The discontinuous Petrov Galerkin (DPG) methodology of Demkowicz and Gopalakrishnan introduced in their first paper has been widely used for problems in computational mechanics. In this investigation, we propose the DPG method for option pricing and sensitivity analysis under the basic Black-Scholes model. In this investigation, primal and ultra-weak formulation of the DPG method is derived for Vanilla options, American options, Asian options, and Barrier options. A wide range of standard numerical experiments is conducted to examine the convergence, stability, and efficiency of the proposed method for each one of the options separately. Besides, a C++ high performance (HPC) code for option pricing with the DPG method is developed which is available to the public to customize it for option pricing problems or other related problems.
翻译：Demkowicz和Gopalakrishnan在第一份论文中采用的不连续的Petrov Galerkin(DPG)方法被广泛用于处理计算力方面的问题;在本次调查中,我们提议采用DPG方法,用于在基本黑雪模型下进行选择定价和敏感性分析;在本次调查中,为Vanilla选项、美国选项、亚洲选项和障碍选项,得出了DPG方法的原始和超弱配制方法;进行了广泛的标准数字实验,分别审查每种选项的拟议方法的趋同、稳定性和效率;此外,还制定了一种C++高性能代码,用于使用DPG方法进行选择定价,供公众定制用于选择定价问题或其他相关问题。
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