Double continuation regions for American and Swing options with negative discount rate in L\'evy models

TL;DR

This paper analyzes perpetual American and Swing options under a negative discount rate in exponential Lévy models, revealing a double continuation region and identifying critical prices, with numerical insights for specific models.

Contribution

It introduces the concept of double continuation regions for American and Swing options with negative discount rates in Lévy models, extending existing theory.

Findings

Double continuation region identified for negative discount rates.

Critical prices for options are explicitly characterized.

Numerical analysis demonstrates the theoretical results in specific models.

Abstract

In this paper we study perpetual American call and put options in an exponential L\'evy model. We consider a negative effective discount rate which arises in a number of financial applications including stock loans and real options, where the strike price can potentially grow at a higher rate than the original discount factor. We show that in this case a double continuation region arises and we identify the two critical prices. We also generalize this result to multiple stopping problems of Swing type, that is, when successive exercise opportunities are separated by i.i.d. random refraction times. We conduct an extensive numerical analysis for the Black-Scholes model and the jump-diffusion model with exponentially distributed jumps.