跳跃扩散下美式期权定价模型的高效算法

研究跳跃扩散模型下美式期权定价问题的高效数值求解方法.首先在空间方向上利用高精度紧致差分格式离散期权定价模型，再对离散后所得到的常微分方程时间离散转化为线性互补问题.对线性互补问题的计算可求得期权价格的数值近似解.最后为了克服初始条件的不光滑性，对美式期权定价模型运用了奇异性分离的方法以提高计算结果的精度.数值实例验证了本文所建立算法的优越性.

An Efficient Algorithm for American Option Pricing in the Jump-Diffusion Model

The efficient numerical methods for solving the American option pricing model under jump-diffusion is studied. First of all, the high accuracy compact difference scheme is applied to discrete the option pricing model in the spatial direction, and discrete the temporal variable of the resulting ordinary differential equation to the linear complementarity problem (LCP). The approximation value of option price is obtained by solving the LCP. Finally, in order to overcome the nonsmoothness of payoff function, the singularity separating method is utilized for the American option pricing model to improve the accuracy of calculation. Numerical examples demonstrate the superiority of the algorithm.