Default risk modelling for small-to-medium enterprises in the context of stressed conditions in an undeveloped economy

In this paper, we establish an intensity based multi-factor model to value LCDS. The pricing model incorporates the modeling of default, prepayment and recovery risks. Using one factor model, negative correlation between the default and prepayment intensities and positive correlation between the default intensity and the loss given default are described. The interest rate and the house price are chosen as the relevant factors. Under these assumption, a Cauthy problem of PDE is derived, which has a closed-form solution. Based on the solution, numerical examples are provided.

The purpose of this paper is to describe a systematic framework of stochastic modelling and prediction of financial default risk of construction contractors. Net-worth-to-asset ratio is identified as an index for default process modelling. The default condition is defined as when the ratio becomes negative the first time. A mean-reverting dynamic model for the contractor default process is found by statistical analysis and is justified by using the theory of optimal capital structure. The stochastic modelling of default uses the time to default as the fundamental random variable. A discrete time trinomial Markov chain model is developed to assess default risk in terms of a cumulative default probability function, a default probability function, and the mean and variance of time to default. Practical examples are given to illustrate the stochastic methods. A default discriminant study on a group of contractors and publicly traded companies validates the methods, and indicates a high predictability of events of default and declines of credit rating.

This paper proposes and estimates a default risk model for agricultural lenders that explicitly accounts for two risks that are endemic to agricultural activities: commodity price volatility and climate. The results indicate that both factors are relevant in explaining the occurrence of default in the portfolio of a rural bank. In addition, the paper illustrates how to integrate the default risk model into standard techniques of portfolio credit risk modeling. The portfolio credit risk model provides a quantitative tool to estimate the loss distribution and the economic capital for a rural bank. The estimated parameters of the default risk model, along with scenarios for the evolution of the risk factors, are used to construct stress tests on the portfolio of a rural bank. These stress tests indicate that climate factors have a larger effect on economic capital than commodity price volatility.

The so-called intensity-based approach to the modelling and valuation of de-faultable securities has attracted a considerable attention of both practitioners and academics in recent years; to mention a few papers in this vein: Duffie [8], Duffie and Lando [9], Duffie et al. [10], Jarrow and Turnbull [13], Jarrow et al. [14], Jarrow and Yu [15], Lando [21], Madan and Unal [23]. In the context of financial modelling, there was also a renewed interest in the detailed analysis of the properties of random times; we refer to the recent papers by Elliott et al. [12] and Kusuoka [20] in this regard. In fact, the systematic study of stopping times and the associated enlargements of filtrations, motivated by a purely mathematical interest, was initiated in the 1970s by the French school, including: Brémaud and Yor [4], Dellacherie [5], Dellacherie and Meyer [7], Jeulin [16], and Jeulin and Yor [17]. On the other hand, the classic concept of the intensity (or the hazard rate) of a random time was also studied in some detail in the context of the theory of Cox processes, as well as in relation to the theory of martingales. The interested reader may consult, in particular, the monograph by Last and Brandt [22] for the former approach, and by Brémaud [3] for the latter. It seems to us that no single comprehensive source focused on the issues related to default risk modelling is available to financial researchers, though. Furthermore, it is worth noting that some challenging mathematical problems associated with the modelling of default risk remain still open. The aim of this text is thus to fill the gap by furnishing a relatively concise and self-contained exposition of the most relevant — from the viewpoint of financial modelling — results related to the analysis of random times and their filtrations. We also present some recent developments and we indicate the directions for a further research. Due to the limited space, the proofs of some results were omitted; a full version of the working paper [19] is available from the authors upon request.KeywordsCredit RiskRandom TimeDefault RiskShort Term Interest RatePredictable ProcessThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Systematic risk has been a focus for stress testing and risk capital assessment. Under the Vasicek asymptotic single risk factor model framework, entity default risk for a risk homogeneous portfolio divides into two parts: systematic and entity specific. While entity specific risk can be modelled by a probit or logistic model using a relatively short period of portfolio historical data, modeling of systematic risk is more challenging. In practice, most default risk models do not fully or dynamically capture systematic risk. In this paper, we propose an approach to modeling systematic and entity specific risks by parts and then aggregating together analytically. Systematic risk is quantified and modelled by a multifactor Vasicek model with a latent residual, a factor accounting for default contagion and feedback effects. The asymptotic maximum likelihood approach for parameter estimation for this model is equivalent to least squares linear regression. Conditional entity PDs for scenario tests and through-the-cycle entity PD all have analytical solutions. For validation, we model the point-in-time entity PD for a commercial portfolio, and stress the portfolio default risk by shocking the systematic risk factors. Rating migration and portfolio loss are assessed.

