基于分形理论的权证定价模型的研究

发布时间：2018-05-17 08:37

本文选题：分形权证定价 + 广义Hurst指数　；参考：《浙江工商大学》2014年硕士论文

【摘要】：目前学者对基于分形理论的权证定价模型的研究多集中于对分形B-S权证定价模型的研究。我们都知道,B-S权证定价模型之所以能够成立的假设条件就是金融市场是一个服从正态分布的市场,然而大量的研究发现金融市场并不是正态的而是分形的,分形B-S权证定价模型正是在这样的大背景下提出的。尽管对分形B-S权证定价模型的相关研究有很多并且该模型也适合我国金融时间序列所具有的“尖峰厚尾”的特征。但是随着“长虹CWB1”认股权证于2011年8月12日终止交易,预示着中国权证又再一次被繁荣发展的金融市场所淘汰。由此可见,分形B-S权证定价模型在我国的应用还没有完善成熟,研究对分形B-S权证定价模型的改进具有十分重要的理论意义和现实意义。本文主要基于多重分形理论对分形B-S权证定价模型进行研究,主要从两个方面对分形B-S权证定价模型进行了改进：第一,对分形B-S权证定价模型中的波动率进行改进：由于大量的研究表明中国金融市场是分形的市场,传统估计波动率的方法不再适合。在全面思考了金融时间序列具有有偏性、“尖峰厚尾”特征、波动聚类性和杠杆效应的基础上,本文将多重分形相关方法应用于分形B-S权证定价模型中,采用构建多重分形波动率(MFV)的方法来估计分形B-S权证定价模型中的波动率。在构建MFV模型时用到多重分形分析方法中的数盒子(Box-counting Method)的方法。第二,对分形B-S权证定价模型中的Hurst指数进行改进：现今分形B-S权证定价模型都是基于单分形研究Hurst指数的并使用单分形分析方法估算Hurst旨数。然而许多研究发现金融市场的价格波动具有多重分形特征,因此本文提出用基于多重分形的广义Hurst指数来替代基于单分形的Hurst指数并使用多重分形方法中的改进的多重分形消除趋势波动分析法(MF-DFA)估算Hurst指数。本文以中国的葛洲坝认购权证为例,分别对基于单分形的和基于多重分形的B-S权证定价模型进行实证,并对比两者的相对误差。结果表明,基于多重分形的B-S权证定价模型的相对误差比基于单分形的B-S权证定价模型的相对误差小。结果说明中国金融市场的价格波动具有多重分形特征,基于多重分形估算Hurst指数比基于单分形估算Hurst指数更合理,并且使用MFV模型测度的波动率代替常数波动率和广义自回归条件异方差模型测度的波动率是有效的。最后本文对分形B-S权证定价模型作了进一步的研究,研究了影响权证价格的因素,分析了导致权证模型的理论价格和市场实际价格之间产生差异的原因,之后提出了相关政策建议并对后续研究方向提出了展望。
[Abstract]:At present, the research of warrant pricing model based on fractal theory is mainly focused on the research of fractal B-S warrant pricing model. We all know that the hypothesis that the B-S warrant pricing model can be established is that the financial market is a market with normal distribution. However, a large number of studies have found that the financial market is not normal but fractal. Fractal B-S warrant pricing model is proposed under this background. Although there are a lot of researches on the fractal B-S warrant pricing model, and the model is suitable for the "peak and thick tail" characteristics of the financial time series in China. But with Changhong CWB1 ending trading on Aug. 12, 2011, it heralds that Chinese warrants are once again being eliminated by booming financial markets. It can be seen that the application of fractal B-S warrant pricing model in China is not yet mature. The research on the improvement of fractal B-S warrant pricing model is of great theoretical and practical significance. In this paper, the fractal B-S warrant pricing model is studied based on multifractal theory, and the fractal B-S warrant pricing model is improved from two aspects: First, the volatility in the fractal B-S warrant pricing model is improved: because of a large number of studies show that the Chinese financial market is a fractal market, the traditional method of volatility estimation is no longer suitable. Based on the comprehensive consideration of the characteristics of financial time series with bias, "peak and thick tail", volatility clustering and leverage effect, this paper applies multifractal correlation method to the pricing model of fractal B-S warrants. A method of constructing multifractal volatility (MFV) To estimate the volatility in the fractal B-S warrant pricing model. The method of multifractal analysis is used to construct the MFV model. Secondly, the Hurst exponent in the fractal B-S warrant pricing model is improved. Nowadays, the fractal B-S warrant pricing model is based on the single-fractal study of the Hurst exponent and uses the single-fractal analysis method to estimate the Hurst tenor number. However, many studies have found that price volatility in financial markets is multifractal. In this paper, we propose to use generalized Hurst exponent based on multifractal instead of Hurst exponent based on single fractal and to estimate Hurst exponent by using the improved multifractal method of eliminating trend volatility in multifractal method. Taking Gezhouba subscription warrant in China as an example, this paper makes an empirical study of B-S warrant pricing model based on single fractal and multifractal, and compares their relative errors. The results show that the relative error of B-S warrant pricing model based on multifractal is smaller than that of B-S warrant pricing model based on single fractal. The results show that the price fluctuation of Chinese financial market is multifractal, and it is more reasonable to estimate Hurst index based on multifractal than to estimate Hurst index based on single fractal. And it is effective to use volatility of MFV model measure instead of constant volatility and generalized autoregressive conditional heteroscedasticity model measure volatility. Finally, this paper makes a further study on the fractal B-S warrant pricing model, studies the factors that affect the warrant price, and analyzes the reasons leading to the difference between the theoretical price of warrant model and the actual market price. Then put forward the relevant policy recommendations and future research direction.
【学位授予单位】：浙江工商大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F832.5;F224

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