Simulation is widely used to estimate losses due to default and other credit events in financial portfolios. The challenge in doing this efficiently results from (i) rareevent aspects of large losses and (ii) complex dependence between defaults of multiple obligors. We discuss importance sampling techniques to address this problem in two portfolio credit risk models developed in the financial i...

We analyzed the convergence properties of likelihood­ weighting algorithms on a two-level, multiply connected, belief-network representation of the QMR knowledge base of internal medicine. Specifically, on two difficult diagnostic cases, we examined the effects of Markov blanket scoring, importance sampling, and self-importance sampling, demonstrating that the Markov blanket scoring and self-im...

We model 1981–2002 annual default frequencies for a panel of US firms in different rating and age classes from the Standard and Poor’s database. The data is decomposed into a systematic and firm-specific risk component, where the systematic component reflects the general economic conditions and default climate. We have to cope with (i) the shared exposure of each age cohort and rating class to ...

In this paper, we construct efficient importance sampling Monte Carlo schemes for finite time exit probabilities in the presence of rest points. We focus on reversible diffusion processes with small noise that have an asymptotically stable equilibrium point. The main novelty of the work is the inclusion of rest points in the domain of interest. We motivate the construction of schemes that perfo...

We propose an importance sampling scheme to estimate the partition function of the two-dimensional ferromagnetic Ising model and the two-dimensional ferromagnetic q-state Potts model, both in the presence of an external magnetic field. The proposed scheme operates on the dual Forney factor graph and is capable of efficiently computing an estimate of the partition function under a wide range of ...

This paper explains how the Gibbs sampler can be used to perform Bayesian inference on GARCH models. Although the Gibbs sampler is usually based on the analytical knowledge of the full conditional posterior densities, such knowledge is not available in regression models with GARCH errors. We show that the Gibbs sampler can be combined with a unidimensional deterministic integration rule applied...

A method is presented to exploit adaptive integration algorithms using importance sampling, like VEGAS, for the task of scanning theoretical predictions depending on a multi-dimensional parameter space. Usually, a parameter scan is performed with emphasis on certain features of a theoretical prediction. Adaptive integration algorithms are wellsuited to perform this task very efficiently. Predic...

In this paper we describe a Sequential Importance Sampling (SIS) procedure for counting the number of vertex covers in general graphs. The optimal SIS proposal distribution is the uniform over a suitably restricted set, but is not implementable. We will consider two proposal distributions as approximations to the optimal. Both proposals are based on randomization techniques. The first randomiza...

Simulated maximum likelihood has proved to be a valuable tool for fitting the log-normal stochastic volatility model to financial returns time series. In this paper, we develop a methodology that generalizes these methods to more general stochastic volatility models that are naturally cast in terms of a positive volatility process. The methodology relies on combining two well known methods for ...