2. Literatures Review
2.2 Quantitative Impact Study 5
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Notice that in the final year, the residual margin should be zero.
2.2 Quantitative Impact Study 5
2Since we review IFRS4 in previous subsector, which provides comprehensive definitions for the measurement of liabilities, we still need more specific information for estimating liabilities, especially for the techniques and parameters.
QIS5 is published by the Committee of European Insurance and Occupational Pensions Supervisors (CEIOPS). It is used to determine the Solvency Capital Requirement (SCR) for the Solvency II users. The concept of SCR and reserve are quite close. They are both regulated to ensure that insurer has sufficient capital to pay the future claims. We can therefore refer to the techniques that QIS5 uses to estimate SCR.
Similarly QIS5 divides SCR into two components: the best estimation and the risk margin. We summarize these two components in following subsections and explain the methods used to estimate these two components.
(a) Best Estimation
QIS5 defines best estimation as the probability weighted average of future cash-flows taking account of the time value of money. The best estimated is defined as the average of the outcomes of all possible scenarios, weighted according to their respective probabilities. Two key elements for calculating the best estimated are cash flows and discount rate. QIS5 suggests that the cash flows should be estimated gross.
The gross cash inflows in QIS5 include future premiums and receivables for salvage
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Some of the descriptions in this subsection are referred to QIS5 Technical Specification/QIS5 Annex
/QIS5 Technical Specification Errata, Sept. 27 2010
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and subrogation, exclude the investment return. And the gross cash outflows include benefits and expenses. Since cash flows are already specifically defined in the IFRS4 section, we therefore focus on the discount rate definition of QIS5.
QIS5 suggests that the discount rates for insurance liabilities should be the risk-free rate with liquidity premium to reflect the illiquidity characteristics of insurance liabilities.
For the long-term characteristic of the insurance liabilities, QIS5 suggests that the insurer should establish a yield curve that can reflect the whole period of the insurer's pool. For the specification of the relevant risk-free interest rate term structures macroeconomic extrapolation techniques are used to derive the
extrapolation beyond the last available data point (which is 20 years interest rate in Taiwan). This requires specification of the following:
(i) Determination of the ultimate forward rate.
(ii) Interpolation method between the last observable liquid forward rate and the unconditional forward rate.
After determine the UFR and method, the insurer should follow the steps of:
(i) Calculation of the non-extrapolated part of the curve, prior to adjustment;
(ii) Adjustment of the non-extrapolated part of the curve.
(iii) Calculation of the illiquidity premium.
(iv) Extrapolation of the interest rate term structure
This gives insurer a 100 years yield curve which is suitable for its long-term characteristic of insurer's liability. But in our simulation we only assume the insurer's activities for 20 years. We therefore need not to extrapolate a yield curve for 100
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years since there exists market data for interest rate in 20 years. Our primary concern here is therefore the method for calculation of the illiquidity premium.
QIS5 provides four methods for estimating liquidity premium:
(i) CDS method.
(ii) Structural model method.
(iii) Covered bond spread method.
(iv) Proxy method.
The concept of these methods is to find an asset with less liquidity and an asset with better liquidity in local financial market. The spread between these two assets reflects the illiquidity of the market. For different countries, QIS5 also provides how much percentage of liquidity premium should takes into account to reflect the country's market status. Next we introduce these four methods.
CDS method
The CDS method considers the negative CDS spread, which is the spread between CDS price and corporate bond spread. Corporate bond spread is the yield of the corporate bond minus the yield of the government bond. We can express as follows:
This method is based on the better liquidity of CDS in foreign markets. The yield of the corporate bond is compensated more because its illiquidity. The spread between these two assets can therefore be defined as the difference between liquidity and illiquidity asset.
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The advantage of this method is the convenience in calculation. Since CDS are frequently traded in foreign market, it is easy to find market price for CDS. But in Taiwan, CDS is neither traded nor issued in the market. Even if we take foreign market as the basis of estimation, the spread may include the risk of exchange rate. It is therefore impractical to use such method for estimating liquidity premium in Taiwan.
Structural model method
Structural model method uses the difference between the Merton model corporate bond price and the actual corporate bond price to estimate the liquidity premium. The Merton model expresses the corporate bond price, which denotes in B, as the difference between the asset and the shareholder's equity of the company as follows:
, where V denotes the asset value of the company, K is the liability value of the company,
The corporate bond price equation from Merton model reflects the expected loss and credit risk (probability of default), we therefore can use the spread between the model's theoretical price and the actual price of the corporate bond to estimate the liquidity premium.
This method is limited by the estimation of parameter . Since affects the price significantly, the calibration of is not easy. Moreover, unpublished company cannot be estimated by this method. There are only a few of life insurers in Taiwan that is published. It is therefore impractical to use such method for estimating liquidity
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premium in Taiwan either.
Covered bond spread method
Covered bond spread method is to estimate the liquidity premium by the spread between the covered bond and financial instruments with more liquidity. This method is based that covered bonds is almost risk-free in credit risk since it has collaterals.
QIS5 suggests that it is reasonable to estimate the liquidity premium by comparing the yield between covered bonds and IRS, since the IRS has lower credit risk and better liquidity.
This method is not in the consideration because there is no covered bond market in Taiwan. It is therefore impractical to use such method for estimating liquidity premium in Taiwan unless we can find an asset that has similar characteristics with the covered bond.
Proxy method
Proxy Method is the primary method for QIS5 in estimation of the liquidity premium. The equation of liquidity premium is expressed as follows:
QIS5 considers that the components of the corporate spread includes cost of expected loss, credit risk and liquidity premium. We can therefore estimate the liquidity premium by dividing the corporate spread. The parameter is represented for the expected loss. QIS5 assumes that after corporate spread minus the cost of expected loss , the proportion in the remained spread is liquidity premium while proportion is credit premium. QIS5 assumes .
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(b) Risk Margin
QIS5 suggests that the risk margin should be calculated by determining the cost of providing an amount of eligible own funds equal to the SCR necessary to support the insurance and reinsurance obligations over the lifetime thereof. The rate used in the determination of the cost of providing that amount of eligible own funds is called cost of capital rate.
QIS5 calculated risk margin based on the SCR of the whole portfolio in the insurance company includes the insurance contract and reinsurance contract. The structure of the SCR is shown in figure 2.
Figure 2. Structure of SCR The SCR of each product lines is estimated as follows:
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Then the risk margin is estimated as:
For the estimation of the cost of capital rate, QIS5 Calibration paper follows three steps:
(i) Estimate the equity risk premium.
(ii) Adjust the equity risk premium.
(iii) Calibrate it by the market price.
QIS5 follows these three steps and suggests that the cost of capital rate should be set greater than 6%.