多资产期权定价模型的数值新方法研究

发布时间：2018-03-21 04:43

本文选题：多资产期权定价模型　切入点：Black-Sholes方程　出处：《华北电力大学》2013年硕士论文　论文类型：学位论文

【摘要】：多资产期权在现代金融交易市场中占有重要的地位,研究多资产期权定价模型的数值解法具有非常重要的理论意义和应用价值。本学位论文研究多资产期权定价模型中的三种典型模型(双币种期权定价模型、双币种交换期权定价模型和一篮子期权定价模型)的数值新方法,利用改进的加性算子分裂(Additional Operator Splitting, AOS)算法对三种模型分别构造了AOS-加权隐格式、AOS-不对称格式、AOS-三时间层格式、AOS-显隐格式和AOS-隐显格式,分析这些差分格式的稳定性、收敛性和计算精度。双币种期权定价模型的差分格式求解：当加权系数取2/1时,AOS-加权隐格式为二阶格式；AOS-不对称格式是一种快速的差分格式,比计算解析解节省近86%的计算时间；AoS-显隐格式和AOS-隐显格式是无条件稳定和收敛的二阶格式,其综合性能优于经典的Crank-Nicolson格式。双币种交换期权定价模型和一篮子期权定价模型的AOS-显隐格式及AOS-隐显格式的计算综合性能较好,具有实际应用价值。理论分析和数值试验表明,本文的AOS-差分数值方法可以有效解决多资产期权定价问题。
[Abstract]:Multi-asset options play an important role in the modern financial market. It is of great theoretical significance and practical value to study the numerical solution of multi-asset option pricing model. This dissertation studies three typical models of multi-asset option pricing model (dual-currency option pricing model). A new numerical method for the pricing of dual-currency exchange options and a basket of options. Using the improved additive Operator spliting algorithm, the AOS-weighted implicit scheme and the AOS-3-time implicit scheme are constructed, respectively, and the stability of these difference schemes is analyzed. Convergence and accuracy. The difference scheme of dual-currency option pricing model: when the weighting coefficient is 2/1, the AOS-weighted implicit scheme is a second-order scheme and the AOS-asymmetric scheme is a fast difference scheme. AoS- explicit schemes and AOS- implicit schemes are unconditionally stable and convergent second-order schemes, which save nearly 86% of computing time compared with analytical solutions. Its comprehensive performance is superior to the classical Crank-Nicolson scheme. The AOS- implicit scheme and the AOS- implicit scheme of the dual-currency exchange option pricing model and the basket option pricing model have good comprehensive performance and have practical application value. Theoretical analysis and numerical experiments show that the AOS- difference numerical method can effectively solve the multi-asset option pricing problem.
【学位授予单位】：华北电力大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F830.9;F224;O241.82

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