scholarly journals Explicit solutions of the exit problem for a class of Lévy processes; applications to the pricing of double-barrier options

2012 ◽  
Vol 122 (3) ◽  
pp. 1034-1067 ◽  
Author(s):  
Sonia Fourati
Keyword(s):  
Lévy Processes ◽  
Levy Processes ◽  
Explicit Solutions ◽  
Barrier Options ◽  
Double Barrier ◽  
Exit Problem

Semi-analytical valuation for discrete barrier options under time-dependent Lévy processes

2017 ◽  
Vol 75 ◽  
pp. 167-183 ◽  
Author(s):  
Guanghua Lian ◽  
Song-Ping Zhu ◽  
Robert J. Elliott ◽  
Zhenyu Cui
Keyword(s):  
Lévy Processes ◽  
Levy Processes ◽  
Time Dependent ◽  
Barrier Options

scholarly journals Exit Problems for Spectrally Negative Lévy Processes Reflected at Either the Supremum or the Infimum

2007 ◽  
Vol 44 (4) ◽  
pp. 1012-1030 ◽  
Author(s):  
Xiaowen Zhou
Keyword(s):  
Lévy Processes ◽  
Stable Process ◽  
Levy Processes ◽  
Exit Problem ◽  
Brownian Motion With Drift ◽  
Spectrally Negative Lévy Process ◽  
The Times ◽  
Exit Problems ◽  
Supremum Process ◽  
Spectrally Negative Lévy Processes

For a spectrally negative Lévy process X on the real line, let S denote its supremum process and let I denote its infimum process. For a > 0, let τ(a) and κ(a) denote the times when the reflected processes Ŷ := S − X and Y := X − I first exit level a, respectively; let τ−(a) and κ−(a) denote the times when X first reaches Sτ(a) and Iκ(a), respectively. The main results of this paper concern the distributions of (τ(a), Sτ(a), τ−(a), Ŷτ(a)) and of (κ(a), Iκ(a), κ−(a)). They generalize some recent results on spectrally negative Lévy processes. Our approach relies on results concerning the solution to the two-sided exit problem for X. Such an approach is also adapted to study the excursions for the reflected processes. More explicit expressions are obtained when X is either a Brownian motion with drift or a completely asymmetric stable process.

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