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Russian and American options under exponential phase-type Lévy models

Asmussen, Sören LU ; Avram, Florin and Pistorius, Martijn R. (2004) In Stochastic Processes and their Applications p.79-111
Abstract
Consider the American put and Russian option (Ann. Appl. Probab. 3(1993)603; Theory Probab. Appl. 39 (1994)103; Ann. Appl. Probab. 3(1993)641) with the stock price modeled as an exponential Lévy process. We find an explicit expression for the price in the dense class of Lévy processes with phase-type jumps in both directions. The solution rests on the reduction to the first passage time problem for (reflected) Lévy processes and on an explicit solution of the latter in the phase-type case via martingale stopping and Wiener-Hopf factorization. The same type of approach is also applied to the more general class of regime switching Lévy processes with phase-type jumps.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
optimal stopping, Wiener-Hop factorization, Wald martingale, first passage time, Lévy process, Markov additive process
in
Stochastic Processes and their Applications
pages
79 - 111
publisher
Elsevier
ISSN
1879-209X
language
English
LU publication?
yes
id
66394a03-312b-431c-8991-6029e2f044d0 (old id 928628)
date added to LUP
2008-01-14 16:01:41
date last changed
2016-11-23 14:19:36
@misc{66394a03-312b-431c-8991-6029e2f044d0,
  abstract     = {Consider the American put and Russian option (Ann. Appl. Probab. 3(1993)603; Theory Probab. Appl. 39 (1994)103; Ann. Appl. Probab. 3(1993)641) with the stock price modeled as an exponential Lévy process. We find an explicit expression for the price in the dense class of Lévy processes with phase-type jumps in both directions. The solution rests on the reduction to the first passage time problem for (reflected) Lévy processes and on an explicit solution of the latter in the phase-type case via martingale stopping and Wiener-Hopf factorization. The same type of approach is also applied to the more general class of regime switching Lévy processes with phase-type jumps.},
  author       = {Asmussen, Sören and Avram, Florin and Pistorius, Martijn R.},
  issn         = {1879-209X},
  keyword      = {optimal stopping,Wiener-Hop factorization,Wald martingale,first passage time,Lévy process,Markov additive process},
  language     = {eng},
  pages        = {79--111},
  publisher    = {ARRAY(0x9042508)},
  series       = {Stochastic Processes and their Applications},
  title        = {Russian and American options under exponential phase-type Lévy models},
  year         = {2004},
}