This paper presents an analysis and default risk modeling on the non-performing loans of an emerging mortgage market. The analysis and the model, unprecedented for the market under study, utilize a large data set over several years with twenty-six variables that are contained in almost a hundred thousand records about the mortgage loan borrowers. The descriptive part of the analyses shows a statistical summary of all the available information on loans, defaults and loss exposures. The structure of the relation between the loan defaults and the borrower features is analyzed in detail with regression and logistic regression models. The exact and explicit probability distributions are derived for the default counts. Then, a compound Binomial distribution model is presented for the loss amounts arising from default events. Upon the obtained probability distributions, policy implications are discussed for the default risk management purposes.

This paper presents a Proposed Java Algorithm for the Default-Recovery Rates (DRR) Model. The DRR Model is the extension to the Black-Scholes-Merton Model focusing on calculating the default and recovery rates of a firm. Default risk is one of the crucial risks in the risk management area that should be managed effectively. The world financial turmoil today will see more poor firms landing to defaults and bankruptcies. The probabilistic assessment of their financial growth would at least minimize the unfavorable impact. Although there are several efforts, instruments and methods used to manage the risk, it is said to be insufficient. To the best of our knowledge, there has been limited innovation in developing the default risk mathematical model into a java program. Therefore, through this study, default risk is predicted quantitatively using the Proposed Java Algorithm. The DRR Model has been integrated in the form of java algorithm and code. The Proposed Java Algorithm is implemented by calculating the default and recovery rates of a company and hence, predicting its level of default risk. It is found that the default risk is predicted high equivalent to the company poor financial performance. This shows that the default and recovery rates predicted by the DRR Model contain significant information on companies' performance. In addition, the proposed java Algorithm can be one of the enhancements to the credit risk modeling field in producing a user-friendly application run by a java program.

Recent advances in the theory of credit risk allow the use of standard term structure machinery for default risk modeling and estimation. The empirical literature in this area often interprets the drift adjustments of the default intensity's diffusion state variables as the only default risk premium. We show that this interpretation implies a restriction on the form of possible default risk premia, which can be justified through exact and approximate notions of ``diversifiable default risk.'' The equivalence between the empirical and martingale default intensities that follows from diversifiable default risk greatly facilitates the pricing and management of credit risk. We emphasize that this is not an equivalence in distribution, and illustrate its importance using credit spread dynamics estimated in Duffee (1999). We also argue that the assumption of diversifiability is implicitly used in certain existing models of mortgage-backed securities.

Credit derivatives are among the most important new financial instruments, but also among the most complicated. Each individual issuer is continuously exposed to default risk, and default intensity looking forward is not constant. It typically has a term structure, as revealed in the CDS market. A portfolio of risky bonds, as in a CDO, aggregates the individual risks, and now the correlations among them also become important. CDO tranches then redistribute and split up this aggregate exposure among a set of new securities. Evaluating the resulting tranche exposures requires a model for the individual default risks and their correlations, but even in the industry-standard Gaussian copula model, the problem is computationally intractable without heroic simplifying assumptions. The plainest vanilla model assumes correlations are equal for all pairs of credits. Then, analogous to the way an implied volatility can be extracted from an option9s market price, the implied correlation can be extracted from a CDO tranche price. But, as with implied volatility, the resulting tranche correlations differ widely for different tranches, leading to the use of „base correlation,” a different implied correlation concept. Base correlation is still inconsistent with the model it is derived from, but it is not quite as badly behaved as tranche correlations. In this article, Hull and White offer an alternative approach that considerably reduces the inconsistencies in calibrating a copula to a set of CDO tranche prices. The secret is to make default intensities and recovery rates stochastic, rather than requiring a single value. By imposing the restrictions that the single-name CDS and the CDO tranches must all be priced by the model just as they are in the market, and that the probabilities for the set of possible individual default intensities must sum to 1 and exhibit maximum smoothness, Hull and White are able to imply tranche correlations that are much better behaved than the standard approach. The last part of the article extends their procedure in a number of directions, to nonstandard attachment points, bespoke portfolios, and CDO-squared securities.

