Advances in Applied Probability
- Adv. in Appl. Probab.
- Volume 48, Number 1 (2016), 274-297.
Joint distribution of a spectrally negative Lévy process and its occupation time, with step option pricing in view
We study the distribution Ex[exp(-q∫0t 1(a,b)(Xs)ds); Xt ∈ dy], where -∞ ≤ a < b < ∞, and where q, t > 0 and x ∈ R for a spectrally negative Lévy process X. More precisely, we identify the Laplace transform with respect to t of this measure in terms of the scale functions of the underlying process. Our results are then used to price step options and the particular case of an exponential spectrally negative Lévy jump-diffusion model is discussed.
Adv. in Appl. Probab., Volume 48, Number 1 (2016), 274-297.
First available in Project Euclid: 8 March 2016
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60G51: Processes with independent increments; Lévy processes
Secondary: 91G20: Derivative securities
Guérin, Hélène; Renaud, Jean-François. Joint distribution of a spectrally negative Lévy process and its occupation time, with step option pricing in view. Adv. in Appl. Probab. 48 (2016), no. 1, 274--297. https://projecteuclid.org/euclid.aap/1457466166