Risk model implementation requires the proper estimation of key input variables. The present issue of The Journal of Risk offers papers that deal with estimation techniques in conjunction with an assessment of their efficiency. The applications featured include risk measure estimation, credit risk model backtesting with a small sample size, and nonmaturing bank deposits.
The rise in prominence of the risk measure expected shortfall (ES) has spurred further interest in its statistical estimation. In “Nonparametric versus parametric expected shortfall”, the first paper in the present issue, R. Douglas Martin and Shengyu Zhang use influence functions to show how parametric and nonparametric estimators differ markedly, especially with regard to standard error and risk coherence.
The standard parameter smoothing tool of the exponentially weighted moving average (EWMA) is revisited in our second paper, “Recursive estimation of the exponentially weighted moving average model” by Radek Hendrych and Toma´sˇ Cipra. The authors use a recursive approach to estimate the weight of a single-parameter EWMA model. They validate their procedure numerically and empirically, showing that it strikes a good balance between computational speed and accuracy, thus making it a competitive contender for volatility estimation relative to existing methods.
Backtesting is central to model assessment, but it is often hampered by limited data. In the issue’s third paper, “The efficiency of the Anderson–Darling test with a limited sample size: an application to backtesting counterparty credit risk internal models”, Matteo Formenti, Luca Spadafora, Marcello Terraneo and Fabio Ramponi propose a modification of the classical Anderson–Darling test in order to efficiently detect volatility underestimation, which is critical in risk management. The authors’ illustration of their method applied to an interest rate model shows that it compares favorably with standard uniform tests.
Bank deposits with no contractual maturity (eg, money market and savings accounts) – part of a group known as nonmaturing deposits – figure prominently on the balance sheets of commercial banks and play a fundamental role in bank stress testing. In the final paper of this issue, “Estimating maturity profiles of nonmaturing deposits”, Fidelis Musakwa and Eric Schaling develop a survival model for deposit retention, with an algorithm that accounts for data censoring. Using a case study, the authors show that their model can capture a bank’s characteristics, such as its customer deposit retention curve.
Warrington College of Business, University of Florida
In this paper, the authors use influence functions as a basic tool to study unconditional nonparametric and parametric expected shortfall (ES) estimators with regard to returns data influence, standard errors and coherence.
The aim of this paper is twofold: (i) to introduce two recursive estimation algorithms suitable for the EWMA process that are applicable for routine volatility predictions, and (ii) to investigate their prediction ability by comparing them with other…
The efficiency of the Anderson–Darling test with a limited sample size: an application to backtesting counterparty credit risk internal models
This paper presents a theoretical and empirical evaluation of the Anderson–Darling test when the sample size is limited.
This paper proposes a method to extract deposit lifetime data from individual account transactions.