基于Copula-SV模型的LPM套期保值研究
發(fā)布時(shí)間：2018-07-23 19:04
【摘要】：期貨市場(chǎng)的一個(gè)主要功能就是套期保值，通過在期貨市場(chǎng)的對(duì)沖操作可以實(shí)現(xiàn)對(duì)現(xiàn)貨市場(chǎng)上風(fēng)險(xiǎn)的轉(zhuǎn)移，從而更加有效的管理投資組合的市場(chǎng)風(fēng)險(xiǎn)。2010年4月16日，我國(guó)首次推出了滬深300指數(shù)期貨，為我國(guó)機(jī)構(gòu)投資者和中大的個(gè)人投資者提供了更加靈活的管理資產(chǎn)組合風(fēng)險(xiǎn)的途徑。但是，由于衍生工具往往具有很大的杠桿效應(yīng)，如果不能正確的使用套期保值頭寸，結(jié)果不但不能有效減少風(fēng)險(xiǎn)，還可能擴(kuò)大風(fēng)險(xiǎn)。因此本文從研究如何計(jì)算最優(yōu)套期保值比率這一問題入手，以期對(duì)投資者的套期保值決策提供建議。 套期保值問題研究的核心是如何確定一個(gè)最優(yōu)的套期保值比率使得能夠最大程度的減少套期保值組合的風(fēng)險(xiǎn)。這一問題涉及到兩個(gè)方面：1）用什么來衡量套期保值組合的風(fēng)險(xiǎn)？2）確定風(fēng)險(xiǎn)的度量方法之后用什么方法去計(jì)算在這個(gè)風(fēng)險(xiǎn)度量方法下的最優(yōu)套期保值比率？本文首先回顧了目前廣泛使用的四種套期保值風(fēng)險(xiǎn)度量的方法：方差、VaR、ES以及下偏矩LPM。根據(jù)套期保值的特征，我們認(rèn)為L(zhǎng)PM是最適合的度量套期保值組合風(fēng)險(xiǎn)的方法。但是在現(xiàn)實(shí)中，由于很難確定期貨現(xiàn)貨的聯(lián)合分布，利用LPM計(jì)算最優(yōu)套期比率存在非常大的計(jì)算難度。正是由于計(jì)算上的復(fù)雜和困難，制約了LPM方法在套期保值上的廣泛應(yīng)用。1959年Sklar提出了一種新的估計(jì)聯(lián)合分布的方法：Copula函數(shù)方法。用一個(gè)Copula函數(shù)去描述變量間的相關(guān)性關(guān)系，通過將一個(gè)聯(lián)合分布分解為k個(gè)邊緣分布和一個(gè)Copula函數(shù)來描述多個(gè)變量的聯(lián)合分布情況。本文選擇LPM方法來度量套期保值組合的市場(chǎng)風(fēng)險(xiǎn)，用Copula函數(shù)方法建立數(shù)學(xué)模型來計(jì)算運(yùn)用股指期貨進(jìn)行套期保值的最優(yōu)套期保值比率。 本文以滬深300股指期貨和滬深300指數(shù)現(xiàn)貨為研究對(duì)象對(duì)基于LPM的最優(yōu)套期保值比率模型進(jìn)行實(shí)證研究。首先，分別使用GARCH、EGARCH及SV三類備選模型去擬合股指期貨和現(xiàn)貨收益率的邊緣分布。通過對(duì)擬合結(jié)果的標(biāo)準(zhǔn)殘差序列進(jìn)行卡方檢驗(yàn)我們發(fā)現(xiàn)，SV-T模型的KS檢驗(yàn)概率值最大，，最能夠刻畫股指期貨現(xiàn)貨風(fēng)險(xiǎn)收益率的邊緣分布。因此根據(jù)邊緣分布擬合優(yōu)度檢驗(yàn)的結(jié)果，本文選擇SV-T模型作為邊緣分布模型來刻畫兩組金融時(shí)間收益率的分布情況。對(duì)單個(gè)的風(fēng)險(xiǎn)資產(chǎn)收益率的邊緣分布進(jìn)行建模之后，我們考察五類常用的二元Copula函數(shù)對(duì)整個(gè)聯(lián)合分布的擬合情況。通過對(duì)擬合結(jié)果的卡方檢驗(yàn)證明t-Copula是最能刻畫樣本數(shù)據(jù)間相關(guān)關(guān)系的連接函數(shù)形式。結(jié)合t-Copula和SV-t模型我們得到的Copula-SV模型。將Copula-SV模型的估計(jì)結(jié)果帶入到LPM最優(yōu)套期保值比率的模型中去，我們得到了在不同目標(biāo)收益率和風(fēng)險(xiǎn)厭惡程度下的LPM最優(yōu)套期保值比率。為了更好的考察Copula函數(shù)方法計(jì)算LPM套期保值比率的優(yōu)劣，本文同時(shí)也給出了兩類非參數(shù)方法的最優(yōu)套期保值比率的計(jì)算結(jié)果。根據(jù)上面得到最優(yōu)套期保值比率，我們對(duì)樣本外數(shù)據(jù)進(jìn)行模擬套期保值，并計(jì)算相應(yīng)的套期保值效率指標(biāo)H值和R/SV。通過對(duì)比模擬套期保值結(jié)果的效率指標(biāo)，我們發(fā)現(xiàn)Copula方法具有比較明顯的優(yōu)勢(shì)，是一種比較符合市場(chǎng)實(shí)際的計(jì)算方法。
[Abstract]:One of the main functions of the futures market is hedging. Through the hedging operation in the futures market, the risk of the spot market can be transferred to the spot market. Thus the market risk of the portfolio is more effectively managed in April 16th. The Shanghai and Shenzhen 300 index futures were first introduced in China for the first time in China, for the institutional investors and the big individual investment in China. It provides a more flexible way to manage portfolio risk. However, because derivatives often have a great leverage effect, if the hedging position can not be used correctly, the result can not effectively reduce the risk, but also may expand the risk. Therefore, this paper studies how to calculate the optimal hedging ratio. In order to provide suggestions for hedging decisions of investors.
