不同残差分布下欧元兑美元汇率的GARCH-VaR模型比较研究

发布时间：2018-06-16 23:09

本文选题：欧债危机 + 风险管理　；参考：《东北财经大学》2012年硕士论文

【摘要】：2011年由于欧债危机的持续爆发,欧元美元作为外汇市场主要的货币对因此大受影响,对于以欧元美元为代表的外汇市场的风险管理技术有必要进行深入研究。交易者在积极参与外汇市场交易之外,必要的风险管理控制是必须的,同时辨识及测量金融风险也已成为金融机构和监管部门关注的焦点。目前,在众多风险测量工具中,VaR模型已成为各金融机构测量市场风险的重要工具。资产收益率的概率分布具有尖峰厚尾特征并具有波动集聚性,但一般资产收益率都假设正态分布,而VaR模型预测的准确度与是否能反映收益率尖峰厚尾的特性是分不开的。GARCH模型在金融领域有着广泛的应用,运用GARCH模型进行资产组合的选择和风险管理,已经在金融市场中得到了广泛的重视。GARCH-VaR模型是进行外汇风险管理的重要工具,但是残差分布的不同对模型风险测量的结果会产生显著差异。通过GED广义误差分布来代替标准正态分布运用,将GARCH模型和GED分布结合以运用VaR方法可以很好地选择资产组合并进行风险管理。这相对于仅对VaR方法进行简单的应用来说,提高了模型的精确度和适用性。本文以欧元兑美元汇率为例,比较了残差分布为正态分布、t分布和GED分布的GARCH-VaR模型。具体的结构为：第一章为本文的绪论,主要阐明本文的选题背景、研究意义和现阶段国内外研究现状,并指出本文的创新与不足。第二章主要介绍VaR方的原理与各种计算方法,为后文做前述准备。第三章主要是结合GARCH模型,介绍了各种基于不同残差分布下的GARCH-VaR模型,并介绍了模型的参数估计和VaR回测检验。第四章为本文的论证核心,通过对欧元美元汇率数据进行序列特征分析,验证了收益率序列的平稳性检验和ARCH效应。在此基础上通过比较模型的样本外预测结果,直观上比较了残差分布为正态分布、t分布和GED分布的GARCH-VaR模型在风险管理上的优劣。同时给出了模型的回测检验结果以证明模型的论证结果是合正确的。本文第五章综合前四章所述,给出本文的研究结论。本文经过比较分析发现：在95%置信水平下,残差分布为正态分布下的模型的失败率过高,说明正态分布下的VaR低估了汇率波动的风险；在99%置信水平下残差分布为t分布的模型失败率明显不合理,说明t分布下的VaR值高估了外汇波动风险。相比之下,残差分布为GED分布的GARCH模的VaR预测在95%和99%置信水平下表现都比较稳定,尤其在更高置信水平下表现更加稳定,对于尖峰厚尾特征明显的外汇市场收益率的风险管理具有指导意义。本文的创新之处在于： (1)相对于传统的VaR,本文的模型将资产收益的尖峰厚尾特征考虑进去,并针对其特点采用GARCH-GED函数来描述。 (2)在实证分析时,本文并不仅仅应用GARCH-GED函数,而是将其与GARCH-N函数、GARCH-t函数所得VaR分别与实际样本外数据进行比较分析,更具有说服力。 (3)在研究GARCH-GED等模型之前,本文对EGARCH模型也进行了研究,并通过实证分析否定了外汇收益率存在不对称性。同时针对这一情况给出自己的解释。当然由于本人的水平有限,本文还有不少不足： (1)应用GARCH模型进行波动率预测时,隐含了一个假设条件即假设历史会重演,历史数据可以反映未来。但相对于压力测试、情景模拟方法,这一假设使得在历史数据的基础上获得的未来预测效果受到局限。 (2)本文GARCH模型进行参数估计时只是采用局部最优化的方法,而非是更为精确的全局最优化方法,例如模拟退火方法。 (3)本文在进行三个模型进行比较时没有考虑VaR模型的历史模拟法和蒙特卡洛随机模拟方法,如果将其也纳入比较中将更能说明问题。同时还有一个实证分析数据选取上的不足,即由于外汇市场每日发布许多可以左右市场情一绪的市场消息和经济数据,外汇数据以每日数据为依据大大降低了市场波动的真实性,可以考虑将每日数据改为高频数据进行研究。
[Abstract]:As a result of the sustained outbreak of the European debt crisis in 2011, the euro dollar as the main currency of the foreign exchange market has been greatly affected. It is necessary to study the risk management technology of the foreign exchange market represented by the euro dollar. Identification and measurement of financial risks have also become the focus of financial institutions and regulatory authorities. At present, in many risk measurement tools, the VaR model has become an important tool for the financial institutions to measure the market risk.
The probability distribution of the rate of return on assets has the characteristics of peak and thick tail and volatility clustering, but the general return on assets assumes normal distribution, and the accuracy of the VaR model and the characteristic that can reflect the thick tail of the yield peak are inseparable from the.GARCH model in the financial field, and the asset group is carried out by using the GARCH model. The combination selection and risk management have gained extensive attention in the financial market. The.GARCH-VaR model is an important tool for the management of foreign exchange risk. However, the difference in residual distribution will produce significant differences in the results of the model risk measurement. The GED generalized error distribution is used to replace the standard normal distribution, and the GARCH model and GED are divided. The combination of cloth to use the VaR method can make a good choice of portfolio and risk management. This improves the accuracy and applicability of the model compared to the simple application of the VaR method only.
In this paper, the euro dollar exchange rate as an example, the residual distribution is normal distribution, t distribution and GED distribution model. The specific structure for GARCH-VaR:
The first chapter is the introduction, mainly expounds the research background, research significance and research status at home and abroad, and points out the innovation and shortcomings of this paper.
