Extreme risks are risks of very bad outcomes or "high consequence", but of low

probability Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speakin ...

. They include the risks of

terrorist Terrorism, in its broadest sense, is the use of criminal violence to provoke a state of terror or fear, mostly with the intention to achieve political or religious aims. The term is used in this regard primarily to refer to intentional violen ...

attack,

biosecurity Biosecurity refers to measures aimed at preventing the introduction and/or spread of harmful organisms (e.g. viruses, bacteria, etc.) to animals and plants in order to minimize the risk of transmission of infectious disease. In agriculture, thes ...

risks such as the invasion of pests, and extreme natural disasters such as major earthquakes.

Introduction

The estimation of the probability of extreme events is difficult because of the lack of data: they are events that have not yet happened or have happened only very rarely, so relevant data are scarce. Thus standard

statistical methods Statistics (from German: ''Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industria ...

are generally inapplicable.

Extreme value theory

If there is some relevant data, the probability of events at or beyond the range of the data may be estimated by the statistical methods of

extreme value theory Extreme value theory or extreme value analysis (EVA) is a branch of statistics dealing with the extreme deviations from the median of probability distributions. It seeks to assess, from a given ordered sample of a given random variable, the pr ...

, developed for such purposes as predicting 100-year floods from a limited range of data of past floods. In such cases a mathematical function may be fitted to the data and

extrapolated In mathematics, extrapolation is a type of estimation, beyond the original observation range, of the value of a variable on the basis of its relationship with another variable. It is similar to interpolation, which produces estimates between kn ...

beyond the range of the data to estimate the probability of extreme events. The results need to be treated with caution because of the possibility that the largest values in the past are unrepresentative, and the possibility that the behavior of the system has changed.

Black swan theory

In cases where the event of interest is very different from existing experience, there may be no relevant guide in the past data. Nassim Nicholas Taleb argues in his

black swan theory The black swan theory or theory of black swan events is a metaphor that describes an event that comes as a surprise, has a major effect, and is often inappropriately rationalized after the fact with the benefit of hindsight. The term is based o ...

that the frequency and impact of totally unexpected events is generally underestimated. With hindsight, they can be explained, but there is no prospect of predicting them.

Bank operational risk

Banks need to evaluate the risk of adverse events other than

credit risk A credit risk is risk of default on a debt that may arise from a borrower failing to make required payments. In the first resort, the risk is that of the lender and includes lost principal and interest, disruption to cash flows, and increased ...

s and

market risk Market risk is the risk of losses in positions arising from movements in market variables like prices and volatility. There is no unique classification as each classification may refer to different aspects of market risk. Nevertheless, the most ...

s. These risks, called operational risks, include the major events most likely to cause bank failure, such as massive internal fraud. The international compliance regime for banks,

Basel II Basel II is the second of the Basel Accords, which are recommendations on banking laws and regulations issued by the Basel Committee on Banking Supervision. It is now extended and partially superseded by Basel III. The Basel II Accord was publ ...

, requires that such risks be quantified using a mixture of statistical theory, such as

, and

scenario analysis Scenario planning, scenario thinking, scenario analysis, scenario prediction and the scenario method all describe a strategic planning method that some organizations use to make flexible long-term plans. It is in large part an adaptation and gener ...

conducted by internal committees of experts. A bank regulator (such as the

Federal Reserve The Federal Reserve System (often shortened to the Federal Reserve, or simply the Fed) is the central banking system of the United States of America. It was created on December 23, 1913, with the enactment of the Federal Reserve Act, after a ...

in the United States) oversees the result. Negotiations between the parties result in a system that combines quantitative methods with informed and scrutinized expert opinion. This gives the potential to avoid as far as possible the problems caused by the paucity of data and the

bias Bias is a disproportionate weight ''in favor of'' or ''against'' an idea or thing, usually in a way that is closed-minded, prejudicial, or unfair. Biases can be innate or learned. People may develop biases for or against an individual, a group ...

of pure expert opinion. Similar methods combining quantitative methods with moderated expert opinion have been used to evaluate

risks such as risks of invasive species that have potentially massive impacts on a country's economy or ecology.

Introduction

Extreme value theory

Black swan theory

Bank operational risk

See also

References

Further reading