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A Spectral Element Method for Option Pricing Under Regime-Switching with Jumps
Journal of Scientific Computing ( IF 2.5 ) Pub Date : 2020-06-12 , DOI: 10.1007/s10915-020-01252-7
Geraldine Tour , Nawdha Thakoor , Jingtang Ma , Désiré Yannick Tangman

In this paper, we propose the spectral element method to price European, digital, butterfly, American, discrete and continuous barrier options in a Markovian jump-diffusion regime-switching economy. The spectral element method discretisation is considered for the approximation of the spatial derivatives in a system of partial integro-differential equations and is chosen because it possesses spectral accuracy such that highly accurate option prices can be obtained using a small number of grid discretisation nodes. Essentially, the spectral element method consists of splitting the computational domain into as many elements as needed and approximating the basis functions by high-order orthogonal polynomials within each element. In order to sustain the high-order convergence in time, we also use an exponential time integration scheme to solve the semi-discrete system. Our numerical examples support our error analysis and indicate that the spectral element method converges exponentially for the values and the hedging parameters of the regime-dependent options. Therefore, the proposed scheme provides a viable alternative to the finite difference or finite element methods which usually converge only algebraically.



中文翻译:

带跳政区切换下期权定价的谱元方法

在本文中,我们提出了一种谱元方法来对马尔可夫跳跃扩散扩散体制转换经济中的欧洲,数字,蝴蝶,美国,离散和连续障碍期权定价。频谱元素方法离散化被认为是用于部分积分微分方程组中空间导数的近似,由于其具有频谱准确性,因此可以使用少量的网格离散化节点获得高精度的期权价格,因此选择频谱元素法进行离散化。本质上,频谱元素方法包括将计算域划分为所需的任意多个元素,并通过每个元素内的高阶正交多项式逼近基本函数。为了保持时间的高阶收敛,我们还使用指数时间积分方案来解决半离散系统。我们的数值示例支持我们的误差分析,并表明,谱元方法对与制度相关的期权的价值和对冲参数呈指数收敛。因此,提出的方案为通常仅代数收敛的有限差分或有限元方法提供了可行的替代方案。

更新日期:2020-06-12
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