【作者】 黄么姑；

【导师】 梅正阳；

【作者基本信息】 华中科技大学 ， 概率论与数理统计， 2007， 硕士

【摘要】 期权定价的数值模拟由来已久,特别是单资产期权定价的数值模拟,已经有很多种方法如: Monte Carlo模拟法、二项式树法、三项式树法、有限差分法等.本文首先介绍了单资产的期权定价的一些基本的模拟方法:二项式树法、三项式树法和有限差分法,同时在文章中用这些方法进行了数值模拟,并给出了算例以及三种方法的比较结果.然后,基于单资产期权定价的方法,本文研究了两资产的期权定价的基本模拟方法:格模型法和有限差分法.对于格模型方法,我们使用的是五项式格模型法,其中对于两资产的有限差分法模拟,本文给出了一个更为直接有效的方法.本文在三元期权定价问题的隐式差分格式基础之上,对两资产极大极小值的期权进行隐式有限差分法的数值模拟,通过追赶法直接解三对角块矩阵方程得到了两资产期权的价格.随机波动率对期权的价格有着重要的影响,人们对于单资产随机波动率的期权定价研究已有一段时间,但对于两资产或是多资产随机波动率期权定价却未研究.最后,本文假设资产价格收益波动率服从有限马尔可夫链,得到一种基于两资产期权定价的格模型方法的随机波动率模型,从而给出容易实现的算法,并论述了我们方法的合理性,最后还给出了数值算例,进一步表明了本文给出的模拟方法是恰当的.更多还原

【Abstract】 Numerical imitation of option pricing has come for a long tine, especially the numerical imitation of one asset option pricing which has many methods. For example, Monte Carlo, binomial tree, trinomial tree and finite difference method and so on. In this paper, firstly we give some basic methods for single-asset option pricing: binomial tree, trinomial tree and finite difference method. At the same time, we give numerical imitation with these methods and some examples and comparing the result.Base on the method of single-asset option pricing, we study the option pricing method of two- asset: lattice framework and finite difference method. We give a more directly efficient method for finite difference method. In this paper, base on trinomial option pricing we give the numerical imitation of finite difference method for two- asset maximal and minimal option pricing. By solving the block-tridiagonal matrices with pursuit method directly, we get the two-asset option price.Stochastic volatility is very important for option pricing. Option pricing of one asset with stochastic volatility has studied by people. But option pricing of two-asset or multi-asset with stochastic volatility has not studied. In this paper, we suppose income of asset price following the finite Markov chain. Then we get a lattice model of two-asset option pricing with stochastic volatility and giving a easy method. At last, we discuss preciseness and rationality of our method and showing a example.更多还原