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March 2016 Joint distribution of a spectrally negative Lévy process and its occupation time, with step option pricing in view
Hélène Guérin, Jean-François Renaud
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Adv. in Appl. Probab. 48(1): 274-297 (March 2016).

Abstract

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.

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Hélène Guérin. Jean-François Renaud. "Joint distribution of a spectrally negative Lévy process and its occupation time, with step option pricing in view." Adv. in Appl. Probab. 48 (1) 274 - 297, March 2016.

Information

Published: March 2016
First available in Project Euclid: 8 March 2016

zbMATH: 1337.60090
MathSciNet: MR3473578

Subjects:
Primary: 60G51
Secondary: 91G20

Rights: Copyright © 2016 Applied Probability Trust

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Vol.48 • No. 1 • March 2016
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