几种随机波动率模型及其比较

发布时间：2018-03-02 14:32

本文选题：期权定价模型　切入点：样本内定价　出处：《华中师范大学》2014年硕士论文　论文类型：学位论文

【摘要】：随着全球经济一体化和金融市场的飞速发展,金融领域衍生产品越来越多,也变得越来越重要,其中期权就是人们广泛使用的一种金融工具。期权按执行时间方式可分为欧式和美式期权,美式期权的持有者可以在期权有效期内任何时间行使权力,欧式期权只能在到期日执行。期权赋予持有者做某件事的权利,持有者不一定必须行使该权利。对于欧式期权,BS模型就是市场上一种比较成熟的期权定价模型,它假设期权的标的股票价格服从几何布朗运动,同时假定股票的价格的波动率为常数,而这与市场的真实情况并不相符。实际上,由期权的市场价格得到的隐含波动率并不为常数,而是随期权的行使价格和到期日的变化而变化,这就是人们所观察到的“波动率微笑”现象。为了弥补BS模型的不足,研究者们提出了大量的改进模型,其中又以随机波动率期权定价模型为主,这些模型对期权定价理论的研究和发展产生了深远的影响。本文研究了当随机波动率引入以后,关于SP500股指期权定价方法的改进,我们实证比较了四种随机波动率期权定价模型(1)AHBS模型(2)GARCH模型(3)SV模型(4)VG模型。实证结果表明SV模型在样本内定价和样本外定价的表现都要优于其它模型；通过在值程度观察,所有模型虚值期权的定价误差均较高,并且随着虚值期权向实值期权转变时,其定价误差也在不断地减小；根据期权在值程度的分类情况,随机波动率模型拟合“波动率微笑”更好,但在定价误差上,并不比BS模型好多少。
[Abstract]:With the rapid development of global economic integration and financial markets, more and more derivative products in the financial field are becoming more and more important. Option is a kind of financial instrument widely used by people. It can be divided into European option and American option according to the execution time. The holder of American option can exercise power at any time during the period of validity of the option. The European option can only be executed on the maturity date. The option gives the holder the right to do something, and the holder does not have to exercise that right. It assumes that the underlying stock price of the option is driven by geometric Brownian motion, while the volatility of the stock price is assumed to be constant, which does not correspond to the real situation in the market. In fact, The implied volatility obtained from the market price of an option is not a constant, but changes with the exercise price and the maturity date of the option. This is the observed phenomenon of "volatility smile", in order to make up for the deficiency of BS model. Researchers have put forward a large number of improved models, including stochastic volatility option pricing model, these models have a profound impact on the research and development of option pricing theory. This paper studies the improvement of SP500 stock index option pricing method after the introduction of stochastic volatility. We have empirically compared four stochastic volatility option pricing models, I. e. 1 / AHBS model and / or GARCH model, respectively. The empirical results show that SV model performs better in both intra-sample pricing and out-of-sample pricing than other models, and the empirical results show that SV model performs better than other models in both intra-sample pricing and out-of-sample pricing, and the empirical results show that SV model performs better than other models in both intra-sample pricing and out-of-sample pricing. The pricing error of all model options is high, and the pricing error decreases continuously with the change of virtual value options to real value options, according to the classification of options in the degree of value, The stochastic volatility model fits "volatility smile" better, but the pricing error is not much better than that of BS model.
【学位授予单位】：华中师范大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F830.91;O212.1

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