基于VaR目标函数下的多元GARCH动态套期保值比率模型研究

发布时间：2018-01-03 10:07

本文关键词：基于VaR目标函数下的多元GARCH动态套期保值比率模型研究　出处：《西南财经大学》2013年硕士论文　论文类型：学位论文

【摘要】：我国在2010年4月16日推出了沪深300股指期货。沪深300股指期货是针对我国资本市场量身定做的一款金融衍生产品。对于国内投资者,尤其是机构投资者来说,沪深300股指期货的推出为他们提供了一个合理有效的风险管理工具。因为通过多年的实践经验来看,用股指期货的套期保值可以有效的规避股票市场的风险。在套期保值的交易中,对于如何确定合理的套期保值比率是十分重要的,因为套期保值比率的不同将会带来不同的套期保值效果。以往的研究大多数是集中在静态套期保值模型的研究中,但本文主要是研究了动态套期保值模型。本文主要是在VaR为目标函数的框架下,运用多元GARCH模型来计算最优套期保值比率从而达到动态套期保值的目的。本文第一章主要探讨了股指期货动态套期保值的研究背景,研究目的及意义和国内外相关的研究文献综述。通过对以往研究文献的梳理总结,笔者发现,在以前对于股指期货套期保值的分析中大部分的研究都是在方差最小目标函数下进行的。所应用的模型都是一些基本的计量经济分析模型,这些模型的一大特点就是他们对于数据的要求极为苛刻,以至于很多分析数据很难达到。一旦不能满足模型对数据的要求那么计算出的结果就可能产生一些系统性的偏差,为最终的结果埋下了隐患。但以VaR为目标函数的套期保值比率模型对数据的要求没有那么严格,更加适合实际情况的需要,迟国泰等(2008)提出了基于VaR确定期货最优套期保值比率的原理,他们的研究发现当期货合约的期望收益率为零,期货和现货的收益率完全相关或者VaR的置信水平接近于100%的情况下,基于VaR确定的期货最优套期保值比率无限接近于最小方差的最优套期保值比率。在动态套期保值比率模型的研究中,核心问题就是如何用模型来拟合金融资产收益率,目前应用最多的就是GARCH模型,本文准备在GARCH模型的基础上通过改进,再引入多元GARCH的方法对模型数据进行拟合。第二章探讨了不同目标函数下的最优套期保值比率模型,本文主要集中在研究方差最小化框架下的最优套期保值比率模型和基于VaR模型下的最优套期保值比率模型。研究发现VaR目标函数下的最优套期保值比率和方差最小化套期保值比率有着完全不同的性质,方差最小化套期保值比率完全是针对风险厌恶的投资者的,VaR目标函数下的最优套期保值比率还兼顾到了投资者在套期保值中投机需求,由于VaR目标函数下的最优套期保值比率模型在一定的情况下可以转化为方差最小化最优套期保值比率模型,所以VaR目标函数下的最优套期保值比率模型拥有更强的适用性。它主要引入了期货期望收益率这个关键的指标,从最后的表达式可以看出,当期望收益率为正的时候,也就是当投资者预期股指期货将要上涨的时候,这时期望收益率为正,算出的最优套期保值比率将比经典模型计算出的最优套期保值比率小。这一现象在现实市场中是可以解释的,当投资者预计市场将会上涨时,他们一般是处于这样的一种情况,即投资者预计在未来的一段时间将有一笔现金收入,但投资者又希望现在入市,由于现在手上没有现金,那么投资者就可以在期货市场上先买入一定量的股指期货,所购买的股指期货的品种与投资者现金到达的时间应该接近。相反,当投资者对未来股票市场的期望收益率预计为负时,也就是未来股票市场会下跌的时候,这时期望收益率为负,由表达式计算出的最优套期保值比率将比前文中经典模型计算出的最优套期保值比率大。同样在现实市场中也可以解释这一现象,一般投资者在预计后市会下跌的时候,他们都会卖出自己的股票,但一些投资者担心自己的判断失误,会犹豫是否卖出股票,尤其是当投资者持有的股票已经存在一定收益的情况下,更难做出决定。第三章主要就是实证分析了方差最小化模型和以VaR为目标函数的套期保值比率模型,从实证分析的结果来看,VaR模型计算出的最优套期保值比率和最小方差条件下的最优套期保值比率差距不是特别大,这可能是由于本文数据选择的原因,因为沪深300股指期货的收盘价格数据和沪深300现货指数之间有着非常强的相关关系,而且他们之间的相关关系几乎是呈线性的相关,所以这几种方法计算出的结果都没有太大的差异,但是从本章最后的计算结果来看,基于VaR方法的最优套期保值比率可以给套期保值者一个选择的就会,如果投资者真的是风险厌恶者,那么VaR方法的最优套期保值比率可以转化为最小方差最优套期保值比率,这样就能让投资者在规避风险的同时也能获得一定的风险收益。在股指期货的操作中,都会涉及到很大的金额,VaR方法还有一个特点就是能够节省套期保值者的交易成本,因为在预期收益率为正的情况下,VaR方法计算的套期保值比率会小于最小方差套期保值比率,这样就可以为套期保值者节省交易保证金的费用。第四章主要是分析了静态套期保值理论的不足、股指期货动态套期保值的意义,最后介绍了一下股指期货动态套期保值的理论以及本文所要用到的模型。