On the drawdown of completely asymmetric Lévy processes
The drawdown process Y of a completely asymmetric Lévy process X is equal to X reflected at its running supremum X¯: Y=X¯−X. In this paper we explicitly express in terms of the scale function and the Lévy measure of X the law of the sextuple of the first-passage time of Y over the level a>0, the time G¯τa of the last supremum of X prior to τa, the infimum X¯τa and supremum X¯τa of X at τa and the undershoot a−Yτa− and overshoot Yτa−a of Y at τa. As application we obtain explicit expressions for the laws of a number of functionals of drawdowns and rallies in a completely asymmetric exponential Lévy model.
Volume (Year): 122 (2012)
Issue (Month): 11 ()
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description|
|Order Information:|| Postal: http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Alexei Chekhlov & Stanislav Uryasev & Michael Zabarankin, 2005. "Drawdown Measure In Portfolio Optimization," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(01), pages 13-58.
- Pospisil, Libor & Vecer, Jan & Hadjiliadis, Olympia, 2009. "Formulas for stopped diffusion processes with stopping times based on drawdowns and drawups," Stochastic Processes and their Applications, Elsevier, vol. 119(8), pages 2563-2578, August.
- Foort HAMELINK & Martin HOESLI, 2003.
"Maximum Drawdown and the Allocation to Real Estate,"
FAME Research Paper Series
rp87, International Center for Financial Asset Management and Engineering.
- Foort Hamelink & Martin Hoesli, 2004. "Maximum drawdown and the allocation to real estate," Journal of Property Research, Taylor & Francis Journals, vol. 21(1), pages 5-29, January.
- Peter Carr & Liuren Wu, 2002.
"The Finite Moment Log Stable Process and Option Pricing,"
- Peter Carr & Liuren Wu, 2003. "The Finite Moment Log Stable Process and Option Pricing," Journal of Finance, American Finance Association, vol. 58(2), pages 753-778, 04.
- Olympia Hadjiliadis & Jan Vecer, 2006. "Drawdowns preceding rallies in the Brownian motion model," Quantitative Finance, Taylor & Francis Journals, vol. 6(5), pages 403-409.
When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:122:y:2012:i:11:p:3812-3836. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Shamier, Wendy)
If references are entirely missing, you can add them using this form.