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在其首篇论文中提出的不连续彼得罗夫-伽辽金（DPG）方法已广泛应用于计算力学问题。本研究针对基础Black-Scholes模型，提出了用于期权定价与敏感性分析的DPG方法。研究中推导了适用于香草期权、美式期权、亚式期权和障碍期权的原始形式与超弱形式DPG方法。通过一系列标准数值实验，分别检验了所提方法对各类期权的收敛性、稳定性和效率。此外，本研究开发了一套基于DPG方法的C++高性能计算（HPC）期权定价代码，该代码已向公众开放，可用于定制期权定价问题或其他相关问题。