Related papers: Parameter estimation of default portfolios using t…
The recent "correlation breakdown" in the modeling of credit default swaps, in which model correlations had to exceed 100% in order to reproduce market prices of supersenior tranches, is analyzed and argued to be a fundamental market…
This paper provides some extended results on estimating parameter matrix of several regression models when the covariate or response possesses weaker moment condition. We study the $M$-estimator of Fan et al. (Ann Stat 49(3):1239--1266,…
We investigate financial market correlations using random matrix theory and principal component analysis. We use random matrix theory to demonstrate that correlation matrices of asset price changes contain structure that is incompatible…
Default risk calculus plays a crucial role in portfolio optimization when the risky asset is under threat of bankruptcy. However, traditional stochastic control techniques are not applicable in this scenario, and additional assumptions are…
We provide closed-form market equilibrium formula consolidating informational imperfections and investors beliefs. Based on Merton's model, we characterize the equilibrium expected excess returns vector with incomplete information. We then…
We study the Merton portfolio management problem within a complete market, non constant time discount rate and general utility framework. The non constant discount rate introduces time inconsistency which can be solved by introducing sub…
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…
The estimation of probabilities of default (PDs) for low default portfolios by means of upper confidence bounds is a well established procedure in many financial institutions. However, there are often discussions within the institutions or…
We consider an approach to credit risk in which the information about the time of bankruptcy is modelled using a Brownian bridge that starts at zero and is conditioned to equal zero when the default occurs. This raises the question whether…
We consider the convergence of the eigenvalues to the support of the equilibrium measure in the $\beta$ ensemble models under a critical condition. We show a phase transition phenomenon, namely that, with probability one, all eigenvalues…
The instability of historical risk factor correlations renders their use in estimating portfolio risk extremely questionable. In periods of market stress correlations of risk factors have a tendency to quickly go well beyond estimated…
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…
We study the phase transition phenomenon inherent in the shuffled (permuted) regression problem, which has found numerous applications in databases, privacy, data analysis, etc. In this study, we aim to precisely identify the locations of…
Principal component analysis (PCA) aims at estimating the direction of maximal variability of a high-dimensional dataset. A natural question is: does this task become easier, and estimation more accurate, when we exploit additional…
First passage models, where corporate assets undergo correlated random walks and a company defaults if its assets fall below a threshold provide an attractive framework for modeling the default process. Typical one year default correlations…
Stable subordinators, and more general subordinators possessing power law probability tails, have been widely used in the context of subdiffusions, where particles get trapped or immobile in a number of time periods, called constant…
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…
In this paper we consider the convergence of the conditional entropy to the entropy rate for Markov chains. Convergence of certain statistics of long range dependent processes, such as the sample mean, is slow. It has been shown in Carpio…
In this paper we present a Bayesian competing risk proportional hazards model to describe mortgage defaults and prepayments. We develop Bayesian inference for the model using Markov chain Monte Carlo methods. Implementation of the model is…
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…