论文标题
基于计数的B-Splines的有效数值方法
An efficient numerical method based on exponential B-splines for time-fractional Black-Scholes equation governing European options
论文作者
论文摘要
在本文中，有时间分数黑色 - 旋风模型（TFBSM）被认为是研究基础分形传输系统的价格变化。我们开发并分析了一种数值方法来解决欧洲选择的TFBSM。数值方法结合了指数B-Spline搭配以在空间中离散和有限的差异方法以分散时间。使用von-neumann分析，该方法表明该方法无条件稳定。同样，该方法被证明是空间中二次订单的收敛，而$ 2-μ$是时间，其中$μ$是分数导数的订单。我们在各种数值示例上实现了该方法，以说明该方法的准确性和验证理论发现。此外，作为一种应用，该方法用于为欧洲呼叫选项，欧洲冠军选项和欧洲双重障碍召唤选项等几种不同的欧洲选择定价。
In this paper a time-fractional Black-Scholes model (TFBSM) is considered to study the price change of the underlying fractal transmission system. We develop and analyze a numerical method to solve the TFBSM governing European options. The numerical method combines the exponential B-spline collocation to discretize in space and a finite difference method to discretize in time. The method is shown to be unconditionally stable using von-Neumann analysis. Also, the method is proved to be convergent of order two in space and $2-μ$ is time, where $μ$ is order of the fractional derivative. We implement the method on various numerical examples in order to illustrate the accuracy of the method, and validation of the theoretical findings. In addition, as an application, the method is used to price several different European options such as the European call option, European put option, and European double barrier knock-out call option.