首先、本文分析的套期保值比率模型通过第三章的实证分析,继续选用以VaR为目标函数的套期保值比率模型来进行套期保值比率的计算。通过加入时间变量,就可以很容易的把套期保值比率的模型改为动态的模型。因为套期保值涉及到两个变量,所以本文采用的是二元GARCH模型。因为沪深300股指期货和沪深300指数的分布都不是正态分布。具有多数金融序列的尖峰厚尾特性,同时具有一定的偏度,在第三章和第四章的分析中,都是采用的正态分布来拟合收益率的分布,这显然是不合适的,所以在本章中,将引入SKST分布,也就是Skewed Student这样的非对称分布来拟合数据。在对收益率波动的拟合中,本文选择了DCC-ECM-BGARCH模型,用DCC-BGARCH模型的原因是DCC模型相对容易估计,而且由于DCC模型是直接针对变量的相关性进行研究,所以它能够更好的符合现实中的真实相关性。在均值方程中引入ECM项的原因是在第三章的实证分析中发现,沪深300股指期货的对数收益率与沪深300现货指数的对数收益率之间存在着协整关系,故而选择DCC-ECM-BGARCH模型来拟合具有时变特征的收益率。第五章实证分析了以VaR为目标函数的DCC-ECM-BGARCH模型的动态套期保值比率,动态套期保值比率计算的过程中出现了最优套期保值比率大于1的情况。这在实际操作中是可以解释的,在计算静态套期保值比率的时候,都是取一段时间跨度的数据来进行计算,而且为了保证最优套期保值比率的适用性,这个时间跨度的选取都比较长,从长期的分析来看,股指期货的价格波动性是会大于现货价格的波动性。但是在本章中,最优套期保值比率都是根据时间而变化的,这就不能排除在一个小段的时间范围内现货价格波动大于股指期货价格波动的情况。在一般的情况下,投资者都觉得由于我国特有的交易模式,股票市场是T+1交易模式,而股指期货市场是T+0的交易模式,那么自然股指期货的波动性肯定会比股票市场的波动更加剧烈,故而最优套期保值比率应该小于1,但本文的计算结果中出现了套期保值比率大于1。其实也可以反过来看,正因为我国股指期货市场能够很快的对市场的信息作出反应,那么在现货市场上的投资者很可能利用股指期货所提供的信息在股票市场里投机,这样一来就有可能出现在短时间内现货市场的波动还大于期货市场的波动。所以总的来说,本文最后计算出的最优套期保值比率大于1,是因为股指期货具有价格发现的功能,能改善现货市场对市场信息的反应模式,在一段时间里会出现股指期货的价格波动性小于现货的波动。
[Abstract]:China launched the Shanghai and Shenzhen 300 stock index futures in April 16, 2010. Shanghai and Shenzhen 300 stock index futures in China's capital market is tailored to a financial derivative products for domestic investors, especially institutional investors, the Shanghai and Shenzhen 300 index futures to provide a reasonable and effective risk management tools for them. Because through years of experience see, the risk of stock index futures hedging can effectively avoid the stock market. In hedging transactions, is very important for how to determine reasonable hedge ratio, because of the different hedging ratios will bring different hedging effects. The majority of previous studies focused on static hedging model but in this paper is to study the dynamic hedging model. This paper is mainly in the VaR framework for the objective function, the use of multiple The GARCH model is used to calculate the optimal hedging ratio so as to achieve the purpose of dynamic hedging.
