by Masato Hisakado of Standard & Poor's, Kenji Kitsukawa of Keio University, and Shintaro Mori of Kitasato University
Abstract: We discuss a general method to construct correlated binomial distributions by imposing several consistent relations on the joint probability function. We obtain self-consistency relations for the conditional correlations and conditional probabilities. The beta-binomial distribution is derived by a strong symmetric assumption on the conditional correlations. Our derivation clarifies the ’correlation’ structure of the beta-binomial distribution. It is also possible to study the correlation structures of other probability distributions of exchangeable (homogeneous) correlated Bernoulli random variables. We study some distribution functions and discuss their behaviors in terms of their correlation structures.
by Xinzheng Huang of Delft University Of Technology & Rabobank, and Cornelis W. Oosterlee of Delft University Of Technology & CWI
Abstract: We propose a new framework for modeling systematic risk in Loss-Given-Default (LGD) in the context of credit portfolio losses. The class of models is very flexible and accommodates well skewness and heteroscedastic errors. The quantities in the models have simple economic interpretation. Inference of models in this framework can be unified. Moreover, it allows efficient numerical procedures, such as the normal approximation and the saddlepoint approximation, to calculate the portfolio loss distribution, Value at Risk (VaR) and Expected Shortfall (ES).