Stochastically ordered random variables with given marginal distributions are combined into a joint distribution preserving the ordering and the marginals using a maximum entropy formulation. A closed-form expression is obtained. An application is in default estimation for different portfolio...

Dependence among defaults both across assets and over time has proven to be an important characteristic of financial risk. A Bayesian approach to default rate estimation is proposed and illustrated using a prior distributions assessed from an experienced industry expert. Two extensions of the...

A Bayesian approach to default rate estimation is proposed and illustrated using a prior distribution assessed from an experienced industry expert. The principle advantage of the Bayesian approach is the potential for coherent incorporation of expert information - crucial when data are scarce or...

Kernel smoothing techniques have attracted much attention and some notoriety in recent years. The attention is well deserved as kernel methods free researchers from having to impose rigid parametric structure on their data. The notoriety arises from the fact that the amount of smoothing (i.e.,...

Incorporation of expert information in inference or decision settings is often important, especially in cases where data are unavailable, costly or unreliable. One approach is to elicit prior quantiles from an expert and then to fit these to a statistical distribution and proceed according to...

Banks using either the Foundation or Advanced option of the Internal Ratings Based approach to credit risk under Basel II must estimate long-run annual average default probabilities for buckets of homogeneous assets. The one-factor model underlying the capital calculations in Basel II has...

Capital allocation decisions are made on the basis of an assessment of creditworthiness. Default is a rare event for most segments of a bank's portfolio and data information can be minimal. Inference about default rates is essential for efficient capital allocation, for risk management and for...

Default is a rare event, even in segments in the midrange of a bank's portfolio. Inference about default rates is essential for risk management and for compliance with the requirements of Basel II. Most commercial loans are in the middle-risk categories and are to unrated companies. Expert...

Default is a rare event, even in segments in the midrange of a bank's portfolio. Inference about default rates is essential for risk management and for compliance with the requirements of Basel II. Most commercial loans are in the middle-risk categories and are to unrated companies. Expert...