Explicit solutions for the exit problem for a class of Lévy processes. Applications to the pricing of double barrier options

2010/03/25 by Sonia Fourati, Fourati, Sonia
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Economic theories and models #Probability and Risk Models #Stochastic processes and financial applications #math.PR #q-fin.CP

paper · pdf · doi:10.48550/arxiv.1003.4917

arxiv created 2010/03/25 · arxiv updated 2010/03/26

Abstract

Lewis and Mordecki have computed the Wiener-Hopf factorization of a Lévy process whose restriction on ]0,+∞[ of their Lévy measure has a rational Laplace transform. That allows to compute the distribution of (X_t,inf_{0≤ s≤ t}X_s). For the same class of Lévy processes, we compute the distribution of (X_t,inf_{0≤ s≤ t}X_s,sup_{0≤ s≤ t} X_s) and also the behavior of this triple at certain stopping time, like the first exit time of an interval containing the origin. Some applications to the pricing of double barrier options with or without rebate are evocated.

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