Study identifies contagion in aggregated defaults despite environmental changes.
problem Identify contagion in aggregated default counts with fluctuating probabilities.
method Compare three contagion mechanisms (Davis-Lo, Torri, Vasicek) under i.i.d. and hierarchical specifications.
result Threshold contagion is largely absorbed into environmental heterogeneity, while cumulative contagion leaves a persistent signature.
Temporal coarse-graining of multi-sector default count data generates effective correlation matrices and rank copulas.
problem Explaining the difference in default dependence between monthly and annual aggregation.
method Dynamic low-rank state-space model with AR(1) latent credit-state factors.
result Effective correlation matrices and rank copulas are generated from monthly default count data.
This paper models default data to capture dynamic dependence across sectors.
problem Static models fail to explain monthly default dependence.
method Dynamic low-rank state-space model for monthly multi-sector default-count data.
result Effective correlation matrices and copulas are induced from monthly data.
Temporal coarse-graining of latent default paths explains effective correlation in corporate defaults.
problem Understanding effective default correlation in corporate defaults.
method Temporal coarse-graining of latent default-probability paths, applied to corporate default-count data.
result Temporal coarse-graining provides a scale-consistent baseline that improves identifiability and reduces over-allocation of long-horizon fluctuations.
Temporal aggregation reveals latent default correlation from monthly data.
problem Understanding effective default correlation from monthly default data.
method Temporal coarse-graining of latent default-probability paths.
result Temporal coarse-graining improves identifiability and reduces over-allocation of long-horizon fluctuations.
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…
Method determines credit transition matrix from cumulative default probabilities.
problem Quantifying changes in bond credit ratings.
method Setup an ill-posed, linear inverse problem with entropy minimization.
result Method successfully determines CTM from cumulative default probabilities.
We compare two different bilateral counterparty valuation adjustment (BVA) formulas. The first formula is an approximation and is based on subtracting the two unilateral Credit Valuation Adjustment (CVA)'s formulas as seen from the two different parties in the transaction. This formula is only a simplified representati…
We study optimal investment in an asset subject to risk of default for investors that rely on different levels of information. The price dynamics can include noises both from a Wiener process and a Poisson random measure with infinite activity. The default events are modelled via a counting process in line with large p…
Firms miscount their customers who stop buying without saying goodbye.
problem Counting non-contractual customers accurately.
method Estimating repeat purchase probabilities and extrapolating to infinite time.
result The count of alive customers is only partially identified, with a wide range of estimates.
We provide analytical pricing formula of corporate defaultable bond with both expected and unexpected default in the case with stochastic default intensity. In the case with constant short rate and exogenous default recovery using PDE method, we gave some pricing formula of the defaultable bond under the conditions tha…
We compare observed corporate cumulative default probabilities to those calculated using a stochastic model based on an extension of the work of Black and Cox and find that corporations default as if via diffusive dynamics. The model, based on a contingent-claims analysis of corporate capital structure, is easily calib…
This paper generalizes Moody's correlated binomial default distribution for homogeneous (exchangeable) credit portfolio, which is introduced by Witt, to the case of inhomogeneous portfolios. As inhomogeneous portfolios, we consider two cases. In the first case, we treat a portfolio whose assets have uniform default cor…
We propose a novel credit default model that takes into account the impact of macroeconomic information and contagion effect on the defaults of obligors. We use a set-valued Markov chain to model the default process, which is the set of all defaulted obligors in the group. We obtain analytic characterizations for the d…
We develop a dynamic point process model of correlated default timing in a portfolio of firms, and analyze typical default profiles in the limit as the size of the pool grows. In our model, a firm defaults at a stochastic intensity that is influenced by an idiosyncratic risk process, a systematic risk process common to…
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…
The paper shows how to calculate risk-neutral default probabilities from bid and ask CDS quotes.
problem Calculating risk-neutral default probabilities from market quotes.
method Using conic finance framework and Poisson process to formulate and solve the calibration problem.
result A unique solution for risk-neutral default probabilities and implied liquidity.
Paper simplifies default process modeling and credit valuation.
problem Modeling and pricing derivative securities with credit risk.
method Integrates default process, probability, and correlation into a unified framework.
result Risky valuation is Martingale in the proposed model.
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.
Paper proposes a framework for precise daily default risk prediction of Chinese credit bonds.
problem Inadequate and inaccurate bond information disclosure creates risk of default for investors.
method Framework includes summarizing factors impacting defaults, constructing a risk index system, and using ConvLSTM neural network for prediction.
result The model provides more responsive and accurate daily default risk predictions than authoritative ratings.
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.
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.
