Drawdowns and Rallies in a Finite Time-horizon: Drawdowns and Rallies

Drawdowns and Rallies in a Finite Time-horizon: Drawdowns and Rallies

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 in...

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Veröffentlicht in:Methodology and computing in applied probability 2010-06, Vol.12 (2), p.293-308
Hauptverfasser: Zhang, Hongzhong, Hadjiliadis, Olympia
Format: Artikel
Sprache:eng
Schlagworte:
Brownian motion
Brownian movements
Business and Management
Computation
Economics
Electrical Engineering
Equivalence
Finance
Life Sciences
Mathematical analysis
Mathematics and Statistics
Methodology
Random walk
Random walk theory
Risk management
Statistics
Studies
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Beschreibung
Zusammenfassung: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.
ISSN:1387-5841
1573-7713
DOI:10.1007/s11009-009-9139-1