  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.
