A Reduced Basis Method for Parabolic Partial Differential Equations with Parameter Functions and Application to Option Pricing
Numerical Analysis
2014-08-13 v1
Abstract
We consider the Heston model as an example of a parameterized parabolic partial differential equation. A space-time variational formulation is derived that allows for parameters in the coefficients (for calibration) as well as choosing the initial condition (for option pricing) as a parameter function. A corresponding discretization in space and time amd initial condition is introduced and shown to be stable. Finally, a Reduced Basis Method (RBM) is introduced that is able to use parameter functions also for the initial condition. Corresponding numerical results are shown.
Cite
@article{arxiv.1408.2709,
title = {A Reduced Basis Method for Parabolic Partial Differential Equations with Parameter Functions and Application to Option Pricing},
author = {Antonia Mayerhofer and Karsten Urban},
journal= {arXiv preprint arXiv:1408.2709},
year = {2014}
}