The Pluto-Tasche method is used to calculate prudent estimates on default probabilities, given some observed defaults. The idea is explained in the note at http://arxiv.org/pdf/cond-mat/0411699. The procedure is roughly equivalent to inverting the cumulative distribution function for the number of successes in correlated Bernoulli trials. Here is a fast plugin for Microsoft Excel to do it. [Download]## Features- Handles large portfolios (e.g. 100,000 obligors), which choke other code.
- Uses an efficient numerical integration scheme for which explicit error bounds can be calculated.
- Newton-Raphson and bisection search methods are combined to invert probabilities.
- Binomial cumulative distribution function efficiently evaluated using a continued fraction representation of the incomplete Beta function.*
- Incorporates rigorous analytic upper bounds similar to Hoeffding's inequality to arrive at the answer faster.
- The Microsoft Excel add-in uses the XLW C++ library, which is well tested in quantitative finance.
- 64 bit and 32 bit versions are available.
- Can be compiled as a stand-alone application (for Linux or Windows) for use in automated reporting, for example.
Download a demo version at the bottom of this page [32 bit version targeting Windows XP onwards. Tested on Windows 10 + Office 2010].Check here for a live demo of an older version.Note that the final answers are easy to validate in standard statistical software packages, if desired. For example in R,
## [1] 0.95002 More extensive simulation tests performed with R can be viewed here. * As in CDFLIB, Boost C++, Cephes, GNU Scientific Library and R's statistical library, which can be used as alternatives. |