【作者】 罗薇；

【导师】 刘建平；

【作者基本信息】 暨南大学 ， 数量经济学， 2006， 硕士

【摘要】 近年来，金融市场的波动日益剧烈，一些影响重大的金融危机事件频频发生，这些都对风险管理提出了挑战，迫切呼唤更加合适的风险模型来处理这些情况。大量的实证表明金融资产大都具有“厚尾分布”的特征，传统的正态分布模型假设会低估了风险，为了更加精确地度量风险，一些学者提出用在工程上广泛应用的极值理论来度量单个资产的风险。极值理论不需要对资产收益分布做任何假设，利用实际数据来拟合分布的尾部，很适合度量风险。同时，更具现实意义的是金融资产的组合情形。由于各种风险因子之间具有一定的相关性，投资组合能够在一定程度上发散风险。传统的投资组合的VaR度量模型对投资组合的边际分布做出各种假设，导致这类VaR模型或者高估或者低估实际VaR值。通过Copula理论，可以选择各种边际分布，通过各种合适的Copula函数连接起来，得到一个更贴近现实分布的联合分布，同时Copula函数不但描述了变量之间的相关程度，更进一步描述了变量间的相依结构，这些都使得Copula模型成为具有更强的刻画现实金融序列分布的动态模型。 本文在假设风险因子对数收益的仿真序列中部服从正态分布，尾部服从极值理论，联合分布分别为正态Copula和t—Copula假设的基础上，利用蒙特卡洛模拟法计算出一天持有期内投资组合的95％VaR。实证表明与传统的正态分布的假设相比，利用极值理论得到的边际分布的尾部能更好地拟合实际风险因子对数收益的概率分布，而基于Copula-EVT模型的仿真序列能够更有效地度量投资组合的VaR值。更多还原

【Abstract】 Recently, with the daily volatility of financial market and some financial catastrophic events happened frequently, which put a challenge for risk management, we have been long for some more appropriate models to deal with such events. Because the "Fat tailed distribution" characteristics of financial risk factors, the conventional method to measure is based on normal distribution assumption which has been proved to underestimate risk, in order to measure the risk more accurate, more and more researchers put forward using extreme-value-theory to measure financial risk factor which has been widely used in engineering. We needn’t put any hypothesis on risk factor returns when use extreme-value-theory. It only uses the empirical data to fit the tail of distribution, which is suitable to measure risk. At the same time, it’s more practical to study the portfolio case. Portfolio can disperse risk on a scale for the correlation amount risk factors. The assumptions of traditional portfolio risk VaR measurement models may underestimate or overestimate VaR. Through Copula theory, a multivariate distribution with all kinds of marginal distribution coupled by a suitable Copula functions can be built. Copula function not only describes the correlation of variables, but also the dependence structure of variables, which makes Copula function a strong dynamic model to describe financial series distribution.In this paper, we estimate a portfolio’s 95% VaR over a one-day holding period with a Monte Carlo Simulation based procedure, assuming the scenarios for risk factors log-returns are generated form a marginal distributions normal in the centre and EVT distributed in the tails and a multivariate distribution with Gaussian-Copula and t-Copula. In this way the tails of the margins fit empirical log-return data better than the normal distribution. It also proves that the Copula-EVT based model outperforms the traditional VaR models assuming a conditional normal multivariate distribution for risk factor log-returns.更多还原