Credit Portfolio Model

A rust implementaiton of a credit portfolio model.

Features

This is an early implementation of a credit portfolio model that simulates correlated rating migrations in a portfolio. The correlation structure is based on a Merton-type factor model. Rating migrations are based on the asset value $z$ exceeding a certain threshold.

z>c

The random variable z is standard normally distributed. Hence, the thresholds are calculated from pre-defined migration or default probabilities using the cumulative normal distribution. The asset value $z$ itself is a linear combination of multiple standard normal random variables

z=\sqrt{r^2}\cdot y+\sqrt{1-r^2}\cdot\left(\sqrt{1-\epsilon}\cdot e_1 + \sqrt{\epsilon}\cdot e_2\right)

Here, the variables are defined as follows:

• $e_1$ is the idiosyncratic risk variable only corresponding to the borrower
• $e_2$ is the idiosyncratic risk variable of the risk group that the borrower belongs to, e.g. linked to other companies through ownership
• $y$ is the systematic risk, which is defined as a linear combination of the vector $x$ which is distributed according to a multivariate normal distribution with covariance matrix $\Sigma$. Besides, the borrower dependency to the risk drives is specified by weights $\phi$. The resulting random variable is then defined as $y=\frac{\phi\cdot x}{\sqrt{\phi^T\cdot\Sigma\cdot\phi}}$.
• $r^2$ and $\epsilon$ specifiy the correlation of the borrowers asset value to the systematic component or the risk group.

The following features are implemented:

• Migration mode
• Risk groups
• Multi-threading

Features that could be implemented, but are not at the moment

• Expected shortfall calculations and other risk measures
• Alternative sampling methods for better tail measure sampling
• Random losses based on random process in case of default

Installation

Install the package via

cargo install credit_portfolio_model

Usage

The crate comes with a binary that reads csv-data with the portfolio information and outputs the loss-distribution. Besides, Mean and quantile information of the loss distribution is provided on stdout.

credit_portfolio_model --input /path/to/read/input/csv/files/from --output /path/to/store/output/csv --num-trials NUMBERTRIALS --chunk-size TRIALSPERTHREAD

The input consists of six files. The files are

correlation_matrix.csv

• risk_factor_1, risk_factor_2 - Number index of column and row, respectively. Starts with 0 and must be continuous
• correlation - Correlation value. Note that the matrix needs to be symmetric and positive semi-definite

borrower.csv

• borrower_id - Unique identifier of Borrower (string-like) that is used to map with other files
• risk_group - Unique identifier of Risk Group (string-like). Risk Groups share one of the idiosyncratic risk drivers
• rating - Current rating, given as index to a vector, i.e. starting at 0 and continuous. The last rating class is considered default, although the current implementation does no special treatment of defaults
• r2 - Correlation to the systematic risk factor, i.e. $\rho$.
• eps - Correlation to the risk group, i.e. $\epsilon$.

risk_factors.csv

• borrower_id - See borrower, must match the other file
• risk_factor - Mapping to risk factor of correlation factor
• weight - Borrower dependency to the risk factor (relative to the other risk factors)

transition_probabilities.csv

• borrower_id - See borrower, must match the other file
• rating - Resulting rating class
• probabiliy - Probability to migrate into this class, must sum to 100%.

exposure.csv

• exposure_id - Unique identifier of Exposure (string-like) that is used to map with other files
• borrower_id - See borrower, must match the other file
• outstanding - Current outstanding, not used at the moment

valuations.csv

• exposure_id - See exposure, must match the other file
• rating - Resulting rating class
• valuation - Valuation of the exposure given the rating class.

Documentation

Full API documentation is available on docs.rs.

License

This project is licensed under the MIT License - see the LICENSE file for details.