Solvency Assessment and Management. SA QIS2 Annexure 1 Possible approach in determining the SCR including the change in risk margin

Transcription

1 Solvency Assessment and Management SA QIS2 Annexure 1 Possible approach in determining the SCR including the change in risk margin 13 July 2012

2 1. Introduction oduction According to paragraph SCR.1.3 of the SA QIS2 technical specifications, for the purposes of the SCR standard formula calculation, technical provisions should be valued in accordance with the specifications laid out in the section on valuation within the SA QIS2 technical specifications. To avoid circularity in the calculation, the default option is that any reference to technical provisions within the calculations for the individual SCR modules is to be understood to exclude the risk margin. However, participants can choose to calculate their SCR using the change in technical provisions including the risk margin. This will require an iterative approach to determine both the SCR and the risk margin. Participants that choose to calculate the SCR using the technical provisions including risk margin will need to ensure that the SCR and risk margin stabilise. This may take several iterations. This document outlines a possible approach which insurers may follow when calculating the SCR using the change in technical provisions including the risk margin. The approach is by no means compulsory, and insurers are allowed to use their own approach if they choose to calculate the SCR using the technical provisions including the risk margin. For insurers opting to calculate the SCR only using the best estimate liabilities, the approach outlined in this document, or any other alternative approach, is not required. SA QIS2 Annexure 1 2

3 2. Possible Approach Suggested Approach The SAM SCR is based on the principles of economic capital calculation. Expressed in its simplest form this approach involves calculating the change from its base value of a quantity, Own Funds (OF), under a number of pre-defined stress scenarios and aggregating the individual capital requirements to produce the overall diversified SCR. OF in this context represents the excess of assets over liabilities: OF = A L A is defined as the total value of assets on the balance sheet including shareholders funds. L is defined as the total market consistent value of liabilities: L = Market Consistent value of liabilities = BEL for all risks + risk margin in respect of non-hedgeable risks The total market consistent value of liabilities (L) consists of two parts: best estimate value of the risk in respect of hedgeable and non-hedgeable components, plus the risk margin in respect of non-hedgeable risks. The challenge in defining L as the total market consistent value of liabilities is that it includes the risk margin which is calculated on a cost of capital approach. The capital used in this cost of capital is the Solvency Capital Requirement, which is dependent on the variability of OF, leading to circularity as illustrated in the following diagram: SA QIS2 Annexure 1 3

4 In an attempt to resolve this circularity, the SAM framework defines the OF for the purpose of the SCR calculation as (Total Balance Sheet Assets BEL) in order to simplify the calculation. Methodology to the approach: 1. Calculate Stress i : i ϵ {1...m } where there are m non-hedgeable risk driver stresses required for the calculation of the SCR for risk margin purposes as fully described in the QIS2 technical specifications. Here we specifically exclude hedgeable risks (or portions of risks) as the risk margin is based on the cost of capital for non-hedgeable risks alone. For this purpose Stress i is defined to be: Stress i (0) = (A base (0) BEL base (0)) (A i (0) BEL i (0)) Stress i = Solvency Capital Requirement for risk i A = Market value of assets BEL = Best Estimate of Liabilties (excl. Risk Margin) base denotes base case before application of any stress 0 indicates calculation at balance sheet date or T 0 i is the index which indicates which of the m stresses is under consideration This is the standard methodology for the SCR and risk margin calculation tested in SA QIS2. 2. Choose proxies for each non-hedgeable risk i In this step suitable proxies for each of the non-hedgeable risks need to be identified; A suitable proxy for risk i will behave in a similar way to Stress i at the balance sheet in response to changes in the risk drivers or variables which affect its value. In addition the proxy must fairly represent the expected runoff profile of that stress; The use of a deterministic proxy will assist in minimising the burden of the iterative calculation approach described below. 3. Project the best estimate of each proxy over the insurance book s period to run-off The projection period for each risk will be determined individually to be appropriate to that risk as determined by the longest outstanding term of an in-force policy exposed to that risk driver. SA QIS2 Annexure 1 4

