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Despite mounting evidence to the contrary, credit migration matrices, used in many credit risk and pricing applications, are typically assumed to be generated by a simple Markov process. Based on empirical evidence we propose a parsimonious model that is a mixture of (two) Markov chains, where the mixing is on the speed of movement among credit ratings. Weâ€¦ (More)

- Halina Frydman
- 2003

This paper considers a new mixture of time homogeneous finite Markov chains where the mixing is on the rate of movement and develops the EM algorithm for the maximum likelihood estimation of the parameters of the mixture. A continuous and discrete time versions of the mixture are defined and their estimation is considered separately. The simulation study isâ€¦ (More)

In the reduced-form approach to credit modeling, default intensity has been found to depend on several firm-specific factors, most notably credit rating. But aggregate default rates also vary substantially over time, presumably reflecting changes in general economic conditions. In this paper, we fit Cox intensity models for major credit events, includingâ€¦ (More)

- Samuel G. Hanson, Til Schuermann, +5 authors Marc Saidenberg
- 2005

In this paper we conduct a systematic comparison of confidence intervals around estimated probabilities of default (PD) using several analytical approaches as well as parametric and nonparametric bootstrap methods. We do so for two different PD estimation methods, cohort and duration (intensity), with 22 years of credit ratings data. We find that theâ€¦ (More)

- Halina Frydman, Jarl G. Kallberg, Duen-Li Kao
- Operations Research
- 1985

- Halina Frydman, Michael Szarek
- Biometrics
- 2009

In many clinical trials patients are intermittently assessed for the transition to an intermediate state, such as occurrence of a disease-related nonfatal event, and death. Estimation of the distribution of nonfatal event free survival time, that is, the time to the first occurrence of the nonfatal event or death, is the primary focus of the data analysis.â€¦ (More)

We explore how general economic conditions impact defaults and major credit rating changes by fitting reduced-form Cox intensity models with a broad range of macroeconomic and firm-specific ratings-related variables. For all corporate issuers in the period 1981 2002 we find both types of factors strongly influenced the risk of a credit event. However, whileâ€¦ (More)

We consider the process dYt = utdt + dWt; where u is a process not necessarily adapted to FY (the ...ltration generated by the process Y ) and W is a Brownian Motion. We obtain a general representation for the likelihood ratio of the law of the Y process relative to Brownian measure. This representation involves only one basic ...lter (expectation of uâ€¦ (More)

- Halina Frydman, Thomas Gerds, Randi GrÃ¸n, Niels Keiding
- Biometrical journal. Biometrische Zeitschrift
- 2013

We develop nonparametric maximum likelihood estimation for the parameters of an irreversible Markov chain on states {0,1,2} from the observations with interval censored times of 0 â†’ 1, 0 â†’ 2 and 1 â†’ 2 transitions. The distinguishing aspect of the data is that, in addition to all transition times being interval censored, the times of two events (0 â†’ 1 and 1â€¦ (More)

- Halina Frydman, Jun Liu
- Lifetime data analysis
- 2013

The nonparametric maximum likelihood estimation (NPMLE) of the distribution function from the interval censored (IC) data has been extensively studied in the extant literature. The NPMLE was also developed for the subdistribution functions in an IC competing risks model and in an illness-death model under various interval-censoring scenarios. But theâ€¦ (More)