SearcharxivSearch

arXiv subjects

Arno Botha

Publications and source records attributed to Arno Botha.

11 recordsLinked to original sources

An extendable, integrated, and dynamic approach to forecasting and stress-testing credit risk

An integrated and extendable approach for stress-testing loan portfolios is presented, which includes both a loan production component and a credit risk component. In this approach, we simulate a completed portfolio using realistic loan parameters and distributional assumptions. Thereafter, we generate the uncertain cash flow history of these loans within a multistate probabilistic framework. We illustrate our approach using a simulation-based study, though the approach can be fit to real-world data. Such a simulation-based approach is ideal for stress-testing since it allows for evaluating a range of conditions. From these completed loans, we compute portfolio-level credit risk metrics, e.g., default and loss rates. Stress scenarios are introduced by varying the loan parameters accordingly within a broader Monte Carlo setup, thereby resulting in a range of portfolios. A classical approach to stress-testing does not typically integrate loan production or embed the correlation structure amongst risk metrics. In our approach, we integrate the forecasting of risk metrics with receipt-generation. Given data, the loan parameters within our extendable approach can be dynamically modelled as functions of input variables using any applicable technique. Overall, our approach can render predictions that are more dynamic and flexibly tuned, which can enhance stress-testing practices within any bank.

q-fin.CP

Deriving the term-structure of loan write-off risk under IFRS 9 by using survival analysis: A benchmark study

The estimation of marginal loan write-off probabilities is a non-trivial task when modelling the loss given default (LGD) risk parameter in credit risk. We explore two types of survival models in estimating the overall write-off probability over default spell time, where these probabilities form the term-structure of write-off risk in aggregate. These survival models include a discrete-time hazard (DtH) model and a conditional inference survival tree. Both models are compared to a cross-sectional logistic regression model for write-off risk. All of these (first-stage) models are then ensconced in a broader two-stage LGD-modelling approach, wherein a loss severity model is estimated in the second stage. In expanding the model suite, a novel dichotomisation step is introduced for collapsing the write-off probability into a 0/1-value, prior to LGD-calculation. A benchmark study is subsequently conducted amongst the resulting LGD-models. We find that the DtH-model outperforms other two-stage LGD-models admirably across most diagnostics. However, a single-stage LGD-model still had the best results, likely due to the peculiar `L-shaped' LGD-distribution in our data. Ultimately, we believe that our tutorial-style work can enhance LGD-modelling practices when estimating the expected credit loss under IFRS 9.

q-fin.RM

Approaches for modelling the term-structure of default risk under IFRS 9: A tutorial using discrete-time survival analysis

Under the International Financial Reporting Standards (IFRS) 9, credit losses ought to be recognised timeously and accurately. This requirement belies a certain degree of dynamicity when estimating the constituent parts of a credit loss event, most notably the probability of default (PD). It is notoriously difficult to produce such PD-estimates at every point of loan life that are adequately dynamic and accurate, especially when considering the ever-changing macroeconomic background. In rendering these lifetime PD-estimates, the choice of modelling technique plays an important role, which is why we first review a few classes of techniques, including the merits and limitations of each. Our main contribution however is the development of an in-depth and data-driven tutorial using a particular class of techniques called discrete-time survival analysis. This tutorial is accompanied by a diverse set of reusable diagnostic measures for evaluating various aspects of a survival model and the underlying data. A comprehensive R-based codebase is further contributed. We believe that our work can help cultivate common modelling practices under IFRS 9, and should be valuable to practitioners, model validators, and regulators alike.

q-fin.RM

Exploring different subtypes of recurrent event Cox-regression models in modelling lifetime default risk: A tutorial

