带固定比例交易费率的跳扩散欧式期权的定价

• 作 者: 吴强 张寄洲 朱海燕
• 机 构: 平安信托有限责任公司风险管理部,上海师范大学数理学院,连云港师范高等专科学校,
• 出 处: 数学的实践与认识
• 发表日期: 2012年01期
• 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

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.

We consider the problem of the pricing of the jump-diffusion European option with the existence of the transaction rate in the market. Since the traditional hedging method is not suitable because of the transaction costs, we transform the problem into a two-variable stochastic control problem. The price of jump-diffusion European option is the constrained viscosity solution of the corresponding integral differential inequality, and the variational problem is discretized by Markov chain, which proves the convergence of the discrete method in viscous sense.Finally numerical results are given .