Hi, What is the difference between ultimate basis and 1-year basis in calculating SCR? Is ultiamte basis equal to underwriting basis, and 1-year basis is equal to accident year basis? Thanks.
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.
I would like to take an example. The outstanding calims will be settled in the next two year. The paid amount in the first year is X~U(10,14) and that in the second year is Y~U(4,8). To simplify the question, 90% VaR is used instead of 99.5% VaR. Under the Ultimate basis, the reserve for the unpaid o/s claims is the 90% percential of (X+Y), which is 20.211. Under the 1-year basis, the reserve will be the 90% percential of X plus the expected value of Y, which is 13.6+6=19.6. Here we will not consider the uncertainty risk after 1 year, just having the expected value. Just a very simple case and hope that does help to you. SII uses 1-year basis and ICA uses Ult basis.
It's perhaps a tad more complicated than this. Your opening balance sheet, i.e. at the beginning of the two-year period under consideration, will contain a provision in respect of these liabilities equal to their total discounted expected value. Sherwin has ignored discounting and for simplicity's sake let's continue to assume a flat 0% yield curve. So the provision in respect of outstanding liabilities on the opening balance sheet will be \(12+6=18\). In addition to this there will be a regulatory capital requirement. Let's assume that the liabilities under consideration represent the company's only risk. On an ultimate basis, the regulatory capital requirement will then be the excess of the 90th percentile of (X+Y) over its expected value, i.e. \(20.211-18=3.211\). Under a Solvency II basis, things get tricky. We have to consider the "run-off result." Essentially this is the change in our best estimate of the ultimate between now and one year's time. So suppose we are at the end of the first year and we now know the value of X. Suppose it has turned out quite high, e.g. 13.6. Would you now book a provision of 6 in respect of the outstanding liabilities? To do so would seem to be ignoring the experience of the year you've just had that suggests the business may not be as profitable as you thought. Depending on the nature of the business this may or may not be reasonable. So suppose instead that we book a figure of 7 on the new balance sheet. Then the run-off result is \((13.8-12)+(7-6)=2.8\). Now for Solvency II the regulatory capital requirement is based on the 99.5th percentile of the run-off result. This requirement has led to practitioner's speaking of an "actuary-in-the-box" approach in which the methodology of a hypothetical actuary estimating the outstanding claims with one year's extra experience is automated in order to simulate the run-off result. We've not really touched on the issue of accident/underwriting year reserving here and perhaps it's best not to because then it gets even more complicated!
"suppose we are at the end of the first year". But we should estimate reserving risk at start of first year, even on 1-year basis?
So we need to look at our estimate of the ultimate now and also what it might be in one year's time. So I'm simply saying imagine you're an actuary in one year's time trying to come up with a revised estimate of the ultimate.
