Russian and American options under exponential phase-type Lévy models
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/928628
- author
- Asmussen, Sören LU ; Avram, Florin and Pistorius, Martijn R.
- organization
- publishing date
- 2004
- 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
- 2016-04-04 12:04:07
- date last changed
- 2018-11-21 21:08:49
@article{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}}, keywords = {{optimal stopping; Wiener-Hop factorization; Wald martingale; first passage time; Lévy process; Markov additive process}}, language = {{eng}}, pages = {{79--111}}, publisher = {{Elsevier}}, series = {{Stochastic Processes and their Applications}}, title = {{Russian and American options under exponential phase-type Lévy models}}, year = {{2004}}, }