On perpetual American put valuation and first-passage in a regime-switching model with jumps

TL;DR

This paper develops an explicit valuation formula for perpetual American put options within a complex regime-switching Lévy model featuring jumps, utilizing novel matrix Wiener-Hopf factorization techniques.

Contribution

It introduces a new explicit solution for perpetual American puts in regime-switching Lévy models with phase-type jumps, advancing first passage problem methods.

Findings

Derived explicit valuation formula for the option.

Developed a new matrix Wiener-Hopf factorization approach.

Extended first passage analysis to regime-switching Lévy processes.

Abstract

In this paper we consider the problem of pricing a perpetual American put option in an exponential regime-switching L\'{e}vy model. For the case of the (dense) class of phase-type jumps and finitely many regimes we derive an explicit expression for the value function. The solution of the corresponding first passage problem under a state-dependent level rests on a path transformation and a new matrix Wiener-Hopf factorization result for this class of processes.