Faculty Advisor or Committee Member

Luis Roman, Advisor

Identifier

etd-050406-151319

Abstract

The maximum drawdown on a time interval [0, T] of a random process can be defined as the largest drop from a high water mark to a low water mark. In this project, expected maximum drawdowns are analyzed in two cases: maximum drawdowns under constant volatility and stochastic volatility. We consider maximum drawdowns of both generalized and geometric Brownian motions. Their paths are numerically simulated and their expected maximum drawdowns are computed using Monte Carlo approximation and plotted as a function of time. Only numerical representation is given for stochastic volatility since there are no analytical results for this case. In the constant volatility case, the asymptotic behavior is described by our simulations which are supported by theoretical findings. The asymptotic behavior can be logarithmic for positive mean return, square root for zero mean return, or linear for negative mean return. When the volatility is stochastic, we assume it is driven by a mean-reverting process, in which case we discovered that if one uses the effective volatility in the formulas obtained for the constant volatility case, the numerical results suggest that similar asymptotic behavior holds in the stochastic case.

Publisher

Worcester Polytechnic Institute

Degree Name

MS

Department

Mathematical Sciences

Project Type

Thesis

Date Accepted

2006-05-04

Accessibility

Unrestricted

Subjects

drawdowns, maximum drawdowns, Stochastic processes, Portfolio management, Mathematical models, Brownian motion processes

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