基于近似对冲的亚式期权定价模型与实证分析

摘要

考虑了标的股票的价格服从跳扩散过程的亚式定价问题。利用无套利原理和广义 Ito＾公式，运用近似对冲跳跃风险的方法，建立了跳扩散过程中算术平均亚式期权的定价模型。然后，通过变量代换，将超抛物型偏微分方程变为一般抛物型方程，基于半离散化方法，给出了基于半离散化的差分求解方法，并且对差分格式的稳定性和误差进行了分析。最后，以北欧电力交易所曾经交易过的亚式期权为例，对亚式期权定价进行了实证分析。%The Asian pricing was considered when underlying stock price obeys jump-diffusion process.An arithmetic mean Asian options pricing model and a partial differential equation of the pricing model were established by using the generalized Ito^formula and the no-arbitrage principle, based on the method of approximating hedge jump risk.Then,the ultra parabolic partial differential equation was transformed into a generalized parabolic equation by using variable substitution method.The semidiscretization numerical arithmetic scheme of the partial differential equation derived by means of semidiscretization,and the stability and error analysis of the difference scheme were also discussed.Finally,the empirical analysis of Asian option pricing was carried out,taking the Asian-style electricity options,as an example which have been traded in the Nord Pool.