Measuring the corporate default risk is broadly important in economics and finance. Quantitative methods have been developed to predictively assess future corporate default probabilities. However, as a more difficult yet crucial problem, evaluating the uncertainties associated with the default predictions remains littl…
In banking practice, rating transition matrices have become the standard approach of deriving multi-year probabilities of default (PDs) from one-year PDs, the latter normally being available from Basel ratings. Rating transition matrices have gained in importance with the newly adopted IFRS 9 accounting standard. Here,…
We develop a finite horizon continuous time market model, where risk averse investors maximize utility from terminal wealth by dynamically investing in a risk-free money market account, a stock written on a default-free dividend process, and a defaultable bond, whose prices are determined via equilibrium. We analyze fi…
We model the term structure of the forward default intensity and the default density by using Lévy random fields, which allow us to consider the credit derivatives with an after-default recovery payment. As applications, we study the pricing of a defaultable bond and represent the pricing kernel as the unique solution …
The classical reduced-form and filtration expansion framework in credit risk is extended to the case of multiple, non-ordered defaults, assuming that conditional densities of the default times exist. Intensities and pricing formulas are derived, revealing how information driven default contagion arises in these models.…
Paper introduces new risk measures for default risk and model uncertainty.
problem Model uncertainty and default risk in rating systems.
method Introduces default risk measures and discusses their properties and impacts.
result Different default risk measures and margins of conservatism affect risk-weighted assets.
We study large deviations and rare default clustering events in a dynamic large heterogeneous portfolio of interconnected components. Defaults come as Poisson events and the default intensities of the different components in the system interact through the empirical default rate and via systematic effects that are comm…
In classical contagion models, default systems are Markovian conditionally on the observation of their stochastic environment, with interacting intensities. This necessitates that the environment evolves autonomously and is not influenced by the history of the default events. We extend the classical literature and allo…
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…
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.
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 multiple defaults where the global market information is modelled as progressive enlargement of filtrations. We shall provide a general pricing formula by establishing a relationship between the enlarged filtration and the reference default-free filtration in the random measure framework. On each default scena…
The mixed-fractional CEV model improves CDS pricing by accounting for default risk.
problem Improving the pricing of Credit Default Swaps (CDS) by accounting for default risk.
method Using a mixed-fractional Brownian motion to model the Constant Elasticity of Variance (CEV) model.
result The mixed-fractional CEV model yields more realistic CDS spreads and default probabilities.
Corporate defaults may be triggered by some major market news or events such as financial crises or collapses of major banks or financial institutions. With a view to develop a more realistic model for credit risk analysis, we introduce a new type of reduced-form intensity-based model that can incorporate the impacts o…
This paper develops a two-dimensional structural framework for valuing credit default swaps and corporate bonds in the presence of default contagion. Modelling the values of related firms as correlated geometric Brownian motions with exponential default barriers, analytical formulae are obtained for both credit default…
In this paper we are concerned with backward stochastic differential equations with random default time and their applications to default risk. The equations are driven by Brownian motion as well as a mutually independent martingale appearing in a defaultable setting. We show that these equations have unique solutions …
Extends XVA valuation under stochastic volatility, characterizing value processes via mild solutions.
problem Valuation of contingent claims in presence of default, collateral, and funding under stochastic volatility.
method Characterizes pre-default value processes via mild solutions to parabolic semilinear PDEs under stochastic volatility.
result Characterizes pre-default value processes via mild solutions to parabolic semilinear PDEs under stochastic volatility, providing sufficient conditions for existence and uniqueness.
RMT-Net tackles biased credit scoring data by learning from both default/non-default and rejection/approval tasks.
problem Missing-not-at-random selection bias in financial credit scoring data.
method Reject-aware Multi-Task Network (RMT-Net) that leverages the correlation between default/non-default and rejection/approval tasks.
result RMT-Net improves credit scoring models by learning from both default/non-default and rejection/approval tasks.
We develop an arbitrage-free framework for consistent valuation of derivative trades with collateralization, counterparty credit gap risk, and funding costs, following the approach first proposed by Pallavicini and co-authors in 2011. Based on the risk-neutral pricing principle, we derive a general pricing equation whe…
Study on sequential defaulting in financial networks, analyzing stability and optimal timing.
problem Understanding which banks default and how much they can fulfill in a sequential financial network.
method Sequential model of financial networks, analyzing stability and optimal timing of defaults.
result Stabilization time can heavily depend on the ordering of announcements, and finding the best time for default is NP-hard.
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…
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.
We consider the optimal investment problem when the traded asset may default, causing a jump in its price. For an investor with constant absolute risk aversion, we compute indifference prices for defaultable bonds, as well as a price for dynamic protection against default. For the latter problem, our work complements S…
Changes in collateralization have been implicated in significant default (or near-default) events during the financial crisis, most notably with AIG. We have developed a framework for quantifying this effect based on moving between Merton-type and Black-Cox-type structural default models. Our framework leads to a singl…
Study connects bank default models using dynamic contagion.
problem Understanding default contagion in heterogeneous interbank systems.
method Proposes a dynamic default contagion model with endogenous early defaults for a finite set of banks, reformulating as a stochastic particle system.
result Existence of clearing systems and continuity of the system response for the mean-field problem.
Paper forecasts corporate default risk using Particle MCMC with expert opinions.
problem Predicting corporate default risk in the U.S. market.
method Bayesian approach with Particle Markov Chain Monte Carlo (Particle MCMC) algorithm.
result Volatility and mean reversion of hidden factor significantly impact default intensities.