基于波动率预测的期权定价研究

发布时间：2018-01-31 02:47

本文关键词： 期权定价模型二叉树波动率预测 GARCH模型　出处：《复旦大学》2013年硕士论文　论文类型：学位论文

【摘要】：随着中国首支个股期权提上日程,期权市场又再次成为了众人注视的焦点。新兴市场的期权的定价是需要迫切研究的课题。在完全市场假定条件下的期权定价模型中,所采用的波动率皆为常数,而现实情况中,标的物的资产收益率是存在异方差性的,单纯使用历史波动率会影响期权定价的准确。通过建模预测未来市场波动率,将预测因素考虑在内的波动率估计值应用于期权定价将会更加准确。本文首先归纳和总结了期权定价的主要方法与模型,包括Black-Sholes定价模型、二叉树模型、有限差分法和蒙特卡洛模拟方法；详细介绍了二叉树定价模型,并提供了一种二叉树定价模型的算法。其次,分别对香港恒生指数欧式看涨期权与欧式看跌期权使用二叉树方法定价,根据模型的定价结果与实际数值进行比较,提出问题和解决问题的方法。最后,由于期权定价模型中的波动率实际上具有一定的异方差性,因此进一步对波动率进行研究。对恒指波动率建立ARMA(1,1)-GARCH(1,1)模型,有效拟合出反应异方差性的模型,并对未来波动率水平进行预测。
[Abstract]:With China's first individual stock option on the agenda. Option market has become the focus of attention again. The pricing of options in emerging markets is an urgent issue to be studied. In the model of option pricing under the assumption of complete market, the volatility is constant. In reality, there is heteroscedasticity in the asset return of the subject matter, and the use of historical volatility will affect the accuracy of option pricing. The future market volatility can be predicted by modeling. It will be more accurate to apply the volatility estimate, which takes into account the forecast factors, to the option pricing. Firstly, this paper summarizes the main methods and models of option pricing, including Black-Sholes pricing model, binary tree model, finite difference method and Monte Carlo simulation method. This paper introduces the binary tree pricing model in detail, and provides an algorithm of the binary tree pricing model. Secondly, the price of Hong Kong Hang Seng index European call option and European put option are priced by binary tree method. According to the comparison between the pricing results of the model and the actual value, the problem and the solution to the problem are put forward. Finally, because the volatility in the option pricing model has a certain heteroscedasticity. Therefore, further study on volatility. To the volatility of the constant index, the ARMA1 / GARCH1) model is established to fit the model of heteroscedasticity effectively. And predict the level of volatility in the future.
【学位授予单位】：复旦大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F224;F832.51

【共引文献】