On the Frequency of Drawdowns for Brownian Motion Processes

18 Pages Posted: 7 Mar 2014

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: February 28, 2014

Abstract

Drawdowns measuring the decline in value from the historical running maxima over a given period of time, are considered as extremal events from the standpoint of risk management. To date, research on the topic has mainly focus on the side of severity by studying the first drawdown over certain pre-specified size. In this paper, we extend the discussion by investigating the frequency of drawdowns, and some of their inherent characteristics. We consider two types of drawdown time sequences depending on whether a historical running maximum is reset or not. For each type, we study the frequency rate of drawdowns, the Laplace transform of the n-th drawdown time, the distribution of the running maximum and the value process at the n-th drawdown time, as well as some other quantities of interest. Interesting relationships between these two drawdown time sequences are also established. Finally, insurance policies protecting against the risk of frequent drawdowns are also proposed and priced.

Keywords: Drawdown; Frequency; Brownian motion

JEL Classification: G01; G13; G22

Suggested Citation

Landriault, David and Li, Bin and Zhang, Hongzhong, On the Frequency of Drawdowns for Brownian Motion Processes (February 28, 2014). Journal of Applied Probability, Vol. 52, No. 1, 2015, Forthcoming, Available at SSRN: https://ssrn.com/abstract=2405091

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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