We propose two structural models for stochastic losses given default which allow to model the credit losses of a portfolio of defaultable financial instruments. The credit losses are integrated into a structural model of default events accounting for correlations between the default events and the associated losses. We…
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48 results for “Loss Given Default”
The single risk factor approach to capital charges in case of correlated loss given default ratescond-mat.other
A new methodology for incorporating LGD correlation effects into the Basel II risk weight functions is introduced. This methodology is based on modelling of LGD and default event with a single loss variable. The resulting formulas for capital charges are numerically compared to the current proposals by the Basel Commit…
A new model calculates LGD distribution based on firm value and credit market conditions.
problem Estimating LGD distribution in credit markets.
method Uses last passage time of a linear diffusion process to model LGD distribution.
result Explicit distributions of default time and LGD are obtained under minimal assumptions.
The purpose of this paper is to identify a relevant statistical correlation between rate of default, RD, and loss given default, LGD, in a major Brazilian financial institution Retail Home Equity exposure rated using the IRB approach, so that we may find a causal relationship between the two risk parameters. Therefore,…
Paper calculates loan loss after default using Bayesian model.
problem Determining loan loss after borrower default.
method Bayesian scheme considering repayment period, volumes, moments, and parameters.
result Allows setting LGD less than or equal to 1 for accurate estimates.
The impact of a stress scenario of default events on the loss distribution of a credit portfolio can be assessed by determining the loss distribution conditional on these events. While it is conceptually easy to estimate loss distributions conditional on default events by means of Monte Carlo simulation, it becomes imp…
The authors examine the concept of probability of default for asset-backed loans. In contrast to unsecured loans it is shown that probability of default can be defined as either a measure of the likelihood of the borrower failing to make required payments, or as the likelihood of an insufficiency of collateral value on…
A simple graphical model for correlated defaults is proposed, with explicit formulas for the loss distribution. Algebraic geometry techniques are employed to show that this model is well posed for default dependence: it represents any given marginal distribution for single firms and pairwise correlation matrix. These t…
Regression models for limited continuous dependent variables having a non-negligible probability of attaining exactly their limits are presented. The models differ in the number of parameters and in their flexibility. Fractional data being a special case of limited dependent data, the models also apply to variables tha…
Central Counterparty Riskq-fin.RM
A clearing member of a Central Counterparty (CCP) is exposed to losses on their default fund and initial margin contributions. Such losses can be incurred whenever the CCP has insufficient funds to unwind the portfolio of a defaulting clearing member. This does not necessarily require the default of the CCP itself. In …
This letter assesses model risk in credit capital requirements and finds substantial tail risk.
problem Uncertainty in the probability of default and loss-given-default parameters in credit capital requirements.
method Models estimation risk in a simple way, analyzing two datasets and testing parameter dependency.
result Parameter dependency significantly increases tail risk in capital requirements, requiring substantial increases in regulatory capital.
The study assesses how financial networks resist simultaneous price shocks and calculates the worst-case loss.
problem Resilience of financial networks to simultaneous price fluctuations and default contagion.
method Introduced a concept of default resilience margin, ε*, and computed worst-case systemic loss through linear programming.
result Threshold value ε* determines the maximum amplitude of asset price fluctuations the network can tolerate.
The paper uses CPI growth rates to improve LGD predictions for CRE loans.
problem Challenges in forecasting LGD for CRE loans due to extended resolution times and restricted data.
method Combines internal and public data, including CPI growth rates, to forecast CRE LGD.
result Incorporating CPI at the time of default improves LGD prediction accuracy.
In this paper, we address the aggregation of dependent stop loss reinsurance risks where the dependence among the ceding insurer(s) risks is governed by the Sarmanov distribution and each individual risk belongs to the class of Erlang mixtures. We investigate the effects of the ceding insurer(s) risk dependencies on th…
A censored transformed model for proportional outcomes with boundary mass and an application to loss given default modeling.
problem Modeling proportional outcomes with boundary mass in loss given default (LGD) modeling.
method Zero-one censored transformed normal (ZOC-TN) model.
result Captures a wider range of qualitative density shapes than benchmark models while being parsimonious, computationally efficient, and numerically stable.
