Related papers: Determining a credit transition matrix from cumula…
We review recent progress in modeling credit risk for correlated assets. We start from the Merton model which default events and losses are derived from the asset values at maturity. To estimate the time development of the asset values, the…
The parameters of a discrete stationary Markov model are transition probabilities between states. Traditionally, data consist in sequences of observed states for a given number of individuals over the whole observation period. In such a…
This paper studies the problem of ergodicity of transition probability matrices in Markovian models, such as hidden Markov models (HMMs), and how it makes very difficult the task of learning to represent long-term context for sequential…
We examine a constrained Markov decision process under uncertain transition probabilities, with the uncertainty modeled as deviations from observed transition probabilities. We construct the uncertainty set associated with the deviations…
How to forecast next year's portfolio-wide credit default rate based on last year's default observations and the current score distribution? A classical approach to this problem consists of fitting a mixture of the conditional score…
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,…
We propose a unifying framework for the pricing of debt securities under general time-inhomogeneous short-rate diffusion processes. The pricing of bonds, bond options, callable/putable bonds, and convertible bonds (CBs) is covered. Using…
We are interested in the analysis of very large continuous-time Markov chains (CTMCs) with many distinct rates. Such models arise naturally in the context of reliability analysis, e.g., of computer network performability analysis, of power…
Performance period determination and bad definition for credit scorecard has been a mix of fortune for the typical data modeler. The lack of literature on these matters led to a proliferation of approaches and techniques to solve the…
We introduce a simple approach for testing the reliability of homogeneous generators and the Markov property of the stochastic processes underlying empirical time series of credit ratings. We analyze open access data provided by Moody's and…
Credit default prediction is a tabular learning problem with severe class imbalance, heterogeneous features, and tight latency budgets. Tabular Foundation Models (TFMs) approach this problem through in-context learning, which makes their…
We consider Markov decision processes (MDPs) in which the transition probabilities and rewards belong to an uncertainty set parametrized by a collection of random variables. The probability distributions for these random parameters are…
Labeled continuous-time Markov chains (CTMCs) describe processes subject to random timing and partial observability. In applications such as runtime monitoring, we must incorporate past observations. The timing of these observations matters…
Bayesian analysis often concerns an evaluation of models with different dimensionality as is necessary in, for example, model selection or mixture models. To facilitate this evaluation, transdimensional Markov chain Monte Carlo (MCMC)…
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…
Time bounded reachability is a fundamental problem in model checking continuous-time Markov chains (CTMCs) and Markov decision processes (CTMDPs) for specifications in continuous stochastic logics. It can be computed by numerically solving…
In this paper we develop a tractable structural model with analytical default probabilities depending on some dynamics parameters, and we show how to calibrate the model using a chosen number of Credit Default Swap (CDS) market quotes. We…
In piecewise-deterministic Markov processes (PDMPs) the state of a finite-dimensional system evolves continuously, but the evolutive equation may change randomly as a result of discrete switches. A running cost is integrated along the…
This report addresses state inference for hidden Markov models. These models rely on unobserved states, which often have a meaningful interpretation. This makes it necessary to develop diagnostic tools for quantification of state…
We present a statistical test that can be used to verify supervisory requirements concerning overlapping time windows for the long-term calibration in rating systems. In a first step, we show that the long-run default rate is approximately…