波动率估计的动态集成方法

发布时间：2018-03-14 05:28

本文选题：随机扩散模型　切入点：波动率函数　出处：《东南大学》2017年硕士论文　论文类型：学位论文

【摘要】：在金融市场中,为了描述、定价以及管理金融衍生物,研究者们提出了不同环境下的随机扩散模型。在模型给定的情况下,模型参数的选择被视为与资产定价,证券调整和风险管理有直接联系的重要因素。波动率函数作为随机扩散模型中的基本参数,被用来衡量投资回报率或资产价格的波动程度,关于其的研究对于金融市场有着重要的意义。本文首先介绍了基础知识及理论依据,包括波动率的含义,研究意义和现状以及局部回归方法的基础理论及性质。然后对随机扩散模型的波动率函数进行了研究,引入非参数估计技术,对时间域与状态域估计量的估计方法进行了改进,分别对单域估计量的估计方法及其具体形式进行了深入讨论,并在合理假设下建立了单域估计量的渐近统计性质及双域估计量的渐近独立性,在此基础上结合改进的动态权重选择方法,提出了与以往不同的时间域与状态域的动态集成波动率估计量。最后,通过数值模拟与实证分析发现,本文所提出的方法相较之前的方法有一定优越的表现。
[Abstract]:In financial markets, in order to describe, price and manage financial derivatives, researchers have proposed random diffusion models in different environments. In the case of a given model, the selection of model parameters is considered to be related to asset pricing. Volatility function, as a basic parameter in stochastic diffusion model, is used to measure the volatility of return on investment or asset price. This paper first introduces the basic knowledge and theoretical basis, including the meaning of volatility. The significance and present situation of the research and the basic theory and properties of the local regression method are discussed. Then, the volatility function of the stochastic diffusion model is studied, and the non-parametric estimation technique is introduced to improve the estimation methods of the time domain and the state domain estimator. The estimation methods and their forms of single-domain estimators are discussed, and the asymptotic statistical properties of single-domain estimators and the asymptotic independence of double-domain estimators are established under reasonable assumptions. Based on the improved dynamic weight selection method, a dynamic integrated volatility estimator in time domain and state domain is proposed. Finally, through numerical simulation and empirical analysis, it is found that, The method proposed in this paper is superior to the previous method.
【学位授予单位】：东南大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F830.9;F224

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