Global regularity and probabilistic schemes for free boundary surfaces of multivariate American derivatives and their Greeks

TL;DR

This paper develops global iterative probabilistic schemes to compute free boundary surfaces and Greeks for multivariate American derivatives, establishing convergence through a proof of their global regularity.

Contribution

It introduces a novel probabilistic approach with front-fixing methods for multivariate American derivatives, ensuring convergence via regularity proofs.

Findings

Successfully derived global iterative schemes for free boundary computation.

Proved global regularity of the free boundary surface.

Demonstrated convergence of the proposed schemes.

Abstract

In a rather general setting of multivariate stochastic volatility market models we derive global iterative probabilistic schemes for computing the free boundary and its Greeks for a generic class of American derivative models using front-fixing methods. Convergence is closely linked to a proof of global regularity of the free boundary surface.