The first chapter of this paper mainly discusses the research background of the stock index futures dynamic hedging, research purpose and significance of domestic and international related research literature review. Based on the previous research literature review, the author found that, in the previous researches on the large part of the analysis of stock index futures hedging in are in the minimum variance under the objective function the application of the model. Are some of the basic econometric model, a major feature of these models is that they have very strict requirements for data analysis, so that a lot of data is difficult to achieve. Once can not meet the requirements of the data model so the calculated results may have some systematic deviations for the final the results of potential problems. But the VaR hedge ratio model of objective function requirement of data is not so strict, need to be more suitable for the actual situation, Chi Guotai (2008) put forward the principle of futures optimal hedging ratio determined based on VaR, they found that when the futures contract the expected rate of return to zero, futures and spot returns the confidence level completely related or VaR is close to 100% under the condition of optimal hedge ratio futures optimal hedging ratio is VaR based on the infinite close to the minimum variance. In the study of dynamic hedging ratio model, the key problem is how to use the model to fit the return of financial assets, is currently the most widely used GARCH model, this paper prepared by the improved model based on GARCH method is introduced to fit the multivariate GARCH model data.
The second chapter discusses the optimal hedge ratio model under different objective functions, the optimal hedge ratio model this paper mainly focuses on the variance minimization framework and optimal hedge ratio model based on VaR model. The study found that the VaR objective function under the optimal hedge ratio and the minimum variance hedge ratio has a completely different nature the minimum Variance Hedge ratio is for risk averse investors, the optimal hedging ratios of VaR under the objective function but also to take into account the investors in hedging and speculative demand, the optimal hedge ratio model of VaR under the objective function under certain conditions can be transformed into the optimal hedge ratio with minimum variance model. So the applicability of the optimal hedge ratio model VaR objective function more. It mainly introduced The futures expected rate of return of the key indicators, from the last expression can be seen when the expected rate of return is a time when investors expect when stock index futures will rise, the expected rate of return is positive, the optimal hedging ratios will calculate the optimal hedge ratio than the classical model to calculate the small. This phenomenon can be explained in the real market, when investors expect the market will rise, they are generally in such a situation, investors are expected to have a cash income in the next period of time, but also hope investors into the market now, because there is no cash on hand, so investors in the futures market before buying a certain amount of the stock index futures, investors buy cash and varieties of stock index futures should be close to the time of arrival. On the contrary, when investors in the future stock market The expected rate of return is expected to be negative, that is when the stock market will decline in the future, when the expected rate of return is negative, the optimal hedging ratios calculated by the expression of the optimal hedge ratio than the classical model previously calculated. Also in the real market can also explain this phenomenon, generally when investors in the market outlook is expected to fall, they will sell their stocks, but some investors worry that mistakes in their own judgments, will hesitate to sell the stock, especially when investors hold stocks have certain benefits under the condition of more difficult to make a decision.
