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

  • Hélène Guérin (a1) and Jean-François Renaud (a2)

We study the distribution Ex[exp(-q0t1(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.

Corresponding author
* Postal address: IRMAR, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France. Email address:
** Postal address: Département de Mathématiques, Université du Québec à Montréal, 201 av. Président-Kennedy, Montréal, QC H2X 3Y7, Canada. Email address:
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Advances in Applied Probability
  • ISSN: 0001-8678
  • EISSN: 1475-6064
  • URL: /core/journals/advances-in-applied-probability
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