Muddun Bhuruth

TL;DR: In this paper, the authors considered high-order compact schemes for quasilinear parabolic partial differential equations to discretise the Black-Scholes PDE for the numerical pricing of European and American options.

TL;DR: An improvement of Han and Wu's algorithm for the Black-Scholes equation of American options converges rapidly and numerical solutions with good accuracy are obtained.

TL;DR: In this article, the authors consider exponential time differencing (ETD) schemes for numerical pricing of options and show that one explicit time step computation gives unconditional second order accuracy for European, Barrier and Butterfly spread options under both Black-Scholes geometric Brownian motion model and Merton's jump diffusion model with constant coefficients.

TL;DR: This work considers exponential time integration schemes for fast numerical pricing of European, American, barrier and butterfly options when the stock price follows a dynamics described by a jump-diffusion process and demonstrates the combination of exponential integrators and finite element discretisations with quadratic basis functions leads to highly accurate algorithms for cases when the jump magnitude is Gaussian.

TL;DR: New computational schemes yielding high-order convergence rates for the solution of multi-factor option problems using Galerkin finite element discretizations with quadratic basis functions for the approximation of the spatial derivatives in the pricing equations for stochastic volatility and two-asset option problems are proposed.