Methodology measures financial impacts using existing credit loss infrastructure.
problem Measuring the impact of financial scenarios on expected credit losses.
method Captures scenario effects through changes in default probabilities; uses existing provisioning infrastructure.
result Methodology validated through standardized climate scenario exercise in Canada and Quebec.
We analyze the fluctuation of the loss from default around its large portfolio limit in a class of reduced-form models of correlated firm-by-firm default timing. We prove a weak convergence result for the fluctuation process and use it for developing a conditionally Gaussian approximation to the loss distribution. Nume…
Deep Evidence Regression improves credit risk prediction uncertainty.
problem Quantifying uncertainty in credit risk predictions.
method Applying Deep Evidence Regression to credit risk settings.
result Demonstrated improved prediction of Loss Given Default.
We build a general model for pricing defaultable claims. In addition to the usual absence of arbitrage assumption, we assume that one defaultable asset (at least) looses value when the default occurs. We prove that under this assumption, in some standard market filtrations, default times are totally inaccessible stoppi…
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…
We apply Geometric Arbitrage Theory to obtain results in mathematical finance for credit markets, which do not need stochastic differential geometry in their formulation. We obtain closed form equations involving default intensities and loss given defaults characterizing the no-free-lunch-with-vanishing-risk condition …
It is a well known fact that recovery rates tend to go down when the number of defaults goes up in economic downturns. We demonstrate how the loss given default model with the default and recovery dependent via the latent systematic risk factor can be estimated using Bayesian inference methodology and Markov chain Mont…
While defaults are rare events, losses can be substantial even for credit portfolios with a large number of contracts. Therefore, not only a good evaluation of the probability of default is crucial, but also the severity of losses needs to be estimated. The recovery rate is often modeled independently with regard to th…
The paper values and hedges EPS products with jumps and default risks.
problem Valuation and risk management of EPS products under financial crises and default risks.
method Developed pricing frameworks using jump-diffusion and default models, derived closed-form formulas, and analysed hedging strategies.
result Quantified residual losses from counterparty default risk and defined default-adjusted premiums.
We consider a large collection of dynamically interacting components defined on a weighted directed graph determining the impact of default of one component to another one. We prove a law of large numbers for the empirical measure capturing the evolution of the different components in the pool and from this we extract …
Model predicts credit portfolio losses with contagion effects.
problem Predicting credit portfolio losses with contagion effects.
method Introduced a model with a recursive algorithm and flexible distributions.
result Good fit for synthetic CDO tranches of the iTraxx index.
We extend the common Poisson shock framework reviewed for example in Lindskog and McNeil (2003) to a formulation avoiding repeated defaults, thus obtaining a model that can account consistently for single name default dynamics, cluster default dynamics and default counting process. This approach allows one to introduce…
We prove a law of large numbers for the loss from default and use it for approximating the distribution of the loss from default in large, potentially heterogenous portfolios. The density of the limiting measure is shown to solve a non-linear SPDE, and the moments of the limiting measure are shown to satisfy an infinit…
This article deals with the problem of optimal allocation of capital to corporate bonds in fixed income portfolios when there is the possibility of correlated defaults. Under fairly general assumptions for the distribution of the total net assets of a set of firms we show that retaining the first few moments of the por…
Paper improves MMD estimation for analytical mean embeddings.
problem Improving MMD estimation for distributions with analytical mean embeddings.
method Proposes a tighter concentration result for MMD estimation under semi-explicit settings and extends to unbounded kernels.
result Demonstrates efficiency in real-world applications like index replication and calibration.
The paper models default probabilities and total defaults in credit portfolios using a contagion process with self-exciting jumps.
problem Modeling default probabilities and total defaults in credit portfolios to mitigate credit risk.
method Developed a contagion process with self-exciting jumps to model credit events and derive closed-form expressions for default probabilities and total defaults.
result The proposed framework captures the feedback effect and can be used to price synthetic CDOs.
Investors optimize equity and CDS trading to mitigate default risk.
problem Optimizing investment in equity and CDS markets to manage default risk.
method Semi-linear PDE for certainty equivalent, proving existence and optimality of policies.
result Optimal CDS policies cover both equity and future trading losses, increasing investor utility.
