copula得到收益率的聯(lián)合分布,并由蒙特卡洛模擬生成收益率的情景,得到的結(jié)果代入廣義熵約束的CVaR模型中,由此得到最優(yōu)的投資權(quán)重。文章隨機(jī)選取了中國股市中的四只股票構(gòu)造投資組合并進(jìn)行實(shí)證分析,本文實(shí)證表明,在考慮不同資產(chǎn)之間的相依結(jié)構(gòu)基礎(chǔ)上得到的最優(yōu)化結(jié)果相比傳統(tǒng)的投資組合M-V模型具有明顯的優(yōu)勢,在分散化和收益性上得到很好的效果。
[Abstract]:In the original M-V model proposed by Markowitz Markowitz, the risk description method of portfolio is described by variance of return rate of assets.Variance, as a statistic describing the discrete level of random variables, includes the upward and downward fluctuations of random variables around the mean.Later, the researcher put forward the VaR(Value at risk value. VaR indicates the maximum loss value of the portfolio in a certain confidence level and in a certain period of time in the future.Therefore, compared with variance, VaR is more partial to downlink risk.However, in the calculation of VaR, the return distribution of assets is assumed to be normal distribution, which is different from the actual situation.Therefore, it is a good method to use Copula to describe the relationship between asset returns and find their joint distribution.In the research of financial asset allocation and portfolio, we will use stochastic optimization model as an analysis tool. The overall analysis idea of stochastic optimization model is to simulate the situation of generating the return rate of assets, and to construct scenario tree according to the generated scenario at the same time.The generated scenario tree is substituted into the model and the optimization result is obtained.In the traditional K-means clustering analysis, the return rate scenarios need to set the number of categories artificially according to the experience K, which is subjective and uncertain, based on the improvement of the above K-means clustering analysis method.In this paper, we choose to use Copula to describe the dependency relationship between asset returns and obtain the joint distribution. At the same time, scenario tree is constructed by scenario generation method based on Copula, and the result is substituted into the model to obtain the optimal portfolio.According to the above ideas, this paper first introduces the Copula and the corresponding edge distribution modeling method, and introduces the VaR and CVaR models to describe the risk.Then this paper uses GARCH model to model the edge distribution of asset return rate, and uses Copula to obtain the joint distribution of return rate, and the Monte Carlo simulation is used to generate the situation of return rate, and the result is substituted into the generalized entropy constrained CVaR model.Thus the optimal investment weight is obtained.This paper randomly selects four stocks in Chinese stock market to construct a portfolio and makes an empirical analysis.Compared with the traditional portfolio M-V model, the optimization results obtained on the basis of considering the dependent structure of different assets have obvious advantages, and have a good effect on decentralization and profitability.
【學(xué)位授予單位】：中國科學(xué)技術(shù)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：F224;F832.51

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