Model Uncertainty in Operational Risk Modeling Due to Data Truncation: A Single Risk Case

Abstract

Abstract:Over the last decade, researchers, practitioners, and regulators have had intense debates about how to treat the data collection threshold in operational risk modeling. Several approaches have been employed to fit the loss severity distribution: the empirical approach, the "naive" approach, the shifted approach, and the truncated approach. Since each approach is based on a different set of assumptions, different probability models emerge. Thus, model uncertainty arises. The main objective of this paper is to understand the impact of model uncertainty on the value-at-risk (VaR) estimators. To accomplish that, we take the bank's perspective and study a single risk. Under this simplified scenario, we can solve the problem analytically (when the underlying distribution is exponential) and show that it uncovers similar patterns among VaR estimates to those based on the simulation approach (when data follow a Lomax distribution). We demonstrate that for a fixed probability distribution, the choice of the truncated approach yields the lowest VaR estimates, which may be viewed as beneficial to the bank, whilst the "naive" and shifted approaches lead to higher estimates of VaR. The advantages and disadvantages of each approach and the probability distributions under study are further investigated using a real data set for legal losses in a business unit (Cruz 2002).

Model Efficiency and Uncertainty in Quantile Estimation of Loss Severity Distributions

“…The construction of the relative efficiency curves (REC) is described in Appendix A.2. Note that more detailed presentations of parts of this material are available in Brazauskas (2009) and Yu and Brazauskas (2017).…”

“…However, when all those models were used to estimate the 90% and 95% quantiles (value-at-risk measures) for ground-up loss, for some data sets they resulted in similar estimates, which would be expected, while for others they were far apart, which is counterintuitive. Moreover, using left-truncated operational risk data, Yu and Brazauskas (2017) have shown that even shifted parametric models (which might seem like a plausible option but nonetheless incorrectly account for data truncation) can pass those standard model validation tests. Next, due to the presence of deductibles and policy limits in insurance contracts, data truncation and censoring are unavoidable modifications of the loss severity variable.…”

Different Estimation Methods of the Stress-Strength Reliability Restricted Exponentiated Lomax Distribution

“…Jha & Chakraborty [3] and Chaves Agudelo [4] respectively related to the distributional properties and continuity of the Lumax norm values. Yu and Brazauskas [5] referred to and submitted applications for this position in support of data resulting from inaccurate and incorrectly truncated Lomax distributions. Chakraborty [6].…”

Editorial: A Celebration of the Ties That Bind Us: Connections between Actuarial Science and Mathematical Finance

“…Carolyn W. Chang and Jack S. K. Chang (Chang and Chang (2017)) utilize an approach that integrates commonly used tools from actuarial science and mathematical finance to price a default-risky catastrophe reinsurance contract. Daoping Yu and Vytaras Brazauskas (Yu and Brazauskas (2017)) study the impact of model uncertainty on value-at-risk (VaR) estimators. In her paper on predicting prices for high profile tech stocks, Nguyet Nguyen (Nguyen (2017)) applies the Hidden Markov Model (HMM) to forecast stock prices and develop an HMM-based trading strategy.…”