The core of the study of hedging is how to determine an optimal hedging ratio to minimize the risk of hedging portfolio. This problem involves two aspects: 1) what is the risk to measure the hedging portfolio? 2) what is the method to calculate the wind after the measurement of the risk? The optimal hedging ratio under the risk measurement method? This paper first reviews the four widely used hedging risk measures at present: variance, VaR, ES and lower moment LPM. according to hedging characteristics, we think that LPM is the most suitable measure of hedging portfolio risk. But in reality, because it is difficult to determine. The joint distribution of futures spot is very difficult to calculate by using LPM to calculate the optimal hedging ratio. It is precisely because of the complexity and difficulty of the calculation, which restricts the extensive application of LPM method on hedging..1959 Sklar proposed a new method of estimating joint distribution: Copula function method. A Copula function is used to describe the change. The correlation between the quantity is divided into K edge distribution and a Copula function to describe the joint distribution of multiple variables. In this paper, we choose the LPM method to measure the market risk of hedging portfolio, and use the Copula function method to establish the mathematical model to calculate the optimal hedging with the stock index futures. Hedging ratio.
This article takes the Shanghai and Shenzhen 300 stock index futures and the Shanghai and Shenzhen 300 index spot as the research object to carry on the empirical study to the optimal hedging ratio model based on LPM. First, we use the GARCH, EGARCH and SV three kinds of alternative models to fit the edge distribution of stock index futures and spot returns respectively. We found that the SV-T model has the largest KS test probability value and can describe the edge distribution of stock index futures spot risk yield. Therefore, according to the result of edge distribution fitting goodness test, the SV-T model is selected as the edge distribution model to describe the distribution of two groups of financial time returns. After the edge distribution of the rate is modeled, we examine the fitting of the five kinds of common two element Copula functions for the whole joint distribution. Through the chi square test of the fitting results, we prove that t-Copula is the most capable connection function that characterizations of the correlation between sample data. The Copula-SV model we have obtained by combining the t-Copula and SV-t models. The estimation results of the a-SV model are brought into the LPM optimal hedging ratio model. We get the LPM optimal hedging ratio under the different target returns and risk aversion. In order to better investigate the Copula function method to calculate the LPM hedging ratio, this paper also gives the two kinds of non parametric methods. According to the optimal hedging ratio, we carry out the simulated hedging of the data from the above sample, and calculate the corresponding hedging efficiency index H and R/SV. by comparing the efficiency indexes of the simulated hedging results, we find that the Copula method has a more obvious advantage, which is a kind of ratio. The calculation method which is more in line with the actual market.
