Credit Risk Modeling

Determining a credit transition matrix from cumulative default probabilities ArXiv ID: 2503.14646 “View on arXiv” Authors: Unknown Abstract To quantify the changes in the credit rating of a bond is an important mathematical problem for the credit rating industry. To think of the credit rating as the state a Markov chain is an interesting proposal leading to challenges in mathematical modeling. Since cumulative default rates are more readily measurable than credit migrations, a natural question is whether the credit transition matrix (CTM) can be determined from the knowledge of the cumulative default probabilities. Here we use a connection between the CTM and the cumulative default probabilities to setup an ill-posed, linear inverse problem with box constraints, which we solve by an entropy minimization procedure. This approach is interesting on several counts. On the one hand, we may have less data that unknowns, and on the other hand, even when we have as much data as unknowns, the matrix connecting them may not be invertible, which makes the problem ill-posed. Besides developing the tools to solve the problem, we apply it to several test cases to check the performance of the method. The results are quite satisfactory. ...

Modelling the term-structure of default risk under IFRS 9 within a multistate regression framework ArXiv ID: 2502.14479 “View on arXiv” Authors: Unknown Abstract 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. ...

Distressed Firm and Bankruptcy Prediction in an International Context: A Review and Empirical Analysis of Altman’s Z-Score Model ArXiv ID: ssrn-2536340 “View on arXiv” Authors: Unknown Abstract The purpose of this paper is firstly to review the literature on the efficacy and importance of the Altman Z-Score bankruptcy prediction model globally and its Keywords: Altman Z-Score, Bankruptcy Prediction, Credit Risk Modeling, Financial Ratios, Distress Analysis, Equity/Fixed Income Complexity vs Empirical Score Math Complexity: 4.0/10 Empirical Rigor: 7.0/10 Quadrant: Street Traders Why: The paper applies a well-established linear model (Z-Score) with basic statistical metrics, showing low math complexity, but uses a large international dataset, cross-country validation, and AUC analysis, indicating high empirical rigor. flowchart TD A["Research Goal<br>Evaluate global efficacy of Altman Z-Score<br>in distressed firm & bankruptcy prediction"] --> B["Methodology & Data<br>Literature review & empirical analysis<br>of international financial data"] B --> C["Input Variables<br>Financial Ratios:<br>Working Capital/Total Assets<br>Retained Earnings/Total Assets<br>EBIT/Total Assets<br>Market Value/Book Value<br>Sales/Total Assets"] C --> D["Computational Process<br>Calculate Altman Z-Score:<br>Z = 1.2A + 1.4B + 3.3C + 0.6D + 1.0E<br>Apply Thresholds: Z < 1.8 (Distress)"] D --> E["Key Findings<br>Model demonstrates moderate predictive power<br>Contextual limitations in global markets<br>Recommendations for sector/region adjustments"]