基于MCMC算法的股指VaR计算

发布时间：2018-01-09 18:15

本文关键词：基于MCMC算法的股指VaR计算　出处：《山东大学》2013年硕士论文　论文类型：学位论文

【摘要】：风险测量是风险管理的核心和基础,是对风险的定量分析和评估。随着金融市场和金融交易的规模、动态性、复杂性的增加,以及金融理论和金融工程的发展,金融市场风险测量技术也更加综合化、复杂化。目前,金融市场风险测量的主要方法有灵敏度分析、波动性方法、VaR、压力测试、以及极值理论(EVT)。其中,VaR是目前金融市场风险测量的主流方法。目前,金融市场上进行风险管理和度量的方法有很多种类,如灵敏度分析法、波动性方法、VaR、压力测试、极值理论(EVT)等。其中,VaR方法在金融市场风险管理和度量中起到了显著作用,可以说是最为主要的方法。 VaR的概念在数学上出现的很早,但是开始被金融行业接受始于20世纪80年代。随着科学技术的发展以及VaR框架的逐步推广,常见的风险度量软件都会提供计算VaR的模型。很多国际著名的商业银行、投资公司等金融机构都将VaR用于日常的风险管理,并且在年报中披露VaR。而很多政府监管部门也明确规定必须使用VaR模型衡量风险。早期,VaR方法并没有受到如此广泛的接受和认可。当时市场上常见和主流的风险管理方法有敏感性分析、止损、名义金额以及风险敞口等。然而衍生产品的出现和发展使得传统风险管理方法出现很多不足。一方面不同的衍生产品即使名义金额、风险敞口相同,其风险程度可能存在很大差异；另一方面,传统的风险管理方法没有充分考虑到市场之间存在的差异性和相关性,对风险无法有效汇总,因此面临诸多挑战。VaR对杠杆、市场差异、相关性等多方面因素进行了综合考量,相比之前的风险管理方法具有非常大而明显的优势。计算VaR的方法主要有三种：第一种是历史模拟法,第二种事分析法,第三种是蒙特卡罗模拟法。这不同的三种方法各有利弊。其中历史模拟法计算速度快,简单易于实现和理解,然而计算过程依赖于大量历史数据,难以满足市场的变化需求。分析法搜集数据和计算都简单易于实现,但是在市场波动时会产生误差,不能有效检验函数分布的有效性。蒙特卡洛模拟法在处理实际问题时的计算精度较高,对于实际问题处理过程中的非线性现象也可以有效处理,但仍然存在高维和静态的不足。 1953年Metropolis, Rosenbluth和Teller最早提出了MCMC方法,他们从某特定分布中随机选取样本点,确定一条均衡于该特定分布的马尔可夫链,通过程序模拟并运行一定的时间,将该链的状态记录下来作为均衡的近似。1970年,Hastings改进了非对称马尔可夫链,推进了MCMC方法的发展。MCMC方法在统计物理学中最早发现并取得迅速发展,随后又被广泛用于研究解决其他领域存在的问题,而且在不同的研究领域中,MCMC方法侧重的研究方向不一致。例如在计算机科学领域,它的侧重点在于运算规模与问题增长的尺度是否相适应。而随着应用的需求,该方法又出现了新的问题需要解决。专家学者们对马尔可夫链及它的收敛性进行了大量研究,最终形成了完全抽样思想,即从马尔可夫链的平稳分布中精确抽样替代原先的近似抽样。1996年Propp和Wilson以及1998年Fill在论文中将这一思想进一步发展和推广。近期,基于遗传法则的仿生学、物理学中MCMC方法也逐渐开始使用,加权MCMC的创新和使用也是近期的新进展。研究者在MCMC方法方面的创造性思想就是在Monte Carlo模拟中引入马尔可夫过程,其本质是Monte Carlo方法的一种特殊形式,传统的Monte Carlo模拟是静态的,然而MCMC方法实现了动态模拟,是对传统的Monte Carlo模拟的创新和改进。通常我们所用到的MCMC方法主要有：Metropolis-Hastings方法,Gibbs抽样,格子Gibbs抽样。本文主要介绍etropolis-Hastings方法、Gibbs抽样方法的原理和步骤,并在最终的上证指数的实证部分应用Gibbs抽样。本文会简单介绍VaR的计算方法和MCMC方法的原理,最后通过运用MCMC方法计算上证指数收益率的VaR,讨论该方法对于VaR计算的重要意义。
[Abstract]:Risk measurement is the core and foundation of risk management, quantitative analysis and assessment to the risk. As the financial market and financial transaction scale, dynamic, complexity increases, and the development of financial theory and financial engineering, financial market risk measurement technology is also more comprehensive, complicated. At present, the main method of measurement of financial market the risk sensitivity analysis, volatility method, VaR, pressure test, and the extreme value theory (EVT). Among them, VaR is the current mainstream financial market risk measurement methods.
At present, there are many kinds of methods of financial market risk management and measurement, such as sensitivity analysis, volatility method, VaR, pressure test, extreme value theory (EVT). Among them, the VaR method of risk management in the financial market and the measure has played a significant role, can be said to be the most important method.
The concept of VaR in mathematics appeared very early, but the financial industry began to be accepted in 1980s. With the development of science and technology and popularization of the VaR framework, the common risk measurement software will provide models to calculate VaR. Many famous international commercial banks, are VaR for the daily risk management of financial institutions and investment companies so, VaR. and disclosure and many government regulators also clearly must use the VaR model to measure the risk in the annual report.
Early, VaR method has not been so widely accepted and recognized. The risk management methods of common and mainstream market with sensitivity analysis, stop, and the nominal amount of exposure. However, derivative products and development makes the traditional risk management method is insufficient. A different derivative products even if nominal amount the same, the risk exposure, the risk degree may vary; on the other hand, the traditional risk management approach does not fully take into account the differences between market and relativity of risk can not be effectively aggregated, so many challenges facing the market differences.VaR on leverage, many factors, the correlation between a comprehensive consideration, risk compared to the previous management method has very large and obvious advantages.
