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Double continuation regions for American and Swing options with negative discount rate in Lévy models
Author(s) -
De Donno Marzia,
Palmowski Zbigniew,
Tumilewicz Joanna
Publication year - 2020
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/mafi.12218
Subject(s) - continuation , swing , jump , double exponential function , economics , lévy process , jump diffusion , econometrics , discounting , interest rate , exponential function , mathematics , mathematical economics , financial economics , computer science , finance , mathematical analysis , physics , acoustics , programming language , quantum mechanics
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.