This chapter describes how validation can be carried out for models used in investment management. This chapter also describes what differentiates investment management models from other models and ends with conceptual framework for validating a few investment management risk models.

Survival analysis studies the time-to-event for various subjects. In the biological and medical sciences, interest can focus on patient time to death due to various (competing) causes. In engineering reliability, one may study the time to component failure due to analogous factors or stimuli. Cure rate models serve a particular interest because, with advancements in associated disciplines, subjects can be viewed as “cured meaning that they do not show any recurrence of a disease (in biomedical studies) or subsequent manufacturing error (in engineering) following a treatment. This chapter generalizes two classical cure-rate models via the development of a COM–Poisson cure rate model. The chapter first describes the COM–Poisson cure rate model framework and general notation, and then details the model framework assuming right and interval censoring, respectively. The chapter then describes the broader destructive COM–Poisson cure rate model which allows for the number of competing risks to diminish via damage or eradication. Finally, the chapter details the various lifetime distributions considered in the literature to date for COM–Poisson-based cure rate modeling.

This chapter focuses on potential issues bank examiners may face while reviewing the quality of a bank’s model risk management practices and validating modeling methodologies used to estimate allowance for loan and lease losses (henceforth ALLL). It discusses both leading and lagging practices in modeling and validating ALLL and examines upcoming challenges in implementing the new standards for allowance computations. In the context of validating ALLL methodologies under the new accounting standards, the author discusses the challenges in forecasting payoffs on existing credit card balances, issues relating to forecasting the economy and long-term losses, issues relating to the application of discounting in ALLL computations etc.

This chapter examines how banks’ Value-at-Risk (VaR) models performed during the COVID-19 crisis using regulatory trading desk-level data. It first evaluates whether banks’ VaR models were incomplete by checking whether various factors predict backtesting exceptions. Backtesting exceptions from the past ten business days and the level of the VIX forecast future exceptions. Predictability from past backtesting exceptions rises during the COVID-19 crisis relative to 2019. The results do not find any single market factor that related to contemporaneous backtesting exceptions. These results hold both in the aggregate and across asset classes.

This chapter defines the COM–Poisson distribution in greater detail, discussing its associated attributes and computing tools available for analysis. This chapter first details how the COM–Poisson distribution was derived, and then describes the probability distribution, and introduces computing functions available in R that can be used to determine various probabilistic quantities of interest, including the normalizing constant, probability and cumulative distribution functions, random number generation, mean, and variance. The chapter then outlines the distributional and statistical properties associated with this model, and discusses parameter estimation and statistical inference associated with the COM–Poisson model. Various processes for generating random data are then discussed, along with associated available R computing tools. Continued discussion provides reparametrizations of the density function that serve as alternative forms for statistical analyses and model development, considers the COM–Poisson as a weighted Poisson distribution, and details discussion describing the various ways to approximate the COM–Poisson normalizing function.

This chapter provides an overview of operational risk modeling techniques used by industry participants and regulators in the USA, recommendations for how modeling techniques can be improved, and a summary of the model risk tools necessary for any operational risk modeling framework.

Stress-testing models pose a unique set of challenges with respect to performance monitoring. In particular, unlike standard forecasting models that generate unconditional forecasts, stress-testing models generate conditional forecasts based on stress scenarios that are unlikely to occur. This critical difference greatly limits one’s ability to assess model projections with observed outcomes. We provide several different methods for this purpose