q-正态分布及其在股票市场VaR估计中的应用

发布时间：2018-03-24 09:24

本文选题：q-微积分　切入点：q-正态分布　出处：《武汉理工大学》2012年硕士论文

【摘要】：股票市场作为金融市场的重要部分,其较大的波动性和交易量使其成为风险管理的主体。中国的股票市场正处于摸索阶段,仍存在着市场风险管理的方法和技术比较落后、市场风险信息披露制度不健全、风险管理体系不够完善等缺陷和不足。如何对股票市场进行有效的计量和管理,是市场各方面必须面对的重要课题。风险价值VaR模型作为目前度量风险的主流方法之一在20世纪90年代的迅速发展,使得各种金融工具和不同的市场风险获得了统一衡量和综合管理。VaR模型成为市场风险管理的一种共同标准,这种影响和变化甚至被称为风险管理的VaR革命。本文在国内外学者的研究基础上,首先简单介绍了金融风险管理的理论基础及VaR的传统计算方法的优缺点,并指出了VaR应用于中国股票市场的必要性。其次运用q-微积分的理论知识推导出相应的部分q-统计分布(q-正态分布、q-指数分布、q-均匀分布)的密度函数和部分特征数(数学期望、方差、k阶矩),将q-正态分布应用于以上证指数1A0001的原始数据为样本数据的VaR值的估计计算中,指出了该统计分布的实用性,进一步证明了上证指数1A0001的口对数收益率服从此q-正态分布；最后将计算的VaR值与Tsallisq'-标准正态分布计算出的VaR值进行比较,说明了q-正态分布和适用于此样本数据。研究表明,q-正态分布能够更好的描述股票收益率的特征,并且适应于VaR值的估计中,更好的解决了股票收益率的“厚尾”特征并提高了精确度。
[Abstract]:As an important part of the financial market, the stock market is subject to risk management due to its high volatility and trading volume. The market risk information disclosure system is not perfect, the risk management system is not perfect, and so on. How to effectively measure and manage the stock market, VaR model of risk value, as one of the mainstream methods to measure risk, developed rapidly in 1990s. It makes all kinds of financial instruments and different market risks get unified measurement and integrated management. VaR model becomes a common standard of market risk management. This kind of influence and change is even called the VaR revolution of risk management. Based on the research of domestic and foreign scholars, this paper firstly introduces the theoretical basis of financial risk management and the advantages and disadvantages of traditional VaR calculation methods. The necessity of applying VaR to Chinese stock market is pointed out. Secondly, the density function and partial special distribution of partial q-statistic distribution and q-exponential distribution are derived by using the theory of q-calculus. Sign number (mathematical expectation, The q-normal distribution is applied to the estimation of the VaR value based on the original data of the 1A0001 index of Shanghai Stock Exchange, and the practicability of the statistical distribution is pointed out. It is further proved that the logarithmic rate of return of 1A0001 is derived from the q-normal distribution, and the calculated VaR value is compared with the VaR value calculated by Tsallisq-standard normal distribution, which shows the q-normal distribution and its applicability to the sample data. The research shows that Q-normal distribution can better describe the characteristics of stock return, and adapt to the estimation of VaR value, better solve the "thick tail" feature of stock yield and improve the accuracy.
【学位授予单位】：武汉理工大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F832.51

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