On the acceleration of explicit finite difference methods for option pricing

Accurate Finite Difference Methods for Option Pricing

Finite Element Methods for Option Pricing

The finite element method is well suited to the numerical solution of the partial differential equations arising in finance because they allow for a posteriori error estimates and mesh adaptivity. The method will be described on three simple examples and its advantages will be emphasized.

Compact finite difference scheme for option pricing in Heston’s model

We present a compact high-order finite difference scheme for option pricing in the well-known Heston stochastic volatility model. The scheme is fourth order accurate in space and second order accurate in time. This is also confirmed by the numerical experiments that we present.

Finite Difference Methods for Option Pricing under Lévy Processes: Wiener-Hopf Factorization Approach

In the paper, we consider the problem of pricing options in wide classes of Lévy processes. We propose a general approach to the numerical methods based on a finite difference approximation for the generalized Black-Scholes equation. The goal of the paper is to incorporate the Wiener-Hopf factorization into finite difference methods for pricing options in Lévy models with jumps. The method is a...

Explicit Finite Difference Methods for the Delay Pseudoparabolic Equations

Finite difference technique is applied to numerical solution of the initial-boundary value problem for the semilinear delay Sobolev or pseudoparabolic equation. By the method of integral identities two-level difference scheme is constructed. For the time integration the implicit rule is being used. Based on the method of energy estimates the fully discrete scheme is shown to be absolutely stabl...