Scenario Analysis in the Measurement of Operational Risk Capital: A Change of Measure Approach

Abstract

At large financial institutions, operational risk is gaining the same importance as market and credit risk in the capital calculation. Although scenario analysis is an important tool for financial risk measurement, its use in the measurement of operational risk capital has been arbitrary and often inaccurate. We propose a method that combines scenario analysis with historical loss data. Using the Change of Measure approach, we evaluate the impact of each scenario on the total estimate of operational risk capital. The method can be used in stresstesting, what-if assessment for scenario analysis, and Loss Given Default estimates used in credit evaluations. IntroductionScenario analysis is an important tool in decision making. It has been used for several decades in various disciplines, including management, engineering, defense, medicine, finance and economics. Mulvey and Erkan (2003) illustrate modeling of scenario data for risk management of a property/casualty insurance company. When properly and systematically used, scenario analysis can reveal many important aspects of a situation that would otherwise be missed. Given the current state of an entity, it tries to navigate situations and events that could impact important characteristics of the entity in the future. Thus, scenario analysis has two important elements:1. Evaluation of future possibilities (future states) with respect to a certain characteristic. 2. Present knowledge (current states) of that characteristic for the entity.Scenarios must pertain to a meaningful duration of time, for the passage of time will make the scenarios obsolete. Also, the current state of an entity and the environment in which it operates give rise to various possibilities in the future.In management of market risk, scenarios also play an important role. Many scenarios on the future state of an asset are actively traded in the market, and could be used for risk management. Derivatives such as call (or put) options on asset prices are linked to its possible future price. Suppose, for example, that Cisco (CSCO) is trading today at $23 in the spot (NASDAQ) market. In the option market we find many different prices available as future possibilities. Each of these is a scenario for the future state of CSCO. The price for each option reflects the probability that the market attaches to CSCO attaining more (or less) than a particular price on (or before) a certain date in the future. As the market obtains more information, prices of derivatives change, and our knowledge of the future state expands. In the language of asset pricing, more information on the future state is revealed.At one time, any risk for a financial institution that was not a market or credit risk was considered an operational risk. This definition of operational risk made data collection and measurement of operational risk intractable. To make it useful for measurement and management, Basel banking regulation narrowed the scope and definition of operational risk. Under this definition, operational risk is ...

A Theoretical Framework for Incorporating Scenarios into Operational Risk Modeling

“…As Dutta and Babbel (2010) rightly point out, pooling does not take into account scenario frequencies. Because pooling substantially overstates the scenario weights (especially those of the most severe scenarios), an overstatement of scenario-driven capital numbers is most likely to exist as well.…”

“…However, Berkowitz's approach is not directly applicable to operational risk modeling mainly because of the necessity to separately model the severity and frequency of losses. Dutta and Babbel (2010) propose a similar simulation-based approach that takes into account the specifics of modeling operational risk. However, the authors do not fully disclose a theoretical justification for their approach.…”

“…A common feature of all these approaches is the lack of a sound theoretical justification behind them. Dutta and Babbel (2010) attempt to resolve the challenge of incorporating scenarios by proposing a simulation-based approach. Although their approach seems reasonable, the authors do not fully disclose its theoretical underpinnings.…”

“…However, such an adjustment is questionable because it implies that true frequencies are those of backward-looking historical losses, which might not necessarily be the case. Dutta and Babbel (2010) propose the replacement of historical frequencies with scenario frequencies whenever the former are lower than the latter. Although this assumption seems conservative, if too many scenarios have been generated from the body relative to the tail of the severity distribution, then this situation might lead to a reduction in capital.…”

“…The approach thatDutta and Babbel (2010) propose works with scenario ranges only. If scenario experts report only point estimates of scenario losses, then one has to create a range around them.…”