In the pursuit of modelling a loan's probability of default (PD) over its lifetime, repeat default events are often ignored when using Cox Proportional Hazard (PH) models. Excluding such events may produce biased and inaccurate PD-estimates, which can compromise financial buffers against future losses. Accordingly, we investigate a few subtypes of Cox-models that can incorporate recurrent default events. We explore both the Andersen-Gill (AG) and the Prentice-Williams-Peterson (PWP) spell-time models using real-world data as an illustration. These models are compared against a baseline that deliberately ignores recurrent events, called the time to first default (TFD) model. Our models are evaluated using Harrell's c-statistic, adjusted Cox-Sell residuals, and a novel extension of time-dependent receiver operating characteristic analysis. From these Cox-models, we demonstrate how to derive a portfolio-level term-structure of default risk, which is a series of marginal PD-estimates over the average loan's lifetime. While the TFD- and PWP-models do not differ significantly across all diagnostics, the AG-model underperformed expectations. We believe that our pedagogical tutorial, as accompanied by a codebase, would be of great value to practitioner and regulator alike. Accordingly, our work enhances the current practice of using Cox-modelling in producing timeous and accurate PD-estimates under IFRS 9.

q-fin.RM

A cost of capital approach to determining the LGD discount rate

Loss Given Default (LGD) is a key risk parameter in determining a bank's regulatory capital. During LGD-estimation, realised recovery cash flows are to be discounted at an appropriate rate. Regulatory guidance mandates that this rate should allow for the time value of money, as well as include a risk premium that reflects the "undiversifiable risk" within these recoveries. Having extensively reviewed earlier methods of determining this rate, we propose a new approach that is inspired by the cost of capital approach from the Solvency II regulatory regime. Our method involves estimating a market-consistent price for a portfolio of defaulted loans, from which an associated discount rate may be inferred. We apply this method to mortgage and personal loans data from a large South African bank. The results reveal the main drivers of the discount rate to be the mean and variance of these recoveries, as well as the bank's cost of capital in excess of the risk-free rate. Our method therefore produces a discount rate that reflects both the undiversifiable risk of recovery recoveries and the time value of money, thereby satisfying regulatory requirements. This work can subsequently enhance the LGD-component within the modelling of both regulatory and economic capital.

q-fin.RM

Modelling the term-structure of default risk under IFRS 9 within a multistate regression framework

The lifetime behaviour of loans is notoriously difficult to model, which can compromise a bank's financial reserves against future losses, if modelled poorly. Therefore, we present a data-driven comparative study amongst three techniques in modelling a series of default risk estimates over the lifetime of each loan, i.e., its term-structure. The behaviour of loans can be described using a nonstationary and time-dependent semi-Markov model, though we model its elements using a multistate regression-based approach. As such, the transition probabilities are explicitly modelled as a function of a rich set of input variables, including macroeconomic and loan-level inputs. Our modelling techniques are deliberately chosen in ascending order of complexity: 1) a Markov chain; 2) beta regression; and 3) multinomial logistic regression. Using residential mortgage data, our results show that each successive model outperforms the previous, likely as a result of greater sophistication. This finding required devising a novel suite of simple model diagnostics, which can itself be reused in assessing sampling representativeness and the performance of other modelling techniques. These contributions surely advance the current practice within banking when conducting multistate modelling. Consequently, we believe that the estimation of loss reserves will be more timeous and accurate under IFRS 9.

q-fin.RM

The TruEnd-procedure: Treating trailing zero-valued balances in credit data

A novel procedure is presented for finding the true but latent endpoints within the repayment histories of individual loans. The monthly observations beyond these true endpoints are false, largely due to operational failures that delay account closure, thereby corrupting some loans. Detecting these false observations is difficult at scale since each affected loan history might have a different sequence of trailing zero (or very small) month-end balances. Identifying these trailing balances requires an exact definition of a "small balance", which our method informs. We demonstrate this procedure and isolate the ideal small-balance definition using two different South African datasets. Evidently, corrupted loans are remarkably prevalent and have excess histories that are surprisingly long, which ruin the timing of risk events and compromise any subsequent time-to-event model, e.g., survival analysis. Having discarded these excess histories, we demonstrably improve the accuracy of both the predicted timing and severity of risk events, without materially impacting the portfolio. The resulting estimates of credit losses are lower and less biased, which augurs well for raising accurate credit impairments under IFRS 9. Our work therefore addresses a pernicious data error, which highlights the pivotal role of data preparation in producing credible forecasts of credit risk.

