A structural hidden Markov model for forecasting scenario probabilities for portfolio loan loss provisions

Abstract

Accounting standards require from financial institutions to consider and forecast multiple macroeconomic scenarios when calculating loan loss provisions. Loan loss provisions protect a financial institutions against losses. But how to determine objectively the number of scenarios and to forecast scenario probabilities is an unsolved problem. This paper shows that embedding the question into the framework of a hidden Markov model (HMM) leads to a natural answer. A disadvantage of employing HMMs to credit risk is the short length of a typical time series of default rates. To overcome this problem the paper proposes to employ for the transition probability matrix (TPM) of the hidden states a crucial adaptation to the standard approach. The adapted TPM is a hybrid version of a continuous-valued TPM and a discrete-valued valued TPM. The adaptation imposes a structure on the TPM and reduces the number of required parameters for a discrete-valued HMM with M hidden states from M(M−1) to M+2. The proposed model is benchmarked using a time series of defaults and is, for the analysed data, considered optimal in terms of the Akaike and Bayesian information criterion. By building the proposed HMM scenario probabilities can be objectively forecasted and have no longer be expertly assessed.