Article

Methodology and Computing in Applied Probability

, Volume 12, Issue 2, pp 293-308

Drawdowns and Rallies in a Finite Time-horizon

Drawdowns and Rallies
  • Hongzhong ZhangAffiliated withDepartment of Mathematics, Graduate Center, C.U.N.Y.
  • , Olympia HadjiliadisAffiliated withDepartment of Mathematics, Brooklyn College and the Graduate Center, C.U.N.Y. Email author 

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Abstract

In this work we derive the probability that a rally of a units precedes a drawdown of equal units in a random walk model and its continuous equivalent, a Brownian motion model in the presence of a finite time-horizon. A rally is defined as the difference of the present value of the holdings of an investor and its historical minimum, while the drawdown is defined as the difference of the historical maximum and its present value. We discuss applications of these results in finance and in particular risk management.

Keywords

Drawdown Rally Random walk Brownian motion

AMS 2000 Subject Classifications

Primary 60G40 Secondary 91A60