In continuation of some previous posts on residual estimation risk (RER), we establish an upper bound for RER when the risk measure is VaR for any arbitrary error distribution , where the error distribution is defined as the difference between an actual loss distribution and a loss estimator (see [1] for more details). Asymmetric Error Distribution For an arbitrary…

# Credit Risk

# Beta Regression Modelling

It is known that the distribution of LGD, EAD, FUC, or CCF (see for the definitions of CCF and FUC) when capped between 0 and 1 exhibits a non-normal shape with bimodal peaks (near 0 and 1). Hence, it is common to use a logistic link function to achieve a unimodal distribution close to normal, prior to running a regression.…

# Implicit Targets of EAD

When modelling to predict a target variable, the relationship between some set of explanatory variables and this target may be unknown or complex. In the context of linear models, transformation by a link function may not be sufficient to capture the linear dependence. In this case it is suitable to model an implicit variable of the target rather than the…

# What is a Margin of Conservatism?

This question comes up a lot in my field of work, and unfortunately, there is no rigorous answer. Everybody seems to have a different (albeit loosely similar) definition of a margin of conservatism. However, we all need a definition, as it drives much of the model development and validation work at financial institutions. Furthermore, AIRB risk parameter estimation models require a margin of conservatism,…

# Non-Linearity and the RWA Formula

Some of you might find this interesting. Often a lot of emphasis is placed on the quantification of , , and under the AIRB approach at banks (recall). Sometimes it is easy to lose sight of what is actually driving , and hence, the amount of capital institutions must hold in reserve. Some banks adopt this AIRB framework in the…

# AIRB Risk-Weighted Assets

When banks adopt the Advanced Internal Ratings-Based approach to calculate risk-weighted assets, they must adhere to the specific guidelines and formulas governing the approach. Banks are allowed to quantify the parameters (e.g. PD, LGD, EAD) used in the Basel capital formula, but cannot deviate from the analytic formula used to determine RWA. RWA is merely the unexpected loss, less the…

# Risk and the Retail Investor

Risk can be elicited in many ways, shapes, and forms. Unfortunately, the typical retail investor is incognisant of how risk affects them financially. It is not surprising why this is the case. In an industry where there are buyers and sellers of financial products, it is more advantageous for the seller to focus on the rewards, rather than the risks…

# Weights of Evidence and the Information Value

In order to determine which variables demonstrate a high level of predictive power, we calculate the binned Weights of Evidence (WoE) and the associate Information Value (IV). Generally speaking, the IV provides a measure of how well an explanatory variable is able to distinguish between binary responses (e.g. "good" versus "bad") in some target variable. The idea is if a variable has…

# Age-Period-Cohort Model for Transition State Forecasting

You may be familiar with transition state models that are governed by the Age-Period-Cohort (APC) modelling framework. If you are, you've likely been witness to the recent insurgence of APC models in the literature -mainly being used to forecast mortgage and bond performance. The content related to APC modelling can be dense (literally, not figuratively) and you may find yourself confused when the the…

# Hypothesis Testing of Regression Coefficients

For a long time I resisted statistics (yes, the subject in general) because of what I deemed to be a lack of objectivity. It was this reason why I chose to study mathematics, and not statistics. As such, I've had little exposure to a formal statistical education, and much of my understanding stems from my own interpretation. At times I…