5 4. Project the Stress i in respect of each risk driver i using the projected proxies according to the formula below. Stress i (t) = (P i (t) / P i (0)) * Stress i (0) P i (t) is the projected best estimate value of proxy i at time t Stress i (0) is calculated as described in step 1 above in the notation indicates that the quantity has been estimated using a proxy runoff 5. Aggregate the projected Stress i (t) at each future time using the correlation matrix approach set out in the SA QIS2 technical specifications to produce the capital vector SCR (t). 6. As per the standard approach the risk margin is then calculated by multiplying the capital requirement at each future point in time (over the run-off of the book) by the cost of capital rate of 6% p.a. and discounting the cost of capital to the balance sheet date (T 0 ) using the risk free term structure of interest rates. This sum is RM base (0), say, which is the estimated risk margin at balance sheet date using proxies. 7. Now recalculate the market consistent value of the assets and liabilities given that each of the (nonhedgeable) stress events required for the standard formula capital calculation have occurred (taken in turn one at a time). No further clarification is required about recalculation of the BEL post stress k where k ϵ {1...m} these calculations have already been done in step 1 above. The re-estimation of the risk margin within stress k requires further explanation. 8. In stress k we need to estimate the risk margin RM k (0) which is the risk margin at time 0 under stress scenario k. There are once again m non-hedgeable risks to consider within in this scenario, indexed by i as before: Let Stress ki (t) represent the stress or SCR component capital requirement at time t for risk i, after application of stress k to the base balance sheet. 9. For each stress, k ϵ {1...m} the following steps are required: For all hedgeable risks i, i ϵ {1...m}, recalculate the deterministic projected values of the proxy for the SCR for risk i (within the current stress k): P ki (t) for all i and t>=0: Use the proxies to estimate the Stress ki (t) for all i and t>=0: Stress ki (t) (P ki (t) / P i (t)) * Stress i (t) for t >= 0 = (P ki (t) / P i (0)) * Stress i (0) for t >= 0 SA QIS2 Annexure 1 5

6 The projected runoff of each of the risks within scenario k has now been calculated. Aggregate the Stress ki (t) across risks i ϵ {1...m} at each future time t to produce SCR k (t) Multiply SCR k (t) by the cost of capital rate (6% p.a.) and discount to balance sheet date using the risk free term structure (as appropriate to scenario k). If interest rate risk is considered fully hedgeable for the book in question then the term structure will always be identical to the base term structure and the set of risks k ϵ {1...m} will not contain interest rate risk. We now have for each k, an estimate of the risk margin in that scenario: RM k (0). 10. Now repeat step 1 with the following amendment: Stress i (0) = (A base (0) BEL base (0) RM base (0)) (A i (0) BEL i (0) RM i (0)) RM base (0) RM i (0) is calculated in step 9 above Aggregation of these revised Stress i (0) produces a revised non-hedgeable risk SCR at time Re-calculate the risk margin at time 0, RM base (0), using the proxy method for each of the risks i to project each of the stresses recalculated in step 10 over the full run-off period. A key assumption made in this step is that the proxies P i (t) which were originally determined to be adequate proxies for the run-off of the standard approach to each Stress i are also good proxies for the run-off of the modified Stress i which are based on changes in the market consistent value of liabilities, not the BEL in isolation. 12. Iterate steps 9 to 11 until the change in the SCR (step 10) and risk margin (step 11) from one loop to the next produces no material change in the result. Note that no extra model runs are required, the only difference on the next iteration is the new base position calculated in steps 10 and 11. Note that this methodology can be extended to the calculation of the SCR to include the change in risk margin when calculating the stress amounts. The main difference would be the inclusion of hedgeable risks, however hedgeable risks need not be projected in step 9 as they do not influence the risk margin calculated under the stress event k and hence do not affect the calculation of the revised stress amount in step 10. SA QIS2 Annexure 1 6