CEV过程下带交易费的期权定价及其数值解法
发布时间：2019-02-16 16:37
【摘要】：Cox和Ross在 1995年对CEV(Constant Elasticity of Variance,不变弹性方差)过程进行了研究,提出了标的资产服从CEV过程的期权定价模型;Leland在1985年提出δ-hedging方法,可在Black-Scholes模型的基础上获得存在交易费用的定价模型。综合Cox和Leland的研究,我们可以得到CEV过程下带交易费的期权定价模型。目前不少研究人员已对这类期权定价模型进行过数值求解,但大多为二叉树法和有限差分法,用有限元法求解该模型的很少。本文尝试使用二次有限元方法求解CEV过程下带交易费的期权定价模型,发现二次有限元方法非常有效,其数值实验结果也与实际观察情况一致。
[Abstract]:In 1995, Cox and Ross studied the process of CEV (Constant Elasticity of Variance, invariant elastic variance, and put forward the option pricing model of underlying asset from CEV process. Leland proposed 未-hedging method in 1985, which can obtain the pricing model with transaction cost on the basis of Black-Scholes model. Based on the research of Cox and Leland, we can get the option pricing model with transaction cost in CEV process. At present, many researchers have solved this kind of option pricing model numerically, but most of them are binary tree method and finite difference method, few of them are solved by finite element method. In this paper, the quadratic finite element method is used to solve the option pricing model with transaction cost in the CEV process. It is found that the quadratic finite element method is very effective, and its numerical experimental results are in agreement with the actual observation.
【学位授予单位】：湘潭大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O241.8
本文编号：2424638
[Abstract]:In 1995, Cox and Ross studied the process of CEV (Constant Elasticity of Variance, invariant elastic variance, and put forward the option pricing model of underlying asset from CEV process. Leland proposed 未-hedging method in 1985, which can obtain the pricing model with transaction cost on the basis of Black-Scholes model. Based on the research of Cox and Leland, we can get the option pricing model with transaction cost in CEV process. At present, many researchers have solved this kind of option pricing model numerically, but most of them are binary tree method and finite difference method, few of them are solved by finite element method. In this paper, the quadratic finite element method is used to solve the option pricing model with transaction cost in the CEV process. It is found that the quadratic finite element method is very effective, and its numerical experimental results are in agreement with the actual observation.
【学位授予单位】：湘潭大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O241.8
【参考文献】
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