The second chapter mainly introduces the principle and calculation method of VaR, do the preparation for the later.
The third chapter is mainly based on the GARCH model, introduced a variety of different GARCH-VaR models based on the distribution of the residuals, and introduces the parameter estimation and VaR model of back testing.
The fourth chapter is the core of the argument. Through the analysis of the sequence characteristics of the exchange rate data of the euro dollar, the stability test and ARCH effect of the yield sequence are verified. On this basis, the GARCH-VaR model of the residual distribution as the normal distribution, the t distribution and the GED distribution is intuitively compared by comparing the sample prediction results of the model. The management of quality. At the same time gives the model of back testing results to prove the model is correct. The results demonstrate
In the fifth chapter, comprehensive chapter four the conclusions of this study are given.
Through the comparison and analysis, we find that the failure rate of the model under the normal distribution under the 95% confidence level is too high, which indicates that the VaR under the normal distribution underestimates the risk of exchange rate fluctuation; the failure rate of the model under the 99% confidence level is obviously unreasonable, which indicates that the VaR value under the t distribution overestimates the Foreign Exchange Volatility wind. In contrast, the VaR prediction of the GARCH model with the residual distribution of GED distribution is more stable at 95% and 99% confidence levels, especially at a higher confidence level, which is of guiding significance for the risk management of the foreign exchange rate of sharp peak and thick tail.
The innovation of this paper lies in:
(1) compared with the traditional VaR, this model will be leptokurtic features of asset returns into account, and aiming at the characteristics of the GARCH-GED function to describe.
(2) in the case of empirical analysis, this paper does not only apply the GARCH-GED function, but compares it with the GARCH-N function, the GARCH-t function and the actual data from the actual sample, and is more convincing.
(3) before studying GARCH-GED and other models, this paper also studies the EGARCH model, and denies the asymmetry of foreign exchange rate by empirical analysis. At the same time, we give an explanation for this situation.
Of course, due to my limited level, there are many deficiencies in this paper:
(1) when using the GARCH model to predict the volatility, a hypothesis is implied that the history will replay and the historical data can reflect the future. But relative to the pressure test, the scenario simulation method makes the future prediction results Limited on the basis of historical data.
(2) only by using the method of local optimization in the GARCH model to estimate the parameters, rather than
Is a more accurate global optimization methods, such as simulated annealing method.
(3) in the comparison of the three models, this paper does not consider the historical simulation method of VaR model and the Monte Carlo stochastic simulation method, if it is also included in the comparison, it will be more able to explain the problem. At the same time, there is a lack of empirical analysis data selection, that is, because the foreign exchange market will publish many markets that can be around the market situation every day. Field news and economic data, foreign exchange data, based on daily data, greatly reduce the authenticity of market volatility, and can consider changing daily data to high frequency data for research.
【学位授予单位】：东北财经大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F831.6;F224

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