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Efficient conservative second-order central-upwind schemes for option-pricing problems
Journal of Computational Finance ( IF 1.417 ) Pub Date : 2019-01-01 , DOI: 10.21314/jcf.2019.363
Omishwary Bhatoo , Arshad Ahmud Iqbal Peer , Eitan Tadmor , Desire Yannick Tangman , Aslam Aly El Faidal Saib

The conservative Kurganov–Tadmor (KT) scheme has been successfully applied to option-pricing problems by Germán I. Ramírez-Espinoza and Matthias Ehrhardt. These included the valuation of European, Asian and nonlinear options as Black–Scholes partial differential equations, written in the conservative form, by simply updating fluxes in the black box approach. In this paper, we describe an improvement of this idea through a fully vectorized algorithm of nonoscillatory slope limiters and the efficient use of time solvers. We also propose the application of second-order extensions of KT to option-pricing problems. Our test problems solve one-dimensional benchmark and convection-dominated European options as well as digital and butterfly options. These demonstrate the robustness and flexibility of the pricing methods and set a basis for complex problems. Further, the computation of option Greeks ensures the reliability of these methods. Numerical experiments are performed on barrier options, early exercisable American options and two-dimensional fixed and floating strike Asian options. To the authors’ knowledge, this is the first time American options have been priced by applying the early exercise condition on the semi-discrete formulation of central-upwind schemes. Our results show second-order, nonoscillatory and high-resolution properties of the schemes as well as computational efficiency.

中文翻译:

期权定价问题的有效保守二阶中央上风方案

Germán I. Ramírez-Espinoza 和 Matthias Ehrhardt 已成功地将保守的 Kurganov-Tadmor (KT) 方案应用于期权定价问题。其中包括将欧式、亚式和非线性期权的估值作为 Black-Scholes 偏微分方程,以保守形式编写,通过简单地更新黑箱方法中的通量。在本文中,我们通过非振荡斜率限制器的完全矢量化算法和时间求解器的有效使用来描述这一想法的改进。我们还建议将 KT 的二阶扩展应用于期权定价问题。我们的测试问题解决了一维基准和对流主导的欧式期权以及数字和蝶式期权。这些证明了定价方法的稳健性和灵活性,并为复杂问题奠定了基础。此外,选项希腊人的计算确保了这些方法的可靠性。对障碍期权、早期行权美式期权和二维固定和浮动执行亚洲期权进行了数值实验。据作者所知,这是美式期权首次通过将提前行权条件应用于中央逆风方案的半离散公式来定价。我们的结果显示了该方案的二阶、非振荡和高分辨率特性以及计算效率。早期行权美式期权和二维固定和浮动执行亚洲期权。据作者所知,这是美式期权首次通过将提前行权条件应用于中央逆风方案的半离散公式来定价。我们的结果显示了该方案的二阶、非振荡和高分辨率特性以及计算效率。早期行权美式期权和二维固定和浮动执行亚洲期权。据作者所知,这是美式期权首次通过将提前行权条件应用于中央逆风方案的半离散公式来定价。我们的结果显示了该方案的二阶、非振荡和高分辨率特性以及计算效率。
更新日期:2019-01-01
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