Double continuation regions for American and Swing options with negative discount rate in Lévy models. (11th July 2019)

• Record Type: Journal Article
• Authors: De Donno, Marzia; Palmowski, Zbigniew; Tumilewicz, Joanna
• Is Part Of: Mathematical finance. Volume 30:Number 1(2020)
• Page Start: 196
• Page End: 227
• Publication Date: 2019-07-11
• Subjects: American option -- Lévy process -- negative rate -- optimal stopping; Business mathematics -- Periodicals; 332
• DOI: 10.1111/mafi.12218
• Languages: English
• ISSNs: 0960-1627

Abstract

Abstract: In this paper, we study perpetual American call and put options in an exponential Lévy model. We consider a negative effective discount rate that 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.