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Title page for ETD etd-050406-151319


Document Typethesis
Author NameNouri, Suhila Lynn
Email Address suhilanouri at hotmail.com
URNetd-050406-151319
TitleExpected Maximum Drawdowns Under Constant and Stochastic Volatility
DegreeMS
DepartmentMathematical Sciences
Advisors
  • Luis Roman, Advisor
  • Keywords
  • drawdowns
  • maximum drawdowns
  • Date of Presentation/Defense2006-05-04
    Availability unrestricted

    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.

    Files
  • snouri.pdf

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