Search Results (2)

Predicting corporate default risk has long been a crucial topic in the finance field, as bankruptcies impose enormous costs on market participants as well as the economy as a whole. This paper aims to forecast frailty-correlated default models with subjective judgements on a sample of U.S. public non-financial firms spanning January 1980–June 2019. We consider a reduced-form model and adopt a Bayesian approach coupled with the Particle Markov Chain Monte Carlo (Particle MCMC) algorithm to scrutinize this problem. The findings show that the 1-year prediction for frailty-correlated default models with different prior distributions is relatively good, whereas the prediction accuracy ratios for frailty-correlated default models with non-informative and subjective prior distributions over various prediction horizons are not significantly different. Full article

To sample from complex, high-dimensional distributions, one may choose algorithms based on the Hybrid Monte Carlo (HMC) method. HMC-based algorithms generate nonlocal moves alleviating diffusive behavior. Here, I build on an already defined HMC framework, hybrid Monte Carlo on Hilbert spaces (Beskos, et al. Stoch. Proc. Applic. 2011), that provides finite-dimensional approximations of measures $\pi$, which have density with respect to a Gaussian measure on an infinite-dimensional Hilbert (path) space. In all HMC algorithms, one has some freedom to choose the mass operator. The novel feature of the algorithm described in this article lies in the choice of this operator. This new choice defines a Markov Chain Monte Carlo (MCMC) method that is well defined on the Hilbert space itself. As before, the algorithm described herein uses an enlarged phase space $\mathsf{\Pi }$ having the target $\pi$ as a marginal, together with a Hamiltonian flow that preserves $\mathsf{\Pi }$. In the previous work, the authors explored a method where the phase space $\pi$ was augmented with Brownian bridges. With this new choice, $\pi$ is augmented by Ornstein–Uhlenbeck (OU) bridges. The covariance of Brownian bridges grows with its length, which has negative effects on the acceptance rate in the MCMC method. This contrasts with the covariance of OU bridges, which is independent of the path length. The ingredients of the new algorithm include the definition of the mass operator, the equations for the Hamiltonian flow, the (approximate) numerical integration of the evolution equations, and finally, the Metropolis–Hastings acceptance rule. Taken together, these constitute a robust method for sampling the target distribution in an almost dimension-free manner. The behavior of this novel algorithm is demonstrated by computer experiments for a particle moving in two dimensions, between two free-energy basins separated by an entropic barrier. Full article