We develop a generalization of the Black-Cox structural model of default risk. The extended model captures uncertainty related to firm's ability to avoid default even if company's liabilities momentarily exceeding its assets. Diffusion in a linear potential with the radiation boundary condition is used to mimic a compa…
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,742 papers · 148 categories
Trend · papers per month
48 results for “default boundaries”
We propose a dynamic mean field model for `systemic risk' in large financial systems, which we derive from a system of interacting diffusions on the positive half-line with an absorbing boundary at the origin. These diffusions represent the distances-to-default of financial institutions and absorption at zero correspon…
Solves financial and non-financial problems using heat potentials.
problem Calibrating default boundaries, calculating default probabilities, and finding hitting time probabilities.
method Classical method of heat potentials, recently extended by the author.
result Successfully solved several financial and non-financial problems.
Model for corporate bond pricing with credit rating migration, solving a double free boundary problem.
problem Corporate bond pricing with credit rating migration risks.
method Established a pricing model as a double free boundary problem, proving existence, uniqueness, and regularity of the solution.
result Two free boundaries are shown to be smooth and converge to a traveling wave solution as time goes to infinity.
Transition probability of Brownian motion in the octant and its application to default modelingq-fin.CP
We derive a semi-analytic formula for the transition probability of three-dimensional Brownian motion in the positive octant with absorption at the boundaries. Separation of variables in spherical coordinates leads to an eigenvalue problem for the resulting boundary value problem in the two angular components. The main…
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.
New mortgage contracts reduce underwater default by adjusting loan balances, but must balance prepayment incentives.
problem Underwater default incentives in mortgages.
method Analyzes automatic balance adjustment and prepayment penalties in mortgage contracts.
result Automatic balance adjustments are preferable to traditional contracts at certain spreads, reducing underwater default.
BONSAI optimizes parameters while respecting a default configuration, reducing unnecessary changes.
problem Standard BO pushes weakly relevant parameters to the boundary, making it hard to distinguish between important and spurious changes.
method BONSAI is a default-aware BO policy that prunes low-impact deviations from a default configuration while controlling acquisition value loss.
result BONSAI matches the GP-UCB regret rate while recovering the minimal- solution, reducing the number of non-default parameters in recommended configurations.
Paper analyzes pricing model for bonds with early redemption.
problem Analyzing pricing of bonds with early redemption features.
method Structural approach for mathematical modeling of bond prices.
result Existence and uniqueness of default and early redemption boundaries proved.
Gaming-Resistant Insurance Contracts for Autonomous AI Agents: Strategy-Proof Toll Mechanism Designcs.GT
Insurance contracts for autonomous AI agents must be actuarially sound and resistant to gaming.
problem Designing insurance contracts for autonomous AI agents that are actuarially sound and resistant to gaming.
method Characterizing a five-attack space and proving the actuarial runtime is gaming-resistant.
result An incentive-compatible layer for actuarial control of autonomous-agent side effects.
A new runtime for AI agents calculates risks in real-time.
problem Managing risks and liabilities in autonomous AI actions.
method A time-consistent counterfactual actuarial layer with explicit underwriting boundaries.
result Establishes a well-defined toll and guarantees executed-action budgets.
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…
Paper proposes an analytical pricing model for puttable bonds with credit risk.
problem Analytical pricing of puttable bonds with credit risk.
method Developed a 2-factor structural PDE model and derived analytical pricing formula under specific conditions.
result Derived analytical pricing formula for puttable bonds with credit risk.
Semi-analytical solution of a McKean-Vlasov equation with feedback through hitting a boundarymath.NA
In this paper, we study the non-linear diffusion equation associated with a particle system where the common drift depends on the rate of absorption of particles at a boundary. We provide an interpretation as a structural credit risk model with default contagion in a large interconnected banking system. Using the metho…
Temporal Coarse-Graining of Latent Default-Probability Paths Generates Effective Default Correlationq-fin.ST
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.
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…
Temporal Coarse-Graining of Latent Default-Probability Paths Generates Effective Default Correlationq-fin.ST
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.
Variance or Standard Deviation? Shell Geometry and Global-Scale Priors in High-Dimensional Shrinkagestat.ME
High-dimensional shrinkage risk depends on the default prior for the common scale.
problem Choosing the default prior for the common scale in high-dimensional shrinkage.
method Using radial-power benchmark to compare variance-flat and standard deviation-flat priors.
result The standard deviation-flat prior has a one-unit asymptotic risk advantage near the origin.
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.
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.
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.
In this paper we propose a method to obtain global explanations for trained black-box classifiers by sampling their decision function to learn alternative interpretable models. The envisaged approach provides a unified solution to approximate non-linear decision boundaries with simpler classifiers while retaining the o…
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…
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…
Credit derivatives pricing with default density term structure modelled by Lévy random fieldsq-fin.PR
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.
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 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…
Identifiability of Contagion Components amid Environmental Fluctuations in Aggregated Default Countsq-fin.RM
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.
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.
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.