A Reduced Basis Method for the Simulation of American Options

TL;DR

This paper introduces a reduced basis method utilizing POD-greedy and angle-greedy procedures to efficiently simulate American options by solving time-dependent variational inequalities.

Contribution

It develops a novel reduced basis approach specifically designed for American option pricing, combining primal and dual space construction techniques.

Findings

High approximation accuracy demonstrated in numerical examples

Fast convergence of the reduced basis method

Effective handling of variational inequalities in option pricing

Abstract

We present a reduced basis method for the simulation of American option pricing. To tackle this model numerically, we formulate the problem in terms of a time dependent variational inequality. Characteristic ingredients are a POD-greedy and an angle-greedy procedure for the construction of the primal and dual reduced spaces. Numerical examples are provided, illustrating the approximation quality and convergence of our approach.