基于Copula-SV模型的LPM套期保值研究

发布时间：2018-07-23 19:04

【摘要】：期货市场的一个主要功能就是套期保值，通过在期货市场的对冲操作可以实现对现货市场上风险的转移，从而更加有效的管理投资组合的市场风险。2010年4月16日，我国首次推出了沪深300指数期货，为我国机构投资者和中大的个人投资者提供了更加灵活的管理资产组合风险的途径。但是，由于衍生工具往往具有很大的杠杆效应，如果不能正确的使用套期保值头寸，结果不但不能有效减少风险，还可能扩大风险。因此本文从研究如何计算最优套期保值比率这一问题入手，以期对投资者的套期保值决策提供建议。套期保值问题研究的核心是如何确定一个最优的套期保值比率使得能够最大程度的减少套期保值组合的风险。这一问题涉及到两个方面：1）用什么来衡量套期保值组合的风险？2）确定风险的度量方法之后用什么方法去计算在这个风险度量方法下的最优套期保值比率？本文首先回顾了目前广泛使用的四种套期保值风险度量的方法：方差、VaR、ES以及下偏矩LPM。根据套期保值的特征，我们认为LPM是最适合的度量套期保值组合风险的方法。但是在现实中，由于很难确定期货现货的联合分布，利用LPM计算最优套期比率存在非常大的计算难度。正是由于计算上的复杂和困难，制约了LPM方法在套期保值上的广泛应用。1959年Sklar提出了一种新的估计联合分布的方法：Copula函数方法。用一个Copula函数去描述变量间的相关性关系，通过将一个联合分布分解为k个边缘分布和一个Copula函数来描述多个变量的联合分布情况。本文选择LPM方法来度量套期保值组合的市场风险，用Copula函数方法建立数学模型来计算运用股指期货进行套期保值的最优套期保值比率。本文以沪深300股指期货和沪深300指数现货为研究对象对基于LPM的最优套期保值比率模型进行实证研究。首先，分别使用GARCH、EGARCH及SV三类备选模型去拟合股指期货和现货收益率的边缘分布。通过对拟合结果的标准残差序列进行卡方检验我们发现，SV-T模型的KS检验概率值最大，，最能够刻画股指期货现货风险收益率的边缘分布。因此根据边缘分布拟合优度检验的结果，本文选择SV-T模型作为边缘分布模型来刻画两组金融时间收益率的分布情况。对单个的风险资产收益率的边缘分布进行建模之后，我们考察五类常用的二元Copula函数对整个联合分布的拟合情况。通过对拟合结果的卡方检验证明t-Copula是最能刻画样本数据间相关关系的连接函数形式。结合t-Copula和SV-t模型我们得到的Copula-SV模型。将Copula-SV模型的估计结果带入到LPM最优套期保值比率的模型中去，我们得到了在不同目标收益率和风险厌恶程度下的LPM最优套期保值比率。为了更好的考察Copula函数方法计算LPM套期保值比率的优劣，本文同时也给出了两类非参数方法的最优套期保值比率的计算结果。根据上面得到最优套期保值比率，我们对样本外数据进行模拟套期保值，并计算相应的套期保值效率指标H值和R/SV。通过对比模拟套期保值结果的效率指标，我们发现Copula方法具有比较明显的优势，是一种比较符合市场实际的计算方法。
[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.
【学位授予单位】：浙江财经学院
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F832.51;F224

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