Transition Matrix

Recap of Part 1 of the Matrix-to-JSON Post Series

In the first installment of this series, Part 1 we discussed the motivation behind representing and serializing matrices as JSON objects. We defined relevant concepts and in particular the concept of unrolling the matrix into a one-dimensional array and the notion of Column and Row Major orders. We outlined some use cases of interest and initiated a benchmarking exercise that looks into various R and Python JSON serialization utilities (available at the matrix2json repository).

Course Objective

Digging into the meaning of credit data collections, the logic that binds them together towards understanding what they can be used for and what limitations and issues they may be affected by, this new course in the Credit Portfolio Management category explores a new angle to look at an old practice.

Summary

This course is a CrashProgram (short course) in the use of Python and the package TransitionMatrix for analysing credit migration data.

Requirements

The course is at a medium technical level. It requires some familiarity with python (and a working installation that includes the common numpy/scipy libraries). On the risk modelling side it requires knowledge of basic credit rating migration concepts.

Motivation and Objective

Representing a Matrix as a JSON object is a task that appears in many modern data science contexts, in particular when one wants to exchange matrix data online in a portable manner. There is no universally agreed way to achieve this task and various options are available depending on the matrix data characteristics and the programming tools and computational environment one has available.

Using Sankey Diagrams

Sankey Diagrams are a type of flow diagram composed of interconnected arrows. The width of the arrows is proportional to the flow rate. Sankey diagrams are often used in physical sciences (physics, chemistry, biology) and engineering but also in economics. They can be used to represent the relative role and significance of various inputs and outputs in a given process.

Release of version 0.4.1 of the transitionMatrix package focuses on stressing transition matrices

Further building the open source OpenCPM toolkit this realease of transitionMatrix features:

1. Feature: Added functionality for conditioning multi-period transition matrices
2. Training: Example calculation and visualization of conditional matrices
3. Datasets: State space description and CGS mappings for top-6 credit rating agencies

Conditional Transition Probabilities

The calculation of conditional transition probabilities given an empirical transition matrix is a highly non-trivial task involving many modelling assumptions. This version of the transitionMatrix includes a canonical implementation that assumes a Gaussian single factor process as the driver of the joint rating dynamics. The technical documentation is available under in Open Risk Manual under the transition matrix category.

Release of version 0.4 of the transitionMatrix package

Further building the open source OpenCPM toolkit this realease of transitionMatrix features:

1. Feature: Added Aalen-Johansen Duration Estimator
2. Documentation: Major overhaul of documentation, now targeting ReadTheDocs distribution
3. Training: Streamlining of all examples
4. Installation: Pypi and wheel installation options
5. Datasets: Synthetic Datasets in long format

Enjoy!

Is the IFRS 9 or CECL standard more volatile? Its all relative

Objective

In this study we compare the volatility of reported profit-and-loss (PnL) for credit portfolios when those are measured (accounted for) following respectively the IFRS 9 and CECL accounting standards.

The objective is to assess the impact of a key methodological difference between the two standards, the so-called Staging approach of IFRS 9. There are further explicit differences in the two standards. Importantly, given the standards are not prescriptive, it is very likely that there will be material differences in interpretation and implementation of the principles (for example on the nature and construction of scenarios). In this study we perform a controlled comparison adopting a ‘ceteris-paribus’ mentality: We assume that all other implementation details are similar and we focus on the impact of the Staging approach.

Credit Portfolio PnL volatility under IFRS 9 and CECL

Objective

We explore conceptually a selection of key structural drivers of profit-and-loss (PnL) volatility for credit portfolios when profitability is measured following the principles underpinning the new IFRS 9 / CECL standards

Methodology

We setup stylized calculations for a credit portfolio with the following main parameters and assumptions:

Transition Matrix Library First Release

Open Risk released version 0.1 of the Transition Matrix Library

Motivation

State transition phenomena where a system exhibits stochastic (random) migration between well-defined discrete states (see picture below for an illustration) are very common in a variety of fields. Depending on the precise specification and modelling assumptions they may go under the name of multi-state models, Markov chain models or state-space models.