Modeling extremes

An example of a Monte Carlo simulation risk analysis model for general risk analysis

Minimum software requirements: ModelRisk Complete edition

Technical difficulty: 3

Techniques used: Monte Carlo simulation in Excel

Model description

A great deal of risk analysis is about trying to figure out what the unlikely scenarios are. The modelling of possible extremes (high winds, largest stock market drop, biggest flood, largest outbreak, etc) is therefore an important aspect of risk analysis.

The mathematics of extreme value theory is enormous and complex – heavy books have been written about the subject. But don’t be put off! ModelRisk has some unique tools that can make extreme value modelling very easy.

Imagine that we have a reasonably large dataset of the impacts of natural disasters that an insurance or reinsurance company covers. [Don’t worry if you are into weather, or diseases, etc – the ideas are exactly the same]. It is quite common to fit such a dataset, or at least the high-end tail values to a Pareto distribution because this has a longer tail than any other distribution (excepting a few curiosities). An insurance company will often run a stress test of a 'worst case' scenario where several really high impacts hit the company within a certain period. So, for example, we might ask:

What could be the size of the largest of 10 000 impacts drawn from a fitted Pareto(5,2) distribution modelling the impact of a risk in $billion?

ModelRisk can perform these types of extreme calculations for all of its univariate distributions: use the tools presented in the Extreme Values window:


This example model illustrates some of the tools:


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