Bayesian estimation of Shannon entropy for bivariate beta priors

Abstract

Having just survived what is arguably the worst financial crisis in time, it is expected that the focus on regulatory capital held by financial institutions such as banks will increase significantly over the next few years. The probability of default is an important determinant of the amount of regulatory capital to be held, and the accurate calibration of this measure is vital. The purpose of this study is to propose the use of the Shannon entropy when determining the parameters of the prior bivariate beta distribution as part of a Bayesian calibration methodology. Various bivariate beta distributions will be considered as priors to the multinomial distribution associated with rating categories, and the appropriateness of these bivariate beta distributions will be tested on default data. The formulae derived for the Bayesian estimation of Shannon entropy will be used to measure the certainty obtained when selecting the prior parameters.