具有非线性波动函数的二维全非线性Black-Scholes方程的多重网格方法

IF 0.8 4区数学

数学研究 Pub Date : 2020-06-01 DOI:10.4208/jms.v53n3.20.02

Aicha Driouch Hassan Al Moatassime

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引用次数: 0

摘要

本文研究了在存在交易成本的情况下对欧洲一篮子期权进行定价的任务。我们开发了一个模型，将市场的非流动性纳入经典的两种资产Black-Scholes框架。我们使用有限差分法进行了数值模拟。为了降低计算成本，我们考虑了一种非线性多重网格方法。本文的目的是研究Barles和Soner模型的确定性扩展，并证明多重网格方法在求解完全非线性的二维Black-Scholes问题时的有效性。AMS受试者分类：65N55、65N06、35K55、65BXX

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Multigrid Method for a Two Dimensional Fully Nonlinear Black-Scholes Equation with a Nonlinear Volatility Function

This paper deals with the task of pricing European basket options in the presence of transaction costs. We develop a model that incorporates the illiquidity of the market into the classical two-assets Black-Scholes framework. We perform a numerical simulation using finite difference method. We consider a nonlinear multigrid method in order to reduce computational costs. The objective of this paper is to investigate a deterministic extension for the Barles’ and Soner’s model and to demonstrate the effectiveness of multigrid approach to solving a fully nonlinear two dimensional Black-Scholes problem. AMS subject classifications: 65N55, 65N06, 35K55, 65BXX

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来源期刊

数学研究 MATHEMATICS-

自引率

0.00%

发文量

1109

期刊介绍： Journal of Mathematical Study (JMS) is a comprehensive mathematical journal published jointly by Global Science Press and Xiamen University. It publishes original research and survey papers, in English, of high scientific value in all major fields of mathematics, including pure mathematics, applied mathematics, operational research, and computational mathematics.