Credit migration: Generating generators
Richard J. Martin
TL;DR
This paper addresses calibration challenges in Markovian credit migration models by introducing a simplified generator approach and applying differential geometry to assess calibration stability.
Contribution
It introduces a simplified matrix generator for credit migration models and demonstrates the necessity of volatility data for risk-neutral calibration.
Findings
Calibration difficulties are resolved with a simplified generator.
Risk-neutral calibration requires volatility information.
Differential geometry aids in understanding calibration stability.
Abstract
Markovian credit migration models are a reasonably standard tool nowadays, but there are fundamental difficulties with calibrating them. We show how these are resolved using a simplified form of matrix generator and explain why risk-neutral calibration cannot be done without volatility information. We also show how to use elementary ideas from differential geometry to make general inferences about calibration stability. This the longer version of an article published by RISK (Feb 2021).
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Taxonomy
TopicsCredit Risk and Financial Regulations · Stochastic processes and financial applications · Probability and Risk Models