The third chapter is the empirical analysis of the variance minimization model and using VaR as the target function of the hedge ratio model, from the empirical analysis results, the VaR model to calculate the optimal hedge ratio and the minimum variance under the condition of the optimal hedging ratio of the gap is not particularly large, this may be due to the data selection. Because there is a strong correlation between the Shanghai and Shenzhen 300 stock index futures price data and the CSI 300 stock index, and the relationship between them is almost linearly related, are not too big difference so that several methods to calculate the results, but from the end of this chapter the calculation results show that the optimal hedging the ratio of VaR method can give the hedgers a choice will be based on, if investors are risk averse, then the VaR method of optimal hedging ratio The rate can be transformed into the minimum variance optimal hedging ratio, which allows investors to avoid the risk of also can get some benefits. The risk in the stock index futures operation, will involve a great amount of VaR has a characteristic that is able to save the transaction cost of hedgers, because the expected rate of return as is the case, the VaR method to calculate the hedging ratio will be less than the minimum variance hedge ratio, so it can save the trading margin for hedging costs.
The fourth chapter mainly analyzes the disadvantages of static hedging theory, stock index futures dynamic hedging significance, finally introduced by the use of a stock index futures dynamic hedging theory and the model of this paper. Firstly, this paper analysis the hedging ratio model through the empirical analysis of the third chapter, continue to choose calculation with VaR hedging the ratio of objective function model of hedging ratio. By adding the time variable, you can easily put the hedge ratio model to a dynamic model. Because the hedging involves two variables, so this paper is two yuan GARCH model. Because the distribution of Shanghai and Shenzhen 300 stock index futures and the Shanghai and Shenzhen 300 index are not normal distribution. The peak thick tail has the characteristics of most financial series, but also has some skewness, in the analysis of the third chapter and the fourth chapter, are used The distribution of normal distribution to fit the yield, which is obviously not suitable, so in this chapter, the introduction of SKST distribution, which is Skewed Student this asymmetric distribution to fit the data. The fitting fluctuation on the rate of return, this paper chose the DCC-ECM-BGARCH model with DCC-BGARCH model is DCC the model is relatively easy to estimate, and the DCC model is studied for direct correlation of variables, so it can accord with the true correlation in reality better. The reasons for the introduction of ECM in the mean equation is found in the third chapter of the empirical analysis, cointegration relationship exists between the logarithm of rate of return and the Shanghai Shenzhen 300 stock index futures the 300 stock index return rate, choose the DCC-ECM-BGARCH model to fit the time-varying characteristics of the rate of return it.
The fifth chapter is the empirical analysis of the dynamic hedge ratio based on VaR DCC-ECM-BGARCH model of the objective function, the process of dynamic hedge ratio calculation in the optimal hedge ratio is greater than 1. This can be explained in the actual operation, when calculating the static hedging ratio, are taken for a period of time span the data to be calculated, and in order to ensure the applicability of the optimal hedging ratio, choose this time span is long, from a long-term perspective, the price volatility of the stock index futures volatility is greater than the spot price. But in this chapter, the optimal hedge ratio is changed according to time it cannot be ruled out, the spot price volatility is greater than the stock index futures price volatility in a short time range. In general, investors feel due to China's special Some trading patterns, the stock market is the T+1 transaction mode, and stock index futures market is T+0 trading model, then the volatility of stock index futures will naturally than the stock market fluctuation, therefore the optimal hedging ratio should be less than 1, but the results of this paper appeared in the hedge ratio is greater than 1. but can also turn look, just because of China's stock index futures market on the market quickly to respond, then on the spot market investors are likely to use stock index futures to provide information in the stock market speculation, so there may be a spot market in a short period of time is greater than the volatility of futures market volatility. In general, the optimal hedge ratio is calculated at the end of more than 1, because the stock index futures has price discovery function, can improve the stock market on the market channel In a period of time, the price volatility of stock index futures is less than the fluctuation of spot.

【学位授予单位】：西南财经大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F832.51;F224

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