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Diffstat (limited to 'Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex')
-rw-r--r-- | Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex | 29 |
1 files changed, 16 insertions, 13 deletions
diff --git a/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex b/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex index 5051ed450c5..10b31b92ba3 100644 --- a/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex +++ b/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex @@ -1,4 +1,4 @@ -%% $Id: pst-func-doc.tex 391 2010-10-02 16:43:32Z herbert $ +%% $Id: pst-func-doc.tex 411 2010-11-03 07:58:25Z herbert $ \documentclass[11pt,english,BCOR10mm,DIV12,bibliography=totoc,parskip=false, smallheadings, headexclude,footexclude,oneside]{pst-doc} \usepackage[utf8]{inputenc} @@ -61,6 +61,7 @@ Rafal Bartczuk, Buddy Ledger, Manuel Luque, Patrice Mégret, + Matthias Rüss, Jose-Emilio Vila-Forcen, Timothy Van Zandt, Michael Zedler, @@ -1473,21 +1474,23 @@ starts \Lcs{psWeinbull} with 0. \clearpage \subsection{Vasicek distribution} -The model specifies that the instantaneous interest rate follows the stochastic differential equation: +For a homogenous portfolio of infinite granularity the portfolio loss +distribution is given by -\begin{align} -\mathrm{d}r_t = a(b-r_t)\, \mathrm{d}t + \sigma \, \mathrm{d}W_t -\end{align} -with the solution: +\[ +\mathbb{P}(L(P)<x)=1-\mathcal{N} + \left(\frac{\mathcal{N}^{-1}(PD)-\sqrt{1-R2}\cdot\mathcal{N}^{-1}(x)}{R} + \right) +\] +$L(P)$ denotes the portfolio loss in percent. $pd$ is the uniform default +probability and $R2$ is the uniform asset correlation. + +They are preset to $pd=0.22$ and $R2=0.11$ and can be overwritten in the +usual way. The macro uses the PostScript function norminv from the package +pst-math +which is loaded by default and also shown in the following example. -\begin{align} - r(t) = r(0) e^{-a t} + b \left(1- e^{-a t}\right) + \sigma e^{-a t}\int_0^t e^{a s}\,dW_s -\end{align} -Possible parameters are \Lkeyword{pd} for the probability of the defualt portfolio -and \Lkeyword{R2}, the R$_\mathrm{squared}$ of the portfolio. They are preset to 0.22 and 0.11 -and can be overwritten in the usual way. The macro uses the PostScript function \Lps{norminv} -from the package \LPack{pst-math} which is loaded by default and also shown in the following example. \begin{LTXexample}[pos=t] \psset{xunit=5} |