Methods and systems for generating transition probability matrices through an optimization framework

Abstract

A method for generating an optimized transition probability matrix (OTPM) is provided. The method is performed using a computer system coupled to a database. The method includes storing in the database financial data including obligor credit ratings, generating multi-period empirical transition probability matrices (ETPMs) for a selected time horizon using the financial data stored within the database, generating a mathematical expression to minimize a difference between target ETPM values and candidate OTPM values, and calculating the OTPM from the generated mathematical expression and the financial data stored within the database, wherein the calculated OTPM includes a first set of optimized transition probability values for predicting a likelihood that a credit rating of an obligor will migrate from one credit state to another credit state during a first time interval in the future.

Description

BACKGROUND OF THE INVENTION[0001]This invention relates generally to calculating credit migration for an obligor over a given time horizon and, more particularly, to network-based methods and systems for calculating an optimized transition probability matrix for more accurately predicting a likelihood that a credit rating of an obligor will migrate from one credit state to another credit state over a given time horizon.[0002]Commercial lenders generally engage in the business of providing financing to individuals and other business entities, generally referred to as obligors, by using financial instruments that include standard loans as well as structured finance products and corporate bonds. Many of these obligors are assigned a letter-based rating grade or some other type of credit rating that is representative of the commercial obligors' credit worthiness. These credit rating grades for an obligor may shift, or migrate, over time as financial conditions associated with each oblig...

AI Technical Summary

Benefits of technology

[0013]The methods, or processes, and systems described herein facilitate calculating TPMs using an optimization methodology. Such methodology includes an optimization framework that incorporates multiple business requirements, such as: ensuring smooth surfaces with consistent probability mass distributions, reduction of impact from time homogeneity and Markov assumptions, and reduction of forecast errors for multiple time steps. The optimization framework includes generating trial values and comparing them with values within empirical TPMs developed using empirical cohort averages. The trial values are iteratively generated and compared with the empirical values until the results of the comparisons are reduced to near zero differences, wherein unsuccessful trial values outside of predetermined difference parameters are discarded and at least one successful trial value within the difference parameters is stored. The stored trial values form at least one resultant optimized TPM, or OTPM, wherein the OTPM closely corresponds to empirical credit rating transition data. The resultant OTPM is subsequently used to predict future transition probabilities, wherein the OTPM may be embedded within risk pricing models. The proposed optimization process results in OTPMs with significantly better predictive power and properties, including monotonicity and smoothness, that better suit many business applications.

Problems solved by technology

Using the aforementioned smoothing techniques may help to reduce the distortions, but such smoothing techniques do not generate a matrix that will accurately predict transition probabilities for an obligor over a multi-year time horizon.

One of the consequences of this method is that in practice, as the time horizon increases, an estimation “bias” induced by shortages in sample sizes is introduced into generation of the TPMs.

Such estimation “bias” may be propagated throughout the entire matrix and may potentially undermine the validity and usefulness of these ETPMs.

For example, monotonicity and / or smoothness of the resultant ETPM may not meet predetermined standards.

The approach described in Credit Metrics™ does not allow for adjusting a desired area in a TPM (e.g., upgrade / downgrade, default, volatility), it does not describe time weights, and it does not mention a technique for solving a large scale problem such as a 23×23 matrix.

Images