Spectral Methods for Parabolic PDEs in Finance

Chebyshev spectral collocation is applied to parabolic pricing PDEs, achieving exponential convergence for smooth payoffs.

Viscosity Solutions and Comparison Principles for Fully Nonlinear PDEs

A self-contained treatment of the comparison principle for viscosity solutions of fully nonlinear second-order elliptic equations arising in control theory.

Numerical Solution of the Heston PDE by ADI Splitting

Alternating direction implicit methods are applied to the two-dimensional Heston PDE and compared on accuracy and computational cost.

The Explicit Euler Scheme for the American Put Option

Convergence of the explicit Euler discretisation applied to the free-boundary problem for the American put is established under a CFL-type condition.

Finite Difference Methods for the Black-Scholes PDE

We analyse explicit and implicit finite difference schemes for the Black-Scholes PDE, establishing stability, consistency, and convergence.