3.2.5 Discounting

3.2.5.1 Determination of yield curves for current estimate discounting

• L1-31. In order to calculate a current estimate, insurance liabilities are discounted using an adjusted yield curve. The adjusted yield curve is based on:
  • a) Risk adjusted liquid interest rate swaps or government bonds (risk-free yield curve); and
  • b) An adjustment.
• L1-32. The adjusted yield curve is determined based on the methodology specified in the Level 2 text (sections 3.2.5.2 and 3.2.5.3).

3.2.5.2 Determination of the risk-free yield curve

• L1-33. The risk-free yield curve is determined based on a three-segment approach:
  • a) Segment 1: based on market information from government bonds or swaps, including a credit risk correction, where necessary;
  • b) Segment 2: extrapolation between the first and third segments; and
  • c) Segment 3: based on a stable currency specific long-term forward rate (LTFR), to which a spread is added in order to represent the expected spread that may be earned from reinvestments in the long-term.
• L1-34. For each currency, the transition from the first to the second segment occurs at the last maturity for which market information can be observed in deep, liquid and transparent financial markets (the last observed term or LOT).
• L1-35. For each currency, the LTFR is the sum of an expected real interest rate and an inflation target.
• L1-36. For the purpose of determining the expected real interest rate, jurisdictions are allocated according to areas that share common macroeconomic characteristics. The same expected real interest rate is used for all currencies within a given area. For each area, the expected real interest rate is based on a simple average of observed real interest rates over a certain period of time.
• L1-37. The two components of the LTFR are reviewed annually, in order to reflect potential changes in macroeconomic expectations. However, the magnitude of annual changes to the LTFR is capped in order to mitigate its potential volatility.
• L1-38. Further specifications on the methodology to determine the risk-free interest rate are provided in the Level 2 text.

3.2.5.2.1 Choice of instrument for and length of Segment 1

• L2-43. The base yield curves are derived from financial instruments that are traded in deep, liquid and transparent (DLT) financial markets. A DLT assessment is carried out at regular intervals in order to identify the financial instruments and maturities for which a DLT market exists.
• L2-44. The DLT assessment determines, in particular, whether swaps or government bonds are the relevant financial instruments for the risk-free interest rates and what the LOT is. The DLT assessment is performed for each currency.

3.2.5.2.2 Credit Risk Adjustment

• L2-53. Inputs from chosen instruments are subject to the Credit Risk Adjustment (CRA).
• L2-54. The CRA is 0 basis points when instruments for Segment 1 are considered risk free. The CRA is 10 basis points otherwise.

3.2.5.2.3 Length of Segment 2

• L2-55. For all currencies, the start of the third segment as referred to in paragraph L1-33 is the later of the following:
  • • 30 years after the LOT; and
  • • 60 years.

3.2.5.2.4 Extrapolation, interpolation and convergence tolerance

• L2-56. Both the interpolation between Segment 1 maturities and the extrapolation beyond the LOT are based on the Smith-Wilson methodology.
• L2-57. The control input parameters for the interpolation and extrapolation are the LOT, the LTFR, the convergence point and the convergence tolerance.
• L2-58. If the reference instruments are swap rates, the market interest rates to be used as inputs are the swap par rates after deduction of the credit risk adjustments. If the reference instruments are zero coupon government bonds, the market interest rates to be used as inputs are the zero-coupon rates.
• L2-59. The parameter alpha that controls the convergence speed is set at the lowest value that produces a yield curve reaching the convergence tolerance of the LTFR by the convergence point. A lower bound for alpha is set at 0.05.
• L2-60. The convergence tolerance is 0.1 basis point, and is achieved at the tenor which marks the end of Segment 2.

3.2.5.2.5 LTFR Components

• L2-61. The LTFR is the sum of the following two components:
  • a. The expected real interest rate, computed as the simple arithmetic mean of annual real interest rates. Annual real rates 𝑟 are calculated as:
    
  $$r = \cfrac{\text{short term nominal rate}- \text{inflation rate}}{1 + \text{inflation rate}}$$
  The expected real interest rate is rounded to the nearest five basis points.
  • b. The expected inflation target, computed as follows:
    • • For currencies for which the central bank has announced an inflation target, the expected inflation is based on that inflation target. In this case the expected inflation rate is:
      • – 1%, where the inflation target is lower than or equal to 1%;
      • – 2%, where the inflation target is higher than 1% and lower than 3%;
      • – 3%, where the inflation target is higher or equal to 3% and lower than 4%; and
      • – 4%, otherwise.
    • • For currencies for which the central bank has not announced an inflation target, the expected inflation rate is set to 2%. However, where past inflation experience and projection of inflation both clearly indicate that the inflation in a currency area is materially higher or lower than 2%, the expected inflation rate is chosen in accordance with those indicators.
• L2-62. In order to determine the expected real interest rate, countries are grouped in the following three geographical areas:
  • a. Geographical area 1, comprised of the following currency areas: AUD, CAD, CHF, CZK, DKK, EUR, GBP, JPY, NOK, NZD, SEK, SGD, USD;
  • b. Geographical area 2, comprised of the following currency areas: HKD, ILS, KRW, TWD;
  • c. Geographical area 3, comprised of all other currency areas.
• L2-63. The initial values of the expected real interest rate component are:
  • • 1.8% for geographical area 1;
  • • 2.4% for geographical area 2; and
  • • 3.0% for geographical area 3. The values will be regularly reviewed.
• L2-64. The maximum annual change to the LTFR is limited to 15 bps. The LTFR is changed according to the following formula:

3.2.5.3 Determination of the adjustment to the risk-free yield curve

• L1-39. The ICS yield curves include an adjustment to the risk-free curves. This adjustment is determined using the Three-Bucket Approach.
• L1-40. The Three-Bucket Approach classifies liabilities into General Bucket, Middle Bucket and Top Bucket, depending on the nature of the liabilities and the assets backing these liabilities. A different yield curve adjustment is determined for each bucket.
• L1-41. The criteria used for the classification of liabilities and the adjustment relevant for each bucket are specified in the Level 2 text.
• L2-65. The following spread over the LTFR is added to all LTFR calculated according to paragraphs L2-61 to L2-64 above:
  • • 20 basis points for geographical area 1;
  • • 25 basis points for geographical area 2; and
  • • 35 basis points for geographical area 3. using the geographical areas laid down in L2-62.

3.2.5.3.1 Classification criteria

3.2.5.3.2 Adjustments to the yield curve

3.2.5.3.2.5 Modulation Factor w

• L2-104. The modulation factor $w_i$ is computed on a portfolio basis. It is computed using all assets, which are sensitive to changes in credit spreads , in the same currency spread bucket as the main currency of the liabilities.
• L2-105. The currency spread buckets are based on the spread mappings which are used for determining the credit spreads for those currencies.
• L2-106. The modulation factor $w_i$ is computed using the following formula:

• • $PVBPU$ stands for the price value of a basis point up, and is calculated in the following way

• • $weight_{spread}$ is the weight of spread contributing assets. $weight_{spread,MB}$ is the weight of the spread contributing assets for the Middle Bucket. These are computed using the parameters as for paragraph L2-91.