MODELING LIFETIME EXPECTED CREDIT LOSSES ON BANK LOANS

The guidelines of various Accounting Standards require every financial institution to measure lifetime expected credit losses (LECLs) on every instrument, and to determine at each reporting date if there has been a significant increase in credit risk since its inception. This paper models LECLs on bank loans given to a firm that has promised to repay debt at multiple points over the lifetime of the contract. The LECL can be written as a sum of ECLs (estimated at reporting date) incurred at debt repayment times. The ECL at any debt repayment time can be written as a product of the probability of default (PD), the expected value of loss given default and the exposure at default. We derive a stochastic dynamical equation for the value of the firm’s asset by incorporating the dynamics of the factors. Also, we show how the LECL and the term structure of the PD can be estimated by solving a Black–Scholes–Merton like partial differential equation. As an illustration, we present the numerical results for the various credit loss indicators of a fictitious firm when the dynamics of the short-term interest rate is characterized by a Cox–Ingersoll–Ross mean-reverting process.

Loss given default in SME leasing

Leasing provides a fundamental source of firm funding, especially for small and medium-sized enterprises. A crucial difference from loans and bonds is that the lessor retains ownership rights of the leased asset during the lease term. This facilitates the asset utilization and work-out process and leads to higher liquidation proceeds. Hence, previous findings on the loan and bond loss given default (LGD) are not transferable to the leasing industry. Our analysis is based on a very granular data set covering a great variety of information on the lessee, the leased asset, as well as contractual and transactional characteristics. We examine novel LGD determinants such as an external credit rating, the lessee’s limited liability, and the number of leased assets and collaterals. Moreover, new results on previously explored factors question earlier findings, for example, on the lease contract type. Most importantly, as proposed by Miller and Töws (J Bank Finance 91:189–201, 2018), we analyze two different LGDs, one based on the asset utilization proceeds, the other on repayments. Our results clearly indicate the crucial importance of this separation when analyzing the drivers of the leasing LGD in detail because several determinants affect these LGDs in different ways. Our study assists both lessors and regulators in assessing the effective risk of lease contracts and enables lessors to enhance their risk management and work-out processes.

Goodness-of-Fit of Logistic Regression of the Default Rate on GDP Growth Rate and on CDX Indices

Under the Basel II and Basel III agreements, the probability of default (PD) is a key parameter used in calculating expected credit loss (ECL), which is typically defined as: PD × Loss Given Default × Exposure at Default. In practice or in regulatory requirements, gross domestic product (GDP) has been adopted in the PD estimation model. Due to the problem of excessive fluctuation and highly volatile ECL estimation, models that produce satisfactory PD and thus ECL estimations in the context of existing risk management techniques are lacking. In this study, we explore the usage of the credit default swap index (CDX), a market’s expectation of future PD, as a predictor of the default rate (DR). By comparing the goodness-of-fit of logistic regression, several conclusions are drawn. Firstly, in general, GDP has considerable explanatory power for the default rate which is consistent with current models in practice. Secondly, although both GDP and CDX fit the DR well for rating B class, CDX has a significantly better fit of DR for ratings [A, Baa, Ba]. Thirdly, compared with low-rated companies, the relationship between the DR and GDP is relatively weak for rating A. This phenomenon implies that, in addition to using macroeconomic variables and firm-specific explanatory variables in the PD estimation model, high-rated companies exhibit a greater need to use market supplemental information, such as CDX, to capture the changes in the DR.

Regulatory Estimates for Defaulted Exposures: A Case Study of Spanish Mortgages

The capital requirements derived from the Basel Accord were issued with the purpose of deploying a transnational regulatory framework. Further regulatory developments on risk measurement is included across several documents published both by the European Banking Authority and the European Central Bank. Among others, the referred additional documentation focused on the models’ estimation and calibration for credit risk measurement purposes, especially the Advanced Internal-Ratings Based models, which may be estimated both for non-defaulted and defaulted assets. A concrete proposal of the referred defaulted exposures models, namely the Expected Loss Best Estimate (ELBE) and the Loss Given Default (LGD) in-default, is presented. The proposed methodology is eventually calibrated on the basis of data from the mortgage’s portfolios of the six largest financial institutions in Spain. The outcome allows for a comparison of the risk profile particularities attached to each of the referred portfolios. Eventually, the economic sense of the results is analyzed.