Stochastic modelling
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[edit] Stochastic Model
"Stochastic" means being or having a random variable. A stochastic model is a tool for estimating probability distributions of potential outcomes by allowing for random variation in one or more inputs over time. The random variation is usually based on fluctuations observed in historical data for a selected period using standard time-series techniques. Distributions of potential outcomes are derived from a large number of simulations (stochastic projections) which reflect the random variation in the input(s).
Its application initially started in physics. It is now being applied in life sciences and social sciences, especially finance.
[edit] Valuation
Like any other company, an insurer has to show that its assets exceed its liabilities to be solvent. In the insurance industry, however, assets and liabilities are not known entities. They depend on how many policies result in claims, inflation from now until the claim, investment returns during that period, and so on.
So the valuation of an insurer involves a set of projections, looking at what is expected to happen, and thus coming up with the best estimate for assets and liabilities, and therefore for the company's level of solvency.
[edit] Deterministic Approach
The easiest way of doing this, and indeed the method which has been the primary one used, is to look at best estimates.
The projections should use the most likely rate of claim, the most likely investment return, the most likely rate of inflation, and so on. This creates a point estimate - the best single estimate of what the company's current solvency position is.
The downside of this approach is it ignores the fact that there is uncertainty in the estimates, and that a whole range of outcomes is possible. It is all very well to know what is most likely, but we are also interested in what range of outcomes are probable.
[edit] Stochastic Modelling
A stochastic model would be to set up a projection model which looks at a single policy, an entire portfolio or an entire company. But rather than setting investment returns according to their most likely estimate, for example, the model uses random variations to look at what investment conditions might be like.
Based on a set of random outcomes, the experience of the policy/portfolio/company is projected, and the outcome is noted. Then this is done again with a new set of random variables. In fact, this process is repeated thousands of times.
At the end, a distribution of outcomes is available which shows not only what the most likely estimate, but what ranges are reasonable too.
This is useful when a policy or fund provides a guarantee, e.g. a minimum investment return of 5% per annum. A deterministic simulation, with varying scenarios for future investment return, does not provide a good way of estimating the cost of providing this guarantee. This is because it does not allow for the volatility of investment returns in each future time period or the chance that an extreme event in a particular time period leads to an investment return less than the guarantee. Stochastic modelling builds volatility and variability (randomness) into the simulation and therefore provides a more accurate representation of real life.
[edit] A Different Result
Using statistical notation, it is a well-known result that: E[ f(X) ] ǂ f( E[X] )
This confirms the usefulness of stochastic modelling, which is that the result which comes from the best estimate of all parameters does not equal the best estimate of the results taking into account all underlying variables.
[edit] The Asset Model
Although the text above referred to "random variations", the stochastic model does not just use any arbitrary set of values. The asset model is based on detailed studies of how markets behave, looking at averages, variations, correlations, and more.
The models and underlying parameters are chosen so that they fit historical economic data, and are expected to produce meaningful future projections.
There are many such models, including the Wilkie Model, the Thompson Model and the Falcon Model.
