浙江大学学报（理学版）2017，Vol.44Issue(3)：296-301,6.DOI:10.3785/j.issn.1008-9497.2017.03.009
随机波动模型的首中时问题
The first hitting time of stochastic volatility models
摘要
Abstract
This paper explores the first passage times of stochastic volatility CEV model.We mainly solve the joint Laplace transform of the first hitting time and volatility.Firstly, we use the It formula to construct the martingale which can convert the problem into the process of solving a differential equation.Then, we introduce an appropriate second order variable coefficient ordinary differential equation, after a change of variable, it is turned to the Whittaker's equation.It's not difficult to get the general solution of Whittaker's equation.Thus, the explicit expressions for the joint Laplace transformation of the first passage times of stochastic volatility CEV model can be derived.Finally, selecting the parameters γ be 0, 1/2 and 1, let the asset price process covers the O-U process, geometric Brownian motion and square root process.Under different parameters, we obtain explicit expression of the joint Laplace transformation function, and use Matlab to draw the corresponding diagram and analyze the trend of graph.关键词
随机波动CEV模型/首中时/鞅方法/联合拉普拉斯变换/Whittaker方程Key words
stochastic volatility CEV model/first passage times/martingale method/joint Laplace transforms/Whittaker's equation分类
数理科学引用本文复制引用
张苗,刘晖,张飞龙..随机波动模型的首中时问题[J].浙江大学学报（理学版）,2017,44(3):296-301,6.基金项目
国家自然科学基金资助项目(11471254). （11471254）
