次分数布朗运动环境下含违约风险的交换期权定价  

Pricing of exchange options with credit risk under sub-fractional Brown motion environment

作　　者：王永茂[1] 常竞文 WANG Yong-mao;CHANG Jing-wen(College of Science,Yanshan University,Qinhuangdao 066004,Hebei,China)

机构地区：[1]燕山大学理学院,河北秦皇岛066004

出　　处：《西北师范大学学报（自然科学版）》2018年第6期9-16,51,共9页Journal of Northwest Normal University(Natural Science)

基　　金：廊坊市科技局科学技术研究项目(2016011031)

摘　　要：研究次分数布朗运动环境下带有违约风险的交换期权定价.采用建立在公司价值基础上的违约风险模型,两种标的资产及公司价值的变化过程均由次分数布朗运动刻画,利用二重Mellin变换法得到交换期权定价公式的闭式解.根据理论模型进行数值模拟,研究结果为:交换期权价格与次分数布朗运动的Hurst指数H呈反比;H>1/2时,次分数Black-Scholes模型下交换期权价格低于标准B-S模型下的价格,原因是次分数布朗运动存在"长记忆性";期限越长,风险越大,期权价格越高;公司资产价值越大,期权价格越高,直至某一价值之后趋于平缓;随着公司破产成本率的增加,风险增大,资产价值会有一定幅度的降低.The pricing of exchange options with credit risk under the sub-fractional Brown motion environment is investigated in this paper.A credit risk model based on the value of the company is adopted,and the change process of the two standard assets and corporate value is characterized by the sub-fractional Brown motion.By using the double Mellin transform and partial differential equation method,the analytical solution to the pricing of exchange option is obtained.Moreover,the numerical simulation is carried out according to the theoretical model.The results are as follows:the price of exchange options is inversely proportional to the Hurst index H,and the price of exchange options under the sub-fractional B-S model is lower than the standard B-S model when H>1/2,the reason is that the sub-fractional Brown motion has a characteristic of“long memory”;the longer the period,the greater the risk,the higher the price of the option;the greater the value of a company s assets,the higher the price of options,until a certain value becomes flat;the risk increases with the increase of the company s bankruptcy cost,and the value of the assets will be reduced to a certain extent.

关 键 词：次分数布朗运动 违约风险 交换期权 HURST指数 二重Mellin变换 

分 类 号：O211.6[理学—概率论与数理统计] F830.9[理学—数学]