帕累托—贝塔跳跃扩散模型的参数估计及其应用

发布时间：2018-05-28 14:57

本文选题：尖峰厚尾 + 帕累托-贝塔跳跃扩散　；参考：《华中师范大学》2012年硕士论文

【摘要】：金融衍生产品的定价模型中影响最大的是1973年,Black和Scholes提出的著名的Black-Scholes期权定价模型。该模型是衍生金融工具的合理定价的里程碑式的成果,它为许多相关学科的发展开创了一个崭新的领域,但随着金融业的不断发展,特别是金融行业中的重大突发事件的发生和一些金融改革,人们发现B-S模型不能完全适应金融市场,于是许多学者基于B-S模型进行推广和改进。1976年,Merton考虑在非连续变化场合下的股价期权定价问题,提出了跳跃扩散模型。随后在跳跃扩散模型的前提下,基于不同参数的设置和不同的假设,Kou提出双指数跳跃扩散模型,Ramezani和Zeng提出帕累托-贝塔跳跃扩散(PBJD)模型,这些模型都能体现资产收益分布尖峰厚尾分布和波动率的“微笑”特征。本文在了解这些描述股价波动规律的模型的基础上,主要研究帕累托-贝塔跳跃扩散模型的实证应用,通过模型的基本统计量和模型中的六个参数的估计值来说明PBJD模型能反映重要消息到达时或突发事件发生时股价产生的“跳跃”。本文通过选取中国股市总体走势的统计指标“上证综合指数”作为研究对象,选择美国金融危机这个突发事件作为背景,以2003-2005年上证综指的日收盘价代表金融危机发生前的数据,以2007年-2008年上证综指的日收盘价代表金融危机发生过程中的数据,利用极大似然估计法和二次近似求解约束优化法得出模型的六个参数估计值。通过分析参数估计值,我们发现金融危机发生时,我国股票市场变得不稳定,对外界消息的反应变得较为敏感,股价的跳跃次数更频繁,跳跃幅度更大。
[Abstract]:In the pricing model of financial derivatives, the famous Black-Scholes option pricing model was put forward by Black and Scholes in 1973. The model is a milestone in the rational pricing of derivative financial instruments. It opens up a new field for the development of many related disciplines, but with the continuous development of the financial industry, In particular, with the occurrence of major emergencies in the financial industry and some financial reforms, it has been found that the B-S model can not fully adapt to the financial market. In 1976, Merton considered the pricing problem of stock price options under discontinuous variation, and put forward a jump diffusion model. Then on the premise of jump diffusion model, based on different parameters and different hypotheses, Kou proposed a double exponential jump diffusion model named Ramezani and Zeng, and Pareto Beta Jump Diffusion (PBJDD) model was proposed. These models can reflect the "smile" characteristics of asset return distribution, peak, thick tail distribution and volatility. On the basis of understanding these models which describe the law of stock price volatility, this paper mainly studies the empirical application of the Pareto-Beta jump diffusion model. Through the basic statistics of the model and the estimated values of the six parameters in the model, it is shown that the PBJD model can reflect the "jump" of the stock price when the important message arrives or the sudden event occurs. This paper selects the statistical index "Shanghai Composite Index", which is the statistical index of the overall trend of Chinese stock market, as the research object, and chooses the sudden event of the US financial crisis as the background. The daily closing price of the Shanghai Composite Index from 2003 to 2005 represents the data before the financial crisis, and the daily closing price of the Shanghai Composite Index from 2007 to 2008 represents the data in the course of the financial crisis. The maximum likelihood estimation method and the quadratic approximation method are used to estimate the six parameters of the model. By analyzing the estimated values of the parameters, we find that when the financial crisis occurs, the stock market of our country becomes unstable, the reaction to the outside news becomes more sensitive, the jump frequency of stock price is more frequent, and the jump range is larger.
【学位授予单位】：华中师范大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F832.51

【共引文献】