In this paper, we study an optimal excess-of-loss reinsurance and investment problem for an insurer in defaultable market. The insurer can buy reinsurance and invest in the following securities: a bank account, a risky asset with stochastic volatility and a defaultable corporate bond. We discuss the optimal investment …
Attributing forecast gaps to component models in complex model suites
problem Attributing forecast gaps between model-suite forecasts and realized outcomes
method Formalizing walk analysis and adapting order-independent attribution frameworks
result Deriving efficient formulas for elementwise and vectorized gap attribution
Optimal credit and consumption strategies in a switching market with default contagion.
problem Optimal portfolio and consumption decisions in a credit market with default contagion.
method Cobb-Douglas utility, recursive ODE system, backward solution from all-default state.
result Existence and uniqueness of optimal feedback controls, verification theorem.
The paper tackles attributing forecast gaps in complex model suites.
problem Attributing forecast gaps to individual component models in complex model suites.
method Formalized walk analysis, adapted LMDI and Shapley value approaches.
result Developed efficient formulas for gap attribution in practical portfolio-scale examples.
In this article, we consider a 2 factors-model for pricing defaultable bond with discrete default intensity and barrier where the 2 factors are stochastic risk free short rate process and firm value process. We assume that the default event occurs in an expected manner when the firm value reaches a given default barrie…
We present a class of flexible and tractable static factor models for the term structure of joint default probabilities, the factor copula models. These high-dimensional models remain parsimonious with pair-copula constructions, and nest many standard models as special cases. The loss distribution of a portfolio of con…
On absolutely continuous compensators and nonlinear filtering equations in default risk modelsmath.PR
We discuss the pricing of defaultable assets in an incomplete information model where the default time is given by a first hitting time of an unobservable process. We show that in a fairly general Markov setting, the indicator function of the default has an absolutely continuous compensator. Given this compensator we t…
We study the gain of an insider having private information which concerns the default risk of a counterparty. More precisely, the default time τis modelled as the first time a stochastic process hits a random barrier L. The insider knows this barrier (as it can be the case for example for the manager of the counterpart…
As it is known in the finance risk and macroeconomics literature, risk-sharing in large portfolios may increase the probability of creation of default clusters and of systemic risk. We review recent developments on mathematical and computational tools for the quantification of such phenomena. Limiting analysis such as …
In recent years research on credit risk modelling has mainly focused on default probabilities. Recovery rates are usually modelled independently, quite often they are even assumed constant. Then, however, the structural connection between recovery rates and default probabilities is lost and the tails of the loss distri…
Paper uses interbank contagion to predict U.S. bank defaults, finding it highly explanatory.
problem Predicting U.S. bank defaults using interbank contagion.
method Regression and neural network models were used to analyze U.S. commercial bank data.
result Interbank contagion is highly explanatory in default prediction, often outperforming established metrics.
Default risk significantly affects the corporate policies of a firm. We develop a model in which a limited liability entity subject to Poisson default shock jointly sets its dividend policy and capital structure to maximize the expected lifetime utility from consumption of risk averse equity investors. We give a comple…
Default-ERM shortcut learning persists even without additional information.
problem Default-ERM shortcut learning in perception tasks despite stable feature sufficiency.
method Studied linear perception task; developed margin control (MARG-CTRL) loss functions.
result Margin control mitigates shortcut learning on various tasks.
The recent financial crisis of 2008 and the 2011 indebtedness of Greece highlight the importance of understanding the structure of the global financial network. In this paper we set out to analyze and characterize this network, as captured by the IMF Coordinated Portfolio Investment Survey (CPIS), in two ways. First, t…
Modeling bank portfolio risk under climate transition impacts.
problem Evaluating risk measures for a bank's collateralized loans in a climate transition economy.
method Developed an end-to-end modeling framework using stochastic processes and dynamic macroeconomic variables.
result Derived expressions for risk measures as functions of climate transition parameters.
What do central counterparties default funds really cover? A network-based stress test answerq-fin.RM
In the last years, increasing efforts have been put into the development of effective stress tests to quantify the resilience of financial institutions. Here we propose a stress test methodology for central counterparties based on a network characterization of clearing members, whose links correspond to direct credits …