Russian and American put options under exponential phase-type Lévy models
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.
Year of publication: |
2004
|
---|---|
Authors: | Asmussen, Søren ; Avram, Florin ; Pistorius, Martijn R. |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 109.2004, 1, p. 79-111
|
Publisher: |
Elsevier |
Keywords: | Lévy process Markov additive process First passage time Wald martingale Wiener-Hopf factorization Russian option Optimal stopping |
Saved in:
Online Resource
Saved in favorites
Similar items by person
-
Avram, Florin, (2011)
-
On the optimal dividend problem for a spectrally negative L\'{e}vy process
Avram, Florin, (2007)
-
On perpetual American put valuation and first-passage in a regime-switching model with jumps
Jiang, Zhengjun, (2008)
- More ...