连续时间随机波动率模型下期权的非参数定价
发布时间：2018-11-06 13:47
【摘要】：连续时间随机波动率模型是目前研究期权定价的主流,波动率作为反应标的资产投资回报率的变化程度的指标,受到多方面的影响,其随机特性是基于大量研究得出的,随机波动率不仅解释了微笑模式的基本形状,也同样适用于隐含波动率的“期限结构”。因此连续时间随机波动率的设定能使得模型更好的模拟出基础资产价格运动的过程,从而为进一步的期权定价问题打好基础。 本文基于DELL公司2010年11月5日至2011年11月5日一年内共计253个交易日股票数据作为基础资产的观测数据研究连续时间随机波动率模型研究期权的非参数定价问题,主要做了以下工作： 在第一部分总结了有关模型选择以及随机波动率模型非参数定价方面的研究现状。第二部分介绍并总结了相关预备知识,包括期权定价的影响因素,几类典型的连续时间随机波动率模型,以及非参数估计方法；在第三部分说明了基础资产价格过程的模型以及各项参数的估计方法,主要运用非参数方法估计出波动率函数形式,再在波动率的基础上估计其他各项参数；第四部分是模拟分析,判断模型设定以及方法的选择是否合理：第五部分是实证研究,根据以上方法代入数据得到最终的估计结果。结果表明非参数定价方法能够很好的拟合期权定价过程,
[Abstract]:Continuous time stochastic volatility model is the mainstream of option pricing at present. Volatility, as an indicator of the degree of change of return on investment of underlying assets, is affected by many aspects, and its stochastic characteristics are based on a large number of studies. Random volatility not only explains the basic shape of smile mode, but also applies to the term structure of implicit volatility. Therefore, the continuous time stochastic volatility can make the model better simulate the process of the underlying asset price movement, thus laying a good foundation for the further option pricing problem. Based on the observation data of 253trading days stock data from November 5, 2010 to November 5, 2011, this paper studies the nonparametric pricing problem of option based on continuous time stochastic volatility model. The main work is as follows: in the first part, the research status of model selection and non-parametric pricing of stochastic volatility model is summarized. The second part introduces and summarizes the relevant preparatory knowledge, including the influence factors of option pricing, several typical continuous-time stochastic volatility models, as well as non-parametric estimation methods. In the third part, the model of the basic asset price process and the estimation method of each parameter are explained. The non-parametric method is mainly used to estimate the volatility function form, and then the other parameters are estimated on the basis of volatility. The fourth part is the simulation analysis to judge whether the model setting and the method choice is reasonable. The fifth part is the empirical research, according to the above method substitute the data to obtain the final estimate result. The results show that the non-parametric pricing method can fit the process of option pricing well.
【学位授予单位】：南京理工大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F830.9;F224
本文编号：2314455
[Abstract]:Continuous time stochastic volatility model is the mainstream of option pricing at present. Volatility, as an indicator of the degree of change of return on investment of underlying assets, is affected by many aspects, and its stochastic characteristics are based on a large number of studies. Random volatility not only explains the basic shape of smile mode, but also applies to the term structure of implicit volatility. Therefore, the continuous time stochastic volatility can make the model better simulate the process of the underlying asset price movement, thus laying a good foundation for the further option pricing problem. Based on the observation data of 253trading days stock data from November 5, 2010 to November 5, 2011, this paper studies the nonparametric pricing problem of option based on continuous time stochastic volatility model. The main work is as follows: in the first part, the research status of model selection and non-parametric pricing of stochastic volatility model is summarized. The second part introduces and summarizes the relevant preparatory knowledge, including the influence factors of option pricing, several typical continuous-time stochastic volatility models, as well as non-parametric estimation methods. In the third part, the model of the basic asset price process and the estimation method of each parameter are explained. The non-parametric method is mainly used to estimate the volatility function form, and then the other parameters are estimated on the basis of volatility. The fourth part is the simulation analysis to judge whether the model setting and the method choice is reasonable. The fifth part is the empirical research, according to the above method substitute the data to obtain the final estimate result. The results show that the non-parametric pricing method can fit the process of option pricing well.
【学位授予单位】：南京理工大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F830.9;F224
【参考文献】
相关博士学位论文 前1条
1 陈萍;随机波动率模型的统计推断及其衍生证券的定价[D];南京理工大学;2004年
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