基于动态对冲关系的股票期权定价研究

发布时间：2018-02-17 04:09

本文关键词： VIX-已实现GARCH 模型期权定价隐含波动率　出处：《吉林大学》2017年硕士论文　论文类型：学位论文

【摘要】：现代期权定价理论有两个发展方向,一个以模型为基础,通过建立无套利等价组合,推导微分方程,随后寻求方程的解析解或者数值解;另一个是从历史信息出发,挖掘历史价格信息,通过预测对期权价格有决定性影响的因子的未来值来确定未来期权价格。尽管目前模型法求解期权价值的研究已经进入较为深入的阶段,取得了较为丰富的成果,但是由于多数模型应用难度大,该方法遇到了普及困难的问题。而通过非模型方法为期权定价,正逐渐得到更多的关注。首先本文对要研究问题的选题背景和意义进行了阐述,对传统模型定价方法进行了梳理,介绍了非模型期权定价基本方法。其次,本文梳理了单元GARCH和多元GARCH模型设定和估计方法,并说明了GARCH模型在期权定价中的应用。本文在以往学者研究的基础上,对隐含波动率和实际波动率动态对冲关系进行建模,并结合正则期权定价模型来为期权进行定价。已实现方法差的加入能显著提高GARCH模型拟合和预测资产波动率的能力。本文借鉴这个思路,在GARCH模型基础上加入了已实现协方差,建立了VIX-已实现GARCH模型,试图提高模型的预测能力。本文采用两阶段拟极大似然估计方法对建立的已实现单元和多元GARCH模型参数进行估计,在第一阶段股价波动率方程中使用了已实现GARCH模型,这样建立了VIX-收益率-已实现方差模型。使用标准普尔500指数,芝加哥交易所发布隐含波动率VIX指数,标准普尔500期权,对提出已实现DCC-GARCH模型期权定价能力进行了检测。选用2000年1月3日到2016年12月21日作为样本,本文分别将使用VIX-已实现GARCH模型来估计的波动率和使用普通GARCH模型估计的波动率代入到正则期权定价模型中去,通过对比误差项,来比较两者定价的效率。最终的研究结果显示:隐含波动率指数和标准普尔500指数收益率具有明显的负相关性,隐含波动率意味着未来收益率的降低;高频已实现协方差对低频隐含波动率和实际方差之间相关性具有显著的影响,在模型中添加已实现协方差是必要的;本文提出的已实现DCC模型可以对未来隐含波动率做出良好的预测,但是仍有系统性低估未来隐含波动率的可能;基于本文提出的已实现DCC-GARCH模型的正则期权定价模型比基于普通GARCH模型的正则期权定价模型更优越。
[Abstract]:Modern option pricing theory has two development directions, one is based on model, by establishing equivalent combination of no arbitrage, deducing differential equation, and then seeking analytic solution or numerical solution of equation, the other is based on historical information. Mining historical price information and predicting the future value of the factors that have a decisive effect on the option price are used to determine the future option price, although the study of solving the option value by the current model method has entered a deeper stage. But because most models are difficult to apply, it is difficult to popularize the method. First of all, this paper expounds the background and significance of the topics to be studied, combs the traditional model pricing methods, and introduces the basic pricing methods of non-model options. This paper reviews the methods of setting and estimating unit GARCH and multivariate GARCH models, and explains the application of GARCH model in option pricing. Based on the previous researches, this paper models the dynamic hedging relationship between implied volatility and actual volatility. The ability of GARCH model to fit and predict the volatility of assets can be significantly improved by adding the difference in the realized methods. This paper uses this idea for reference and adds realized covariance to the GARCH model. The VIX- implemented GARCH model is established to improve the prediction ability of the model. In this paper, the parameters of the implemented unit and the multivariate GARCH model are estimated by using the two-stage quasi-maximum likelihood estimation method. The realized GARCH model is used in the first stage of the stock price volatility equation, thus the VIX- yield realized variance model is established. Using the Standard & Poor's 500 Index, the Chicago Exchange issues the implied volatility VIX Index, the Standard & Poor's 500 option. The option pricing ability of the proposed DCC-GARCH model is tested. The sample is from January 3rd 2000 to December 21st 2016. In this paper, the volatility estimated by using VIX- implemented GARCH model and the volatility estimated by ordinary GARCH model are substituted into the regular option pricing model, and the error terms are compared. Finally, the results show that the yield of implied volatility index and S & P 500 index have obvious negative correlation, and implied volatility rate means the decline of future rate of return; The high frequency realized covariance has a significant influence on the correlation between the low frequency implied volatility and the actual variance, so it is necessary to add the realized covariance to the model. The realized DCC model proposed in this paper can make a good prediction of the future implied volatility, but it is still possible to systematically underestimate the future implied volatility. The regular option pricing model based on the realized DCC-GARCH model is superior to the regular option pricing model based on the ordinary GARCH model.
【学位授予单位】：吉林大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224;F830.9

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