Advances in Applied Probability

Joint distribution of a spectrally negative Lévy process and its occupation time, with step option pricing in view

Hélène Guérin and Jean-François Renaud

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We study the distribution Ex[exp(-q0t 1(a,b)(Xs)ds); Xt ∈ dy], where -∞ ≤ a < b < ∞, and where q, t > 0 and xR 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.

Article information

Adv. in Appl. Probab., Volume 48, Number 1 (2016), 274-297.

First available in Project Euclid: 8 March 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G51: Processes with independent increments; Lévy processes
Secondary: 91G20: Derivative securities

Occupation time spectrally negative Lévy process fluctuation theory scale function step option


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.

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