The modelling of default risk in debt securities involves making assumptions about the stochastic process driv- ing default, the process generating the write-down in default, and risk-free interest rates. Three generic approaches have been used. The first relies on modelling the value of the assets on which the debt is written. The second involves modelling default as an arrival process. The third involves directly modelling the interest rate spreads to which default gives rise. Each of these approaches may be applied to the impact of default risk on derivative products such as swaps and options. One application is to the valuation of derivative products that may default. The other is to the new class of ‘credit derivatives’ that represent derivative products written on credit risk.

Purpose: The purpose of this study was to identify the threat of default risk among commodity-related companies in European equity markets. Design/Methodology/Approach: Determination of the default risk of companies listed on several stock exchanges followed the Merton model by comparing the probability of bankruptcy in the time intervals from 1 January 2019 to 30 June 2019, and from 1 January 2020 to 30 June 2020. The calculations were based on data from the Wall Street Journal database. The companies selected for the study represent the main indexes of five European stock exchanges. In total, the analysis covers 40 commodity-related companies and 20 companies from the control groups. Findings: It was observed that commodity-related companies stood out against the control group in terms of default risk in the times of Covid-19 pandemic. The growing risk of default among stock market companies from significant European stock exchanges is a threat which - if unrecognized - may lead to a new financial crisis that can undermine the foundations of European economy. Practical Implications: The research results can be used by financial institutions in the process of creating a more customized approach to the modeling of credit risk of commodity-related companies. This will enable rationalization of risk management costs. Originality/Value: This study lies in the research area orientated towards exploration of relations between types of risks, which is an original aspect of this paper. More broadly, the research seeks to build risk assessment models that will be more adaptable to actual market situations in the times of Covid-19 pandemic.

Survival models have become popular for credit risk estimation. Most current credit risk survival models use an underlying linear model. This is beneficial in terms of interpretability but is restrictive for real-life applications since it cannot discover hidden nonlinearities and interactions within the data. This study uses discrete-time survival models with embedded neural networks as estimators of time to default. This provides flexibility to express nonlinearities and interactions between variables and hence allows for models with better overall model fit. Additionally, the neural networks are used to estimate age–period–cohort (APC) models so that default risk can be decomposed into time components for loan age (maturity), origination (vintage), and environment (e.g., economic, operational, and social effects). These can be built as general models or as local APC models for specific customer segments. The local APC models reveal special conditions for different customer groups. The corresponding APC identification problem is solved by a combination of regularization and fitting the decomposed environment time risk component to macroeconomic data since the environmental risk is expected to have a strong relationship with macroeconomic conditions. Our approach is shown to be effective when tested on a large publicly available US mortgage dataset. This novel framework can be adapted by practitioners in the financial industry to improve modeling, estimation, and assessment of credit risk.

Firm-level default models are important for bottom-up modeling of the default risk of corporate debt portfolios. However, models in the literature typically have several strict assumptions which may yield biased results, notably a linear effect of covariates on the log-hazard scale, no interactions, and the assumption of a single additive latent factor on the log-hazard scale. Using a sample of US corporate firms, we provide evidence that these assumptions are too strict and matter in practice and, most importantly, we provide evidence of a time-varying effect of the relative firm size. We propose a frailty model to account for such effects that can provide forecasts for arbitrary portfolios as well. Our proposed model displays superior out-of-sample ranking of firms by their default risk and forecasts of the industry-wide default rate during the recent global financial crisis.

Recent advances in the theory of credit risk allow the use of standard term structure machinery for default risk modeling and estimation. The empirical literature in this area often interprets the drift adjustments of the default intensity's diffusion state variables as the only default risk premium. We show that this interpretation implies a restriction on the form of possible default risk premia, which can be justified through exact and approximate notions of default The equivalence between the empirical and martingale default intensities that follows from diversifiable default risk greatly facilitates the pricing and management of credit risk. We emphasize that this is not an equivalence in distribution, and illustrate its importance using credit spread dynamics estimated in Duffee (1999). We also argue that the assumption of diversifiability is implicitly used in certain existing models of mortgage-backed securities.

Corporate credit risk modeling and the macroeconomy