离散分红标的资产上的美式期权定价

Pricing American Options on the Underlying Assets Paying Discrete Dividends

本文利用Fourier变换的方法,对服从几何Lévy过程的离散分红标的资产上的美式期权进行定价。对于离散观测的美式期权对应的最优停时问题,可以用逆向归纳表示,然后利用Fourier变换将其转化成为Fourier空间中的逆向归纳,最后利用Fourier逆变换得到美式期权的价格。在定价美式期权的同时,该方法可以计算出每个观测时间点的行权边界值,从而得到提前行权边界。不同于无离散分红标的资产上美式期权的提前行权边界,在离散分红情形下行权边界不是连续变化的。在进行合理的模型参数调整后,本文比较了不同模型下美式期权的提前行权边界,发现提前行权边界之间存在着显著的差异。

This paper employs the Fourier transform to price American options on the underlying assets paying discrete dividends in geometrie Levy processes.The optimal stopping problem of discretely monitored American options can be expressed by the backward induction, then we use the Fourier transform to convert it into the backward induction in the Fourier space.At last the price of American option is obtained by using inverse Fourier transform.At the same time, the boundary value at each monitoring time is evaluated and then we obtain the early exercise boundary.:The early exercise boundary is discontinuous in the discrete dividend case,which is different from that in the non-dividend case.By adjusting the parameters in different models,we compare the early exercise boundaries of American options in these models and obtain the significant difference between the early exercise boundaries.