SCR Calculator User Manual

Version Last modified 2024-3-21

Notch-level Interpolation

Using the UK PRA's MA Methodology

When 'PRA' is selected, the SCR Calculator will:

  • Use the UK PRA's published risk free rates, fundamental spread components (probability of default, cost of downgrade, long-term average spreads) and symmetric adjustments where possible. (These data are stored in the SCR Calculator's database for API use by the programme.) Note, however, that the UK PRA publishes these data on a smaller set of countries than EIOPA does, and also on a later date (usually around the 8th) every month than EIOPA does (usually around the 5th). Where UK PRA data is not available, EIOPA data is used instead.
  • Use the UK PRA's notch-level interpolation methodology of the fundamental spread components wherever possible.

How the Interpolation Works

  • Interpolation is only carried out when it is a corporate or covered bond (not a government bond), and where the bond's rating is not a central notch (e.g. A1 or A3, but not A2), and is not AAA or CCC-and-below.
  • "Fundamental Spread components" refer to
    • Probability of Default in bps (PD)
    • Cost of Downgrade in bps (CoD) and
    • Long-Term Average Spread in bps (LTAS)
    These are the parameters to be interpolated.
  • The Fundamental Spread itself is always calculated as a derived quantity from the above 3 parameters.
    • For corporate bonds, the formula is FS = max(PD + CoD, 0.35 * LTAS), where the components are interpolated where necessary.
    • For government bonds, the formula is FS = max(PD + CoD, 0.3 * LTAS), where the components are maintained at rating level and not interpolated.
  • For an 'upper' notch corporate or covered bond, 1/3 of higher rating's FS components and 2/3 of its own rating's FS components are weight-added to arrive at the notch-level components. I.e.
    • PD (AA1) = 1/3 * PD (AA) + 2/3 * PD (A)
    • CoD (AA1) = 1/3 * CoD (AA) + 2/3 * CoD (A)
    • LTAS (AA1) = 1/3 * LTAS (AA) + 2/3 * LTAS (A)
    and naturally, the scaling factors are swapped for 'lower' notch bonds.
  • The above is called the "full component interpolation method" and is used by the SCR Calculator. The UK PRA also described a simplified (PD + overall) method, which is not used by the SCR Calculator, as it is less accurate.

Explanatory Notes

Where notch-level interpolation does occur, the user will be reminded in the explanatory notes of the single asset panel. Below are example screenshots under the two choices:

Inputs and explanatory notes under the EIOPA method, for a Spanish A1-rated corporate bond:

Explanatory notes under the PRA interpolation method: