Radial basis functions with application to finance: American put option under jump diffusion
Radial basis functions with application to finance: American put option under jump diffusion
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径向基函数在金融中的应用：跳跃扩散下的美式看跌期权
DOI：
10.1016/j.mcm.2011.10.014
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发表时间：
2012
影响因子：
--
通讯作者：
Mariyan Milev
中科院分区：
文献类型：
--
作者：
A. Golbabai;D. Ahmadian;Mariyan Milev
在本文中，我们考虑了一个带有自由边界的偏积分微分方程（PIDE）问题，该问题出现在美式期权模型中，当股票价格服从一个带跳跃分量的扩散过程时。我们使用一个前固定转换的标的资产变量来固定的自由边界条件和近似的积分项的Laguerre多项式。我们使用径向基函数（RBF）方法来实现一阶隐式非线性方程组，并应用Crank-Nicholson格式。我们采用预测-校正方法来处理非线性方程组。该方法是稳定的，所得结果与文献中其他数值方法所得结果一致。
In this paper, we consider a partial integro-differential equation (PIDE) problem with a free boundary, arising in an American option model when the stock price follows a diffusion process with jump components. We use a front-fixing transformation of the underlying asset variable to fix the free boundary conditions and approximate the integral term by the Laguerre polynomials. We use the Radial basis functions (RBF) method to achieve an implicit nonlinear system of first order equations and apply the Crank–Nicholson scheme. We apply the Predictor–Corrector method, to deal with the system of nonlinear equations. The proposed method is stable and the results are in agreement with those obtained by other numerical methods in literature.