河北科技大学学报2017，Vol.38Issue(6)：542-547,6.DOI:10.7535/hbkd.2017yx06006
具有随机波动率的美式期权定价
American option pricing with stochastic volatility processes
摘要
Abstract
In order to solve the problem of option pricing more perfectly,the option pricing problem with Heston stochastic volatility model is considered.The optimal implementation boundary of American option and the conditions for its early execu-tion are analyzed and discussed.In view of the fact that there is no analytical American option pricing formula,through the space discretization parameters,the stochastic partial differential equation satisfied by American options with Heston stochastic volatility is transformed into the corresponding differential equations,and then using high order compact finite difference method,numerical solutions are obtained for the option price.The numerical experiments are carried out to verify the theoreti-cal results and simulation.The two kinds of optimal exercise boundaries under the conditions of the constant volatility and the stochastic volatility are compared,and the results show that the optimal exercise boundary also has stochastic volatility.Under the setting of parameters,the behavior and the nature of volatility are analyzed,the volatility curve is simulated,the calculation results of high order compact difference method are compared,and the numerical option solution is obtained,so that the method is verified.The research result provides reference for solving the problems of option pricing under stochastic volatility such as multiple underlying asset option pricing and barrier option pricing.关键词
金融市场/随机分析/美式期权/随机波动率/自由边界/有限差分法Key words
finance markets/stochastic analysis/American option/stochastic volatility/free boundary/finite difference method分类
数理科学引用本文复制引用
李萍,李建辉..具有随机波动率的美式期权定价[J].河北科技大学学报,2017,38(6):542-547,6.基金项目
陕西省自然科学基金(2016JM1009) （2016JM1009）
陕西省教育厅专项科研计划基金(15JK2183,15JK2134) （15JK2183,15JK2134）
