On Magnitude, Asymptotics and Duration of Drawdowns for Levy Models

Bernoulli Volume 23, Number 1 (2017), 432-458, Forthcoming

24 Pages Posted: 29 Jun 2015 Last revised: 27 Oct 2016

See all articles by David Landriault

David Landriault

University of Waterloo

Bin Li

University of Waterloo - Department of Statistics and Actuarial Science

Hongzhong Zhang

Columbia University

Date Written: June 28, 2015

Abstract

This paper considers magnitude, asymptotics and duration of drawdowns for some Levy processes. First, we revisit some existing results on the magnitude of drawdowns for spectrally negative Levy processes using an approximation approach. For any spectrally negative Levy process whose scale functions are well-behaved at 0 , we then study the asymptotics of drawdown quantities when the threshold of drawdown magnitude approaches zero. We also show that such asymptotics is robust to perturbations of additional positive compound Poisson jumps. Finally, thanks to the asymptotic results and some recent works on the running maximum of Levy processes, we derive the law of duration of drawdowns for a large class of Levy processes (with a general spectrally negative part plus a positive compound Poisson structure). The duration of drawdowns is also known as the "Time to Recover" (TTR) the historical maximum, which is a widely used performance measure in the fund management industry. We find that the law of duration of drawdowns qualitatively depends on the path type of the spectrally negative component of the underlying Levy process.

Keywords: Asymptotics, Drawdown, Duration, Levy process, Magnitude, Parisian stopping time

JEL Classification: C69

Suggested Citation

Landriault, David and Li, Bin and Zhang, Hongzhong, On Magnitude, Asymptotics and Duration of Drawdowns for Levy Models (June 28, 2015). Bernoulli Volume 23, Number 1 (2017), 432-458, Forthcoming, Available at SSRN: https://ssrn.com/abstract=2624265

David Landriault

University of Waterloo ( email )

Waterloo, Ontario N2L 3G1
Canada

Bin Li

University of Waterloo - Department of Statistics and Actuarial Science ( email )

Waterloo, Ontario N2L 3G1
Canada

Hongzhong Zhang (Contact Author)

Columbia University ( email )

3022 Broadway
New York, NY 10027
United States

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