摘要
在次分数Ho-Lee随机利率模型下,利用Δ对冲原理,建立了次分数跳-扩散过程下,带有交易费和红利支付的几何平均亚式期权定价的偏微分方程模型;通过变量代换将定价模型化为Cauchy问题;利用有限差分法和复合梯形法给出了定价模型的数值解,并通过一个算例检验了算法设计的有效性.
Under the assumption of the sub-fractional Ho-Lee stochastic interest rate model, this research firstly uses the delta hedging principle and establishes the partial differential equation of geometric average Asian options under the sub-fractional jump-diffusion process with transaction costs and dividends. Secondly, the pricing model is simplified to the Cauchy problem by using the variable substitution. Finally, a numerical solution of the pricing model is given by using the finite difference method and the composite trapezoid method. An example is also given to verify the effectiveness of the algorithm design.
作者
胡攀
HU Pan(Department of Mathematics,Sichuan University of Arts and Science,Dazhou 635000,China)
出处
《云南民族大学学报(自然科学版)》
CAS
2019年第5期462-469,共8页
Journal of Yunnan Minzu University:Natural Sciences Edition
基金
四川文理学院应用创新团队项目(2018KC0012)
关键词
Ho-Lee随机利率模型
次分数布朗运动
跳-扩散模型
亚式期权
数值解
Ho-Lee stochastic interest rate model
sub-fractional Brownian motion
jump-diffusion model
Asian options
numerical solution