基于Lie代数解法的时间依赖型期权模型

Time-dependent option pricing model based on the Lie Algebra

以Fokker-P lanck方程和L ie代数为基础,通过对时间依赖型期权定价模型的研究,结合有交易费的欧式期权的定价公式,运用证券组合技术与无套利原理,推导出时间依赖型有交易费的期权定价模型。通过对方程的化简、分析,在一定的条件下将非线性的期权定价模型化为线性的Fokker-P lanck方程的类型进行求解,并得出具体的有交易费的时间依赖型期权定价公式。

By studying the time-dependent fixed striking price and combining the pricing formula of European Option with transaction costs,the securities combination technology and the nonarbitrage theory are applied to a pricing model of the option with Transaction costs. This model is based on the Fokker-Planck equation, the nonlinear model is transformed into linear Fokker-Planck equation in certain conditions, thus a specific pricing formula of the time-dependent option with transaction costs is deduced.