In this chapter we study the problem of valuing a (possibly defaultable) derivative asset
contingent on the underlying economic state modeled as a Markov process. To gain …

An increasingly popular and promising approach to solve option pricing models is the use of
numerical methods based on radial basis functions (RBF). These techniques yield high …

We derive and analyze a penalty method for solving American multi-asset option problems.
A small, non-linear penalty term is added to the Black–Scholes equation. This approach …

We propose a numerical method to compute the survival (first-passage) probability density
function in jump-diffusion models. This function is obtained by numerical approximation of …

This paper studies the problem of pricing multi-asset American-style options in the Black–
Scholes–Merton framework. The value function of an option contract is known to satisfy a …

We consider the problem of computing the survival (first-passage) probability density
function of jump-diffusion models with two stochastic factors. In particular the Fokker–Planck …

In this work, we apply the local Wendland radial basis function (RBF) for solving the time-
dependent multi dimensional option pricing nonlinear PDEs. Firstly, cross derivative terms of …

This work addresses the problem of pricing American basket options in a multivariate
setting, which includes among others, the Bachelier and Black–Scholes models. In high …

Numerical solution of the multi-dimensional partial differential equations arising in the
modelling of option pricing is a challenging problem. Mesh-free methods using global radial …

A novel adaptive radial basis function scheme based on the radial basis function methods is
presented for the numerical solution of the Black-Scholes equation, which has been used …