Fast Laplace Transform Methods for Free-Boundary Problems of Fractional Diffusion Equations
Fast Laplace Transform Methods for Free-Boundary Problems of Fractional Diffusion Equations
复制标题
DOI：
10.1007/s10915-017-0423-x
复制
发表时间：
2018
影响因子：
2.5
通讯作者：
Zhiqiang Zhou;Jingtang Ma;Hai-wei Sun
中科院分区：
文献类型：
--
作者：
Zhiqiang Zhou;Jingtang Ma;Hai-wei Sun
本文提出了一种快速拉普拉斯变换方法来求解美式期权定价中出现的一类自由边界分数扩散方程。我们发展了求解自由边界分数阶扩散方程的拉普拉斯变换方法，而不是使用时间步长方法。通过近似自由边界，在固定的空间区域上进行拉普拉斯变换，以代替对时间变量的离散化。利用双曲线轮廓线积分法恢复期权的值。同时，从理论上证明了该系数矩阵是扇形的。因此，保证了快速拉普拉斯变换方法的高精度逼近。数值结果表明，该方法在计算精度和计算复杂度上均优于全差分方法。
In this paper we develop a fast Laplace transform method for solving a class of free-boundary fractional diffusion equations arising in the American option pricing. Instead of using the time-stepping methods, we develop the Laplace transform methods for solving the free-boundary fractional diffusion equations. By approximating the free boundary, the Laplace transform is taken on a fixed space region to replace discretizing the temporal variable. The hyperbola contour integral method is exploited to restore the option values. Meanwhile, the coefficient matrix has theoretically proven to be sectorial. Therefore, the highly accurate approximation by the fast Laplace transform method is guaranteed. The numerical results confirm that the proposed method outperforms the full finite difference methods in regard to the accuracy and complexity.