2017/12/31 by Marzia De Donno, De Donno, Marzia, Zbigniew Palmowski +3
Economics, Econometrics and Finance · Social Sciences · #Economic theories and models #FOS: Economics and business #Insurance, Mortality, Demography, Risk Management #Mathematical Finance (q-fin.MF) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1801.00266
openalex publication_date 2017/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study perpetual American call and put options in an\nexponential L 'evy model. We consider a negative effective discount rate which\narises in a number of financial applications including stock loans and real\noptions, where the strike price can potentially grow at a higher rate than the\noriginal discount factor. We show that in this case a double continuation\nregion arises and we identify the two critical prices. We also generalize this\nresult to multiple stopping problems of Swing type, that is, when successive\nexercise opportunities are separated by i.i.d. random refraction times. We\nconduct an extensive numerical analysis for the Black-Scholes model and the\njump-diffusion model with exponentially distributed jumps.\n