There are three main methods of VaR: the first is the historical simulation method, second kinds of business analysis, third kinds of Monte Carlo simulation method. These three methods have advantages and disadvantages. The historical simulation method the calculation speed is fast, simple and easy to realize and understand, but the calculation process depends on a large number of historical data, it is difficult to meet the changes in market demand. Analysis to collect data and calculations are simple and easy to implement, but market volatility will have error, can not effectively test the validity of the function distribution. The calculation precision of Monte Carlo method in dealing with practical problems of higher degree, can also be effective for nonlinear phenomena of practical problems in the process, but the lack of there are still high dimensional and static.
In 1953, Metropolis, Rosenbluth and Teller first proposed the MCMC method, they were randomly selected from a specific distribution of sample points, determine a balance in the specific distribution of the Markov chain, through the simulation program and run for a certain time, the state record of the chain down as a balanced approximation.1970, improved non Hastings symmetric Markov chain, to promote the development of MCMC methods and.MCMC methods in statistical physics first discovered and achieved rapid development, and has been widely used in other fields to study and solve the existing problems, and in different fields of study, research methods focus on the direction of MCMC is not consistent. For example in the field of computer science, it is the emphasis the size of the operation and the problem of growing scale. It is fit with the needs of the application, the method and the emergence of new problems to be solved. The experts and scholars on Markov Markov chain and its convergence is studied, and eventually formed a complete sampling idea, namely from the stationary distribution of Markov chain in accurate sampling.1996 Propp alternative approximate sampling and Wilson and Fill in 1998 for further development and promotion in this thesis, the original thought. Recently, the genetic algorithm based on bionics, MCMC physics it has been used, the innovation and the use of weighted MCMC and recent progress.
Researchers in the MCMC method of creative thought is in the Monte Carlo simulation is introduced in the Markov process, its essence is a kind of special form of Monte Carlo method, the traditional Monte Carlo simulation is static, however, to realize the dynamic simulation of the MCMC method, is a simulation of the traditional Monte Carlo innovation and improvement.
Usually, the MCMC methods we use include: Metropolis-Hastings method, Gibbs sampling and lattice Gibbs sampling. This paper mainly introduces the principles and steps of etropolis-Hastings method and Gibbs sampling method, and applies Gibbs sampling to the empirical part of the final Shanghai stock index.
This paper will briefly introduce the calculation method of VaR and the principle of MCMC method. Finally, we will calculate the VaR of Shanghai stock index return rate by using MCMC method, and discuss the significance of this method for VaR computing.

【学位授予单位】：山东大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F224;F830.91

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