指数效用下有交易费期权定价的伪谱方法
A pseudospectral method for Option Pricing with Transaction Costs under Exponential Utility
摘要：
针对Davis，Panas和Zariphopoulou提出的指数效用下有交易费的欧式期权定价模型，设计了一种基于Fourier的拟谱数值方法.计算期权价格涉及到解决两个随机最优控制问题。使用指数效用函数，可以减少问题的维度，但必须处理目标函数中的高绝对值。在本文中，我们提出了两个变量的变化，减少了指数增长性的影响。我们提出了一种傅立叶拟谱方法来求解所得到的非线性方程。数值分析的稳定性，一致性，收敛性和局部化误差的方法。数值实验支持了理论结果。并研究了引入交易费用的影响。
英文摘要：
This paper concerns the design of a Fourier based pseudospectral numerical method for the model of European Option Pricing with transaction costs under Exponential Utility derived by Davis, Panas and Zariphopoulou. Computing the option price involves solving two stochastic optimal control problems. With a Exponential Utility function, the dimension of the problem can be reduced, but one has to deal with high absolute values in the objective function. In this paper, we propose two changes of variables that reduce the impact of the exponential growth. We propose a Fourier pseudospectral method to solve the resulting non linear equation. Numerical analysis of the stability, consistency, convergence and localization error of the method are included. Numerical experiments support the theoretical results. The effect of incorporating transaction costs is also studied.
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