Occupation Times Related to Drawdowns

Zhang Hongzhong

Chapter 5 in Stochastic Drawdowns, 2018, pp 81-97 from World Scientific Publishing Co. Pte. Ltd.

Abstract: The amount of time when the underlying price is in distress can characterize investment risks from a different angle. In Chapter 5, we propose to study a number of occupation times that are related to the drawdowns and drawups of a linear diffusion process. To that end, we derive analytical formulas for the Laplace transform of the occupation time of the underlying below a fixed threshold y upon leaving a given finite interval. We then use Lehoczky’s approximation technique and progressive enlargement of filtration to extend these results to occupation times of the drawdown or drawup process. In special cases of drifted Brownian motion and threedimensional Bessel process, our results imply that the occupation time of the drawdown process has the same distribution as the first passage time of the drawdown process. We also demonstrate how our analytical results can be used for computing probabilities of drawdown events under Omega default models, and for evaluation of Parisian-like or α-quantile options written on the drawdowns.

Keywords: Drawdown; Maximum Drawdown; Insurance; Optimal Trading (search for similar items in EconPapers)
JEL-codes: C02 G32 (search for similar items in EconPapers)
Date: 2018
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.worldscientific.com/doi/pdf/10.1142/9789813141643_0005 (application/pdf)
https://www.worldscientific.com/doi/abs/10.1142/9789813141643_0005 (text/html)
Ebook Access is available upon purchase.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:wschap:9789813141643_0005

Ordering information: This item can be ordered from

Access Statistics for this chapter

More chapters in World Scientific Book Chapters from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().