带固定比例交易费率的跳扩散欧式期权的定价  

The Pricing of Jump-diffusion European Options with Fixed Ratio Transaction Cost

作　　者：吴强 张寄洲[2] 朱海燕[3] 

机构地区：[1]平安信托有限责任公司风险管理部,上海210210 [2]上海师范大学数理学院,上海200234 [3]连云港师范高等专科学校,江苏连云港222006

出　　处：《数学的实践与认识》2012年第1期1-12,共12页Mathematics in Practice and Theory

基　　金：国家重点基础研究发展计划(973计划)课题(2007CB814903);上海市计算数学重点学科项目;上海市教委科学计算重点实验室项目;上海师范大学前瞻与原创性项目

摘　　要：考虑市场存在交易费率的跳扩散欧式期权的定价问题.由于交易费的存在使得传统的对冲方法不适用,我们将该问题转化为两元的随机控制问题.证明了带固定比例交易费率的跳扩散欧式期权的价格是对应的积分微分不等方程的约束粘性解,并通过马尔科夫链对变分问题进行离散,证明了在粘性意义下离散方法的收敛性.最后给出了数值结果.In this paper, the pricing problem of jump-diffusion European options is considered in a market with transaction costs. As for the trading cost the traditional hedging method can not be applied, we transform the problem into the stochastic control problem with two control variables. We show that the pricing of jump-diffusion European options with fixed ratio transaction cost are the constrained viscosity solution of the corresponding nonlinear integraldifferential inequation. The variational problem is dispersed by the Markov chain. We also show the convergence of discrete schemes in the viscosity sense. In final, the numerical results are given.

关 键 词：欧式期权 交易费 跳扩散 马尔科夫链 积分微分不等方程 约束粘性解 随机控制 

分 类 号：F830.91[经济管理—金融学] O211.6[理学—概率论与数理统计]