Modeling a correlated insurance portfolio | Vose Software

Modeling a correlated insurance portfolio

See also: Insurance and finance risk analysis modeling introduction, Measures of risk - Value at Risk, Measures of risk - Expected shortfall, Vose Aggregate Multivariate Monte Carlo

Imagine that you are an insurance company with several different policies. For each policy, you have the number of policy holders, the expected number of accidents per policy per year, the mean and standard deviation of the cost of each accident, and each policy has its own deductible and limit. It is a simple, though perhaps laborious, exercise to model the total payout associated with one policy and to sum the aggregate payout using simulation. Now imagine that you feel there is likely to be some correlation between these aggregate payouts: perhaps historic data has shown this to be the case. Using simulation, we cannot correlate the aggregate payout distributions. However, we can include a correlation if we use FFT methods to construct the aggregate loss distribution. The model shown below shows the aggregate loss distribution of five different policies being correlated together via a Clayton(10) copula. Note that the equations used in Cells C10:C14 use one minus the Clayton copula values which will make the large aggregate claim values correlate more tightly than at the low end.

Example model   Correlated_insurance_portfolio  - simulating the loss distribution for a number of policies where the aggregate loss distribution for policies are correlated in some fashion.

Other examples of adding correlation to aggregate calculations can be found in this topic.

Read on: Modeling extremes