q-fin.RM

Defining and comparing SICR-events for classifying impaired loans under IFRS 9

The IFRS 9 accounting standard requires the prediction of credit deterioration in financial instruments, i.e., significant increases in credit risk (SICR). However, the definition of such a SICR-event is inherently ambiguous, given its current reliance on evaluating the change in the estimated probability of default (PD) against some arbitrary threshold. We examine the shortcomings of this PD-comparison approach and propose an alternative framework for generating SICR-definitions based on three parameters: delinquency, stickiness, and the outcome period. Having varied these framework parameters, we obtain 27 unique SICR-definitions and fit logistic regression models accordingly using rich South African mortgage and macroeconomic data. For each definition and corresponding model, the resulting SICR-rates are analysed at the portfolio-level on their stability over time and their responsiveness to economic downturns. At the account-level, we compare both the accuracy and dynamicity of the SICR-predictions, and discover several interesting trends and trade-offs. These results can help any bank with appropriately setting the three framework parameters in defining SICR-events for prediction purposes. We demonstrate this process by comparing the best-performing SICR-model to the PD-comparison approach, and show the latter's inferiority as an early-warning system. Our work can therefore guide the formulation, modelling, and testing of any SICR-definition, thereby promoting the timeous recognition of credit losses; the main imperative of IFRS 9.

q-fin.RM

The loss optimisation of loan recovery decision times using forecast cash flows

A theoretical method is empirically illustrated in finding the best time to forsake a loan such that the overall credit loss is minimised. This is predicated by forecasting the future cash flows of a loan portfolio up to the contractual term, as a remedy to the inherent right-censoring of real-world `incomplete' portfolios. Two techniques, a simple probabilistic model as well as an eight-state Markov chain, are used to forecast these cash flows independently. We train both techniques from different segments within residential mortgage data, provided by a large South African bank, as part of a comparative experimental framework. As a result, the recovery decision's implied timing is empirically illustrated as a multi-period optimisation problem across uncertain cash flows and competing costs. Using a delinquency measure as a central criterion, our procedure helps to find a loss-optimal threshold at which loan recovery should ideally occur for a given portfolio. Furthermore, both the portfolio's historical risk profile and forecasting thereof are shown to influence the timing of the recovery decision. This work can therefore facilitate the revision of relevant bank policies or strategies towards optimising the loan collections process, especially that of secured lending.

q-fin.RM

Simulation-based optimisation of the timing of loan recovery across different portfolios

A novel procedure is presented for the objective comparison and evaluation of a bank's decision rules in optimising the timing of loan recovery. This procedure is based on finding a delinquency threshold at which the financial loss of a loan portfolio (or segment therein) is minimised. Our procedure is an expert system that incorporates the time value of money, costs, and the fundamental trade-off between accumulating arrears versus forsaking future interest revenue. Moreover, the procedure can be used with different delinquency measures (other than payments in arrears), thereby allowing an indirect comparison of these measures. We demonstrate the system across a range of credit risk scenarios and portfolio compositions. The computational results show that threshold optima can exist across all reasonable values of both the payment probability (default risk) and the loss rate (loan collateral). In addition, the procedure reacts positively to portfolios afflicted by either systematic defaults (such as during an economic downturn) or episodic delinquency (i.e., cycles of curing and re-defaulting). In optimising a portfolio's recovery decision, our procedure can better inform the quantitative aspects of a bank's collection policy than relying on arbitrary discretion alone.

q-fin.RM

A procedure for loss-optimising default definitions across simulated credit risk scenarios

A new procedure is presented for the objective comparison and evaluation of default definitions. This allows the lender to find a default threshold at which the financial loss of a loan portfolio is minimised, in accordance with Basel II. Alternative delinquency measures, other than simply measuring payments in arrears, can also be evaluated using this optimisation procedure. Furthermore, a simulation study is performed in testing the procedure from `first principles' across a wide range of credit risk scenarios. Specifically, three probabilistic techniques are used to generate cash flows, while the parameters of each are varied, as part of the simulation study. The results show that loss minima can exist for a select range of credit risk profiles, which suggests that the loss optimisation of default thresholds can become a viable practice. The default decision is therefore framed anew as an optimisation problem in choosing a default threshold that is neither too early nor too late in loan life. These results also challenges current practices wherein default is pragmatically defined as `90 days past due', with little objective evidence for its overall suitability or financial impact, at least beyond flawed roll rate analyses or a regulator's decree.

q-fin.RM