[Returnanalytics-commits] r2775 - in pkg/PerformanceAnalytics/sandbox/pulkit: . week7

[noreply at r-forge.r-project.org]

Author: pulkit
Date: 2013-08-13 22:34:50 +0200 (Tue, 13 Aug 2013)
New Revision: 2775

Added:
   pkg/PerformanceAnalytics/sandbox/pulkit/week7/
   pkg/PerformanceAnalytics/sandbox/pulkit/week7/ExtremeDrawdown.R
Log:
Drawdown using Generalized Pareto Distribution

Added: pkg/PerformanceAnalytics/sandbox/pulkit/week7/ExtremeDrawdown.R
===================================================================
--- pkg/PerformanceAnalytics/sandbox/pulkit/week7/ExtremeDrawdown.R	                        (rev 0)
+++ pkg/PerformanceAnalytics/sandbox/pulkit/week7/ExtremeDrawdown.R	2013-08-13 20:34:50 UTC (rev 2775)
@@ -0,0 +1,39 @@
+#'@title
+#'Modelling Drawdown using Extreme Value Theory
+#'
+#"@description
+#'It has been shown empirically that Drawdowns can be modelled using Modified Generalized Pareto 
+#'distribution(MGPD), Generalized Pareto Distribution(GPD) and other particular cases of MGPD such 
+#'as weibull distribution \eqn{MGPD(\gamma,0,\psi)} and unit exponential distribution\eqn{MGPD(1,0,\psi)}
+#'
+#' Modified Generalized Pareto Distribution is given by the following formula
+#'
+#' \deqn{G_{\eta}(m) = \begin{array}{l} 1-(1+\eta\frac{m^\gamma}{\psi})^(-1/\eta), if \eta \neq 0 \\ 1- e^{-frac{m^\gamma}{\psi}}, if \eta = 0,\end{array}}
+#'
+#' Here \eqn{\gamma{\epsilon}R} is the modifying parameter. When \eqn{\gamma<1} the corresponding densities are
+#' strictly decreasing with heavier tail; the GDP is recovered by setting \eqn{\gamma = 1} .\eqn{\gamma \textgreater 1}
+#' 
+#' The GDP is given by the following equation. \eqn{MGPD(1,\eta,\psi)}
+#'
+#'\deqn{G_{\eta}(m) = \begin{array}{l} 1-(1+\eta\frac{m}{\psi})^(-1/\eta), if \eta \neq 0 \\ 1- e^{-frac{m}{\psi}}, if \eta = 0,\end{array}}
+#'
+#' The weibull distribution is given by the following equation \eqn{MGPD(\gamma,0,\psi)}
+#'
+#'\deqn{G(m) =  1- e^{-frac{m^\gamma}{\psi}}}
+#'
+#'The unit exponential distribution is given by the following equation \eqn{MGPD(1,0,\psi)}
+#'
+#'\deqn{G(m) =  1- e^{-m}}
+#'
+#'
+#' @param R an xts, vector, matrix, data frame, timeSeries or zoo object of asset return 
+#' 
+#'@references
+#'Mendes, Beatriz V.M. and Leal, Ricardo P.C., Maximum Drawdown: Models and Applications (November 2003). Coppead Working Paper Series No. 359. Available at SSRN: http://ssrn.com/abstract=477322 or http://dx.doi.org/10.2139/ssrn.477322.
+#'
+#'
+
+
+
+
+