A Discontinuous Galerkin Method for Pricing American Options Under the Constant Elasticity of Variance Model (Communications in Computational Physics, 2018)
The pricing of option contracts is one of the classical problems in MathematicalFinance. While useful exact solution formulas exist for simple contracts, typicallynumerical simulations are mandated due to the fact that standard features, suchas early-exercise, preclude the existence of such solutions. In this paper we considerderivatives which generalize the classical Black-Scholes setting by not only admittingthe early-exercise feature, but also considering assets which evolve by the ConstantElasticity of Variance (CEV) process (which includes the Geometric Brownian Motionof Black-Scholes as a special case). In this paper we investigate a DiscontinuousGalerkin method for valuing European and American options on assets evolvingunder the CEV process which has a number of advantages over existing approachesincluding adaptability, accuracy, and ease of parallelization.