Fernando Moreira

Nonstationary Z-Score Measures

In this work we develop advanced techniques for measuring bank insolvency risk. More specifically, we contribute to the existing body of research on the Z-Score. We develop bias reduction strategies for state-of-the-art Z-Score measures in the literature. We introduce novel estimators whose aim is to effectively capture nonstationary returns; for these estimators, as well as for existing ones in the literature, we discuss analytical confidence regions. We exploit moment-based error measures to assess the effectiveness of these estimators. We carry out an extensive empirical study that contrasts state-of-the-art estimators to our novel ones on over ten thousand banks. Finally, we contrast results obtained by using Z-Score estimators against business news on the banking sector obtained from Factiva. Our work has important implications for researchers and practitioners. First, accounting for nonstationarity in returns yields a more accurate quantification of the degree of solvency. Second, our measure allows researchers to factor in the degree of uncertainty in the estimation due to the availability of data.

Copula-Based Formulas to Estimate Unexpected Credit Losses (the Future of Basel Accords?)

The model used to estimate the capital required to cover unexpected credit losses in financial institutions (Basel II) has some drawbacks that reduce its ability to capture potential joint extreme losses in downturns. This paper suggests an alternative approach based on Copula Theory to overcome such flaws. Similarly to Basel II, the suggested model assumes that defaults are driven by a latent variable which varies as a response to an unobserved factor. On the other hand, the use of copulas allows the identification of asymmetric dependence between defaults which has been registered in the literature. As an example, a specific copula family (Clayton) is adopted to represent the association between the latent variables and a formula to estimate potential unexpected losses at a certain level of confidence is derived. Simulations reveal that, in most of the cases, the alternative model outperforms Basel II for portfolios with right-tail-dependent probabilities of default (supposedly, a good representation for real loan portfolios).

Inflated Mixture Models: Applications to Multimodality in Loss Given Default

In this paper, we propose an inflated mixture model to deal with multimodality in loss given default data. We propose a mixed of degenerate distributions, to handle zeros and ones excess, with a mixture of to-be-chosen bounded distributions for non-zeros and non-ones proportions. By applying the methodology in four retail portfolios of a large Brazilian commercial bank, we show that the inflated mixture of beta distributions plays better role minimizing model risk in fitting an inadequate model, in comparison with others considered competitive models. We explore the use of maximum likelihood estimation procedure. Monte Carlo simulations are carried out in order to check its finite sample performance.

A zero-inflated non-default rate regression model for credit scoring data

ABSTRACT The aim of this paper is to propose a survival credit risk model that jointly accommodates three types of time-to-default found in bank loan portfolios. It leads to a new framework that extends the standard cure rate model introduced by Berkson and Gage (1952) regarding the accommodation of zero-inflations. In other words, we propose a new survival model that takes into account three different types of individuals which have so far not been jointly accounted for: (i) an individual with an event at the starting time (zero time); (ii) non susceptible for the event, or (iii) susceptible for the event. Considering this, the zero-inflated Weibull non default rate regression models, which include a multinomial logistic link for the three classes, are presented using an application for credit scoring data. The parameter estimation is reached by the maximum-likelihood estimation procedure and Monte Carlo simulations are carried out to assess its finite sample performance.

The zero-inflated promotion cure rate model applied to financial data on time-to-default

In this paper, we extend the promotion cure rate model studied in Yakovlev and Tsodikov (1996) and Chen et al. (1999) by incorporating an excess of zeros in the modeling. Despite relating covariates to the cure fraction, the current approach does not enable us to relate covariates to the fraction of zeros. The presence of excess of zeros in credit risk survival data stems from a group of loans that became defaulted shortly after the granting process. Through our proposal, all survival data available of customers is modeled with a multinomial logistic link for the three classes of banking customers: (i) individual with an event at the starting time (zero time), (ii) non-susceptible for the event, or (iii) susceptible for the event. The model parameter estimation is reached by the maximum likelihood estimation procedure and Monte Carlo simulations are carried out to assess its finite sample performance.

Zero-inflated cure rate regression models for time-to-default with applications

In this paper, we introduce a methodology based on the zero-inflated cure rate model to detect fraudsters in bank loan applications. In fact, our approach enables us to accommodate three different types of loan applicants, i.e., fraudsters, those who are susceptible to default and finally, those who are not susceptible to default. An advantage of our approach is to accommodate zero-inflated times, which is not possible in the standard cure rate model. To illustrate the proposed method, a real dataset of loan survival times is fitted by the zero-inflated Weibull cure rate model. The parameter estimation is reached by maximum likelihood estimation procedure and Monte Carlo simulations are carried out to check its finite sample performance.

The Zero-Inflated Promotion Cure Rate Regression Model Applied to Fraud Propensity in Bank Loan Applications

In this paper we extend the promotion cure rate model proposed by Chen et al. (1999), by incorporating excess of zeros in the modelling. Despite allowing to relate the covariates to the fraction of cure, the current approach, which is based on a biological interpretation of the causes that trigger the event of interest, does not enable to relate the covariates to the fraction of zeros. The presence of zeros in survival data, unusual in medical studies, can frequently occur in banking loan portfolios, as presented in Louzada et al. (2015), where they deal with propensity to fraud in lending loans in a major Brazilian bank. To illustrate the new cure rate survival method, the same real dataset analyzed in Louzada et al. (2015) is fitted here, and the results are compared.

Estimating Portfolio Credit Losses in Downturns

This paper suggests formulas able to capture potential strong connection among credit losses in downturns without assuming any specific distribution for the variables involved. We first show that the current model adopted by regulators (Basel) is equivalent to a conditional distribution derived from the Gaussian Copula (which does not identify tail dependence). We then use conditional distributions derived from copulas that express tail dependence (stronger dependence across higher losses) to estimate the probability of credit losses in extreme scenarios (crises). Next, we use data on historical credit losses incurred in American banks to compare the suggested approach to the Basel formula with respect to their performance when predicting the extreme losses observed in 2009 and 2010. Our results indicate that, in general, the copula approach outperforms the Basel method in two of the three credit segments investigated. The proposed method is extendable to other differentiable copula families and this gives flexibility to future practical applications of the model.