基于蒙特卡罗法的算术平均亚式外汇期权定价模型.PDFVIP

西北大学学报(自然科学网络版) 2015 年 5 月，第 13 卷，第 3 期 Science Journal of Northwest University Online May. 2015，Vol.13，No.3 基于蒙特卡罗法的算术平均亚式 外汇期权定价模型 刘祎龙，许永峰 （西北大学 数学学院，陕西 西安，710127） 摘 要：外汇期权是一种非常复杂的外汇衍生工具，在金融衍生品市场中占据着重要的地位。本文在 风险中性测度下，应用蒙特卡罗方法，建立了利率与波动率分别服从 CIR 随机利率模型和 Heston 随 机波动率模型的算术平均亚式外汇期权的定价模型，对定价的理论模型进行了数理分析。在此基础上 应用对偶变量、控制变量方差减小技术并将两种技术相结合得到一种混合的方差减小方法，通过实验 模拟结果的分析，混合的方差减小方法更优。 关 键 词：蒙特卡罗法；亚式外汇期权；CIR 模型；Heston 模型；方差减小 中图分类号：O211.9 文献识别码：A 文章编号：1000-274X(2015)0579-11 Research of arithmetic average asian foreign exchange options pricing model based on Monte Carlo method LIU Yi-long，XU Yong-feng (School of Mathematics, Northwest University, Xi’an 710127，China) Abstract: Foreign Exchange Option is a kind of very complex Foreign Exchange Derivatives which plays an important role in the financial derivative market. Under the risk neutral measure, this paper built an Arithmetic Average Asian Foreign Exchange Options Pricing Model in which interest rate and volatility obey CIR random interest rate Model and Heston stochastic volatility Model respectively. This paper also made mathematical analysis of the pricing theory model. Based on the analysis and by using the dual variables reduction technique, control variables reduction technique and a better variance reduction technique created by combining both reduction techniques，this paper made simulations of Numerical examples and made contrastive analysis of simulation value. Key words: Monte Carlo method; asian foreign exchange options; CIR model; Heston model; variables reduction 上世纪后期以美国为首的布雷顿森林体系逐步瓦解，世界各国逐渐开