Algebraic Optimized Schwarz Methods for Black-Scholes Models

15.10.2019 14:00 – 15:00

Black-Scholes Models are know to predict price options of the market. There are mainly two
approaches to solve these equations. One approach is based on Monte Carlo simulations
solving stochastic differential equations, and the other approach is based on solving partial
differential equations using FEM or FD methods. In this talk we will consider the latter
approach. We will explore the applicability and the efficiency of Algebraic Optimized Schwarz
Methods (AOSMs) for solving Black-Scholes models. We will consider the European Vanilla Call and
Put Options. Both semi and fully implicit schemes in time will be considered. At each time step we
need to solve a large-scale linear system. The main idea of AOSMs is based on modifying
the classical transmission blocks into optimized blocks obtained from the neighboring sub-domains.
The convergence of the optimal AOSM in the case of a two sub-domain decomposition is in
two iterations for the present model. Some numerical examples will be presented at the end.

Lieu

Room 623, Séminaire d'analyse numérique

entrée libre