Pricing European and American Options under Heston Model using Discontinuous Galerkin Finite Elements

TL;DR

This paper presents an advanced discontinuous Galerkin finite element method for efficiently and accurately pricing European and American options under the Heston model, including handling nonsmooth conditions and the American option free boundary problem.

Contribution

It introduces a novel application of dGFEM with Rannacher smoothing and a PSOR method for American options under the Heston model, demonstrating improved efficiency and accuracy.

Findings

dGFEM effectively handles nonsmooth initial conditions.

The method efficiently solves the convection-dominated Heston model.

Numerical experiments confirm superior accuracy and speed.

Abstract

This paper deals with pricing of European and American options, when the underlying asset price follows Heston model, via the interior penalty discontinuous Galerkin finite element method (dGFEM). The advantages of dGFEM space discretization with Rannacher smoothing as time integrator with nonsmooth initial and boundary conditions are illustrated for European vanilla options, digital call and American put options. The convection dominated Heston model for vanishing volatility is efficiently solved utilizing the adaptive dGFEM. For fast solution of the linear complementary problem of the American options, a projected successive over relaxation (PSOR) method is developed with the norm preconditioned dGFEM. We show the efficiency and accuracy of dGFEM for option pricing by conducting comparison analysis with other methods and numerical experiments.