Optimal stopping and perpetual options for Lévy processes
AbstractConsider a model of a financial market with a stock driven by a Lévy process and constant interest rate. A closed formula for prices of perpetual American call options in terms of the overall supremum of the Lévy process, and a corresponding closed formula for perpetual American put options involving the infimum of the after-mentioned process are obtained. As a direct application of the previous results, a Black-Scholes type formula is given. Also as a consequence, simple explicit formulas for prices of call options are obtained for a Lévy process with positive mixed-exponential and arbitrary negative jumps. In the case of put options, similar simple formulas are obtained under the condition of negative mixed-exponential and arbitrary positive jumps. Risk-neutral valuation is discussed and a simple jump-diffusion model is chosen to illustrate the results.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoArticle provided by Springer in its journal Finance and Stochastics.
Volume (Year): 6 (2002)
Issue (Month): 4 ()
Note: received: June 2000; final version received: November 2001
Contact details of provider:
Web page: http://www.springerlink.com/content/101164/
Find related papers by JEL classification:
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- Luis H. R. Alvarez & Teppo A. Rakkolainen, 2006.
"A Class of Solvable Optimal Stopping Problems of Spectrally Negative Jump Diffusions,"
9, Aboa Centre for Economics.
- Luis H. R. Alvarez E. & Pekka Matom\"aki & Teppo A. Rakkolainen, 2013. "A Class of Solvable Optimal Stopping Problems of Spectrally Negative Jump Diffusions," Papers 1302.4181, arXiv.org.
- Asmussen, Søren & Avram, Florin & Pistorius, Martijn R., 2004. "Russian and American put options under exponential phase-type Lévy models," Stochastic Processes and their Applications, Elsevier, vol. 109(1), pages 79-111, January.
- Boyarchenko, Svetlana & Levendorskii, Sergei, 2010. "Optimal stopping in Levy models, for non-monotone discontinuous payoffs," MPRA Paper 27999, University Library of Munich, Germany.
- Yu-Ting Chen & Cheng-Few Lee & Yuan-Chung Sheu, 2007. "An ODE approach for the expected discounted penalty at ruin in a jump-diffusion model," Finance and Stochastics, Springer, vol. 11(3), pages 323-355, July.
- Gapeev, Pavel V., 2008. "The integral option in a model with jumps," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2623-2631, November.
- Albert Ferreiro-Castilla & Kees van Schaik, 2013. "Applying the Wiener-Hopf Monte Carlo simulation technique for Levy processes to path functionals such as first passage times, undershoots and overshoots," Papers 1306.3923, arXiv.org.
- Christensen, Sören & Salminen, Paavo & Ta, Bao Quoc, 2013. "Optimal stopping of strong Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 1138-1159.
- Luis Alvarez & Teppo Rakkolainen, 2010. "Investment timing in presence of downside risk: a certainty equivalent characterization," Annals of Finance, Springer, vol. 6(3), pages 317-333, July.
- Bilkic, Natasa & Gries, Thomas, 2012. "When to Attack an Oppressive Government?," Annual Conference 2012 (Goettingen): New Approaches and Challenges for the Labor Market of the 21st Century 62031, Verein für Socialpolitik / German Economic Association.
- Lee, Sangjun & Zhao, Jinhua & Thornsbury, Suzanne, 2013. "Extreme Events and Land Use Decisions under Climate Change in Tart Cherry Industry in Michigan," 2013 Annual Meeting, August 4-6, 2013, Washington, D.C. 150568, Agricultural and Applied Economics Association.
- Michi Nishihara & Takashi Sshibata, 2011. "Investment timing with fixed and proportional costs of external financing," Discussion Papers in Economics and Business 11-29, Osaka University, Graduate School of Economics and Osaka School of International Public Policy (OSIPP).
- Aase, Knut K, 2005. "The perpetual American put option for jump-diffusions with applications," University of California at Los Angeles, Anderson Graduate School of Management qt31g898nz, Anderson Graduate School of Management, UCLA.
- Chuancun Yin & Yuzhen Wen & Ying Shen, 2013. "The first passage time problem for mixed-exponential jump processes with applications in insurance and finance," Papers 1302.6762, arXiv.org.
- Pavel V. Gapeev, 2006. "Integral Options in Models with Jumps," SFB 649 Discussion Papers SFB649DP2006-068, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
- Jukka Lempa, 2006. "On Infinite Horizon Optimal Stopping of General Random Walk," Discussion Papers 3, Aboa Centre for Economics.
- L. Alili & A. E. Kyprianou, 2005. "Some remarks on first passage of Levy processes, the American put and pasting principles," Papers math/0508487, arXiv.org.
- Denis Belomestny & Markus Reiß, 2006.
"Spectral calibration of exponential Lévy Models ,"
SFB 649 Discussion Papers
SFB649DP2006-034, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
- Davis, Graham A. & Cairns, Robert D., 2012. "Good timing: The economics of optimal stopping," Journal of Economic Dynamics and Control, Elsevier, vol. 36(2), pages 255-265.
- Aase, Knut K., 2005. "The perpetual American put option for jump-diffusions with applications," Discussion Papers 2005/12, Department of Business and Management Science, Norwegian School of Economics.
- repec:ner:carlos:info:hdl:10016/12179 is not listed on IDEAS
- Christensen, Sören & Irle, Albrecht, 2009. "A note on pasting conditions for the American perpetual optimal stopping problem," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 349-353, February.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Guenther Eichhorn) or (Christopher F Baum).
If references are entirely missing, you can add them using this form.