【學(xué)位授予單位】：浙江財(cái)經(jīng)學(xué)院
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2013
【分類號(hào)】：F832.51;F224
本文編號(hào)：2140364
[Abstract]:One of the main functions of the futures market is hedging. Through the hedging operation in the futures market, the risk of the spot market can be transferred to the spot market. Thus the market risk of the portfolio is more effectively managed in April 16th. The Shanghai and Shenzhen 300 index futures were first introduced in China for the first time in China, for the institutional investors and the big individual investment in China. It provides a more flexible way to manage portfolio risk. However, because derivatives often have a great leverage effect, if the hedging position can not be used correctly, the result can not effectively reduce the risk, but also may expand the risk. Therefore, this paper studies how to calculate the optimal hedging ratio. In order to provide suggestions for hedging decisions of investors.
The core of the study of hedging is how to determine an optimal hedging ratio to minimize the risk of hedging portfolio. This problem involves two aspects: 1) what is the risk to measure the hedging portfolio? 2) what is the method to calculate the wind after the measurement of the risk? The optimal hedging ratio under the risk measurement method? This paper first reviews the four widely used hedging risk measures at present: variance, VaR, ES and lower moment LPM. according to hedging characteristics, we think that LPM is the most suitable measure of hedging portfolio risk. But in reality, because it is difficult to determine. The joint distribution of futures spot is very difficult to calculate by using LPM to calculate the optimal hedging ratio. It is precisely because of the complexity and difficulty of the calculation, which restricts the extensive application of LPM method on hedging..1959 Sklar proposed a new method of estimating joint distribution: Copula function method. A Copula function is used to describe the change. The correlation between the quantity is divided into K edge distribution and a Copula function to describe the joint distribution of multiple variables. In this paper, we choose the LPM method to measure the market risk of hedging portfolio, and use the Copula function method to establish the mathematical model to calculate the optimal hedging with the stock index futures. Hedging ratio.
This article takes the Shanghai and Shenzhen 300 stock index futures and the Shanghai and Shenzhen 300 index spot as the research object to carry on the empirical study to the optimal hedging ratio model based on LPM. First, we use the GARCH, EGARCH and SV three kinds of alternative models to fit the edge distribution of stock index futures and spot returns respectively. We found that the SV-T model has the largest KS test probability value and can describe the edge distribution of stock index futures spot risk yield. Therefore, according to the result of edge distribution fitting goodness test, the SV-T model is selected as the edge distribution model to describe the distribution of two groups of financial time returns. After the edge distribution of the rate is modeled, we examine the fitting of the five kinds of common two element Copula functions for the whole joint distribution. Through the chi square test of the fitting results, we prove that t-Copula is the most capable connection function that characterizations of the correlation between sample data. The Copula-SV model we have obtained by combining the t-Copula and SV-t models. The estimation results of the a-SV model are brought into the LPM optimal hedging ratio model. We get the LPM optimal hedging ratio under the different target returns and risk aversion. In order to better investigate the Copula function method to calculate the LPM hedging ratio, this paper also gives the two kinds of non parametric methods. According to the optimal hedging ratio, we carry out the simulated hedging of the data from the above sample, and calculate the corresponding hedging efficiency index H and R/SV. by comparing the efficiency indexes of the simulated hedging results, we find that the Copula method has a more obvious advantage, which is a kind of ratio. The calculation method which is more in line with the actual market.
【學(xué)位授予單位】：浙江財(cái)經(jīng)學(xué)院
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2013
【分類號(hào)】：F832.51;F224
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