Hi there,
You’ve really opened a whole can of worms with this one! The capital model is designed to model the evolution of the company’s balance sheet over time. It then calculates a capital requirement according to a particular risk measure. For present purposes the risk measure is VaR (value at risk) but we need to specify a confidence level, p, and a time horizon, T. In simple terms then, we are determining the amount of capital we need to hold in order to have a probability p of still being solvent at time T.
On a one-year basis, T is set equal to one year. On an ultimate basis, T is set equal to the time period over which all the liabilities are extinguished. For long-tailed business this time period could be significant. The liabilities in question will be defined by the regulation. Under Solvency II they will include liabilities already on the balance sheet and liabilities relating to new business written over the course of the coming year. (This is all subject to some complicated rules regarding contract boundaries, but that’s another discussion.)
Now we’ve said we’re looking at the evolution of the company’s balance sheet over time. The insurance liabilities will affect this in two ways. First, when claims are paid, the assets and liabilities will both reduce. Second, the best estimates of the outstanding liabilities will evolve over time. As mentioned, in theory the liabilities under consideration are everything to which the company is already legally obligated. This is much closer to an underwriting year approach than an accident year approach.
So that’s the theory. However, the practical aspects of how we implement this are far from standardised. Several companies build their models under the assumption that, until business starts to be earned, their estimate of the loss cost as entered on the balance sheet will not change. This makes the one-year time horizon look much more like an accident year approach because the uncertainty surrounding losses incurred after the new year is not captured.
In summary…
There’s a lot here to get you head around and most practitioners do not have all the complexities in mind all the time. The important thing is that the difference between ultimate and one-year does not really have a lot to do with accident or underwriting year approaches and is actually about the timeframe over which risks are considered. We therefore expect the risks over an ultimate time horizon to be greater than over a one-year time horizon. The shorter-tailed the business, the closer the two values will be.