Expected Loss Covered Bond Model

APPENDIX D3: REFINANCING RISK – CALCULATION OF REFINANCING MARGINS
Moody’s has built a refinancing margin generator which calculates the refinancing margins used in the Moody’s EL
Model. The generator is defined as (the “Formula”):
dS = η(ζ − S)dt + σdW
Where:
dS is the spread change;
η is the speed the time series reverts to its long term meanζ ;
dt is the change in time;
2
σ is the volatility of the spread time series; and
dW represents the standard Wiener process. 11
The parameters of the Formula (adjusted for timing) were set by minimising the differences of the results produced
for parts of the Formula and the data historically observed on refinancing margins. This exercise was repeated to
calculate the long-term mean and standard deviation for each rating category for each collateral type. 12
The
Formula is then run for a large number of simulations. From these simulations refinancing curves are generated by
working to the desired confidence levels. The confidence levels used for calculating refinancing margins are:
• 99% for margins used when refinancing must be completed within six months; and
• 95% for margins when more than six months is available for refinancing.
The following graph illustrates the refinancing margins produced when working to a 99% confidence level. The
main assumptions used are broadly in line with those used to calculate the refinancing margins for Aaa-rated
residential mortgage pools. The assumptions used include a standard deviation of 20 bps, and a long-term
average refinancing margin of 30 bps.
Refinancing Margins for a Aaa-rated Pool of
Prime-Quality Residential Mortgages
1.20%
1.00%
0.80%
0.60%
0.40%
0.20%
0.00%
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58
Months
For a discussion of the meaning of these refinancing margins, see Appendix D1.
11
For further information, refer to “The Moody’s Capital Model Version 1.0, January 2004”.
12
Moody’s has not used the calculated factor for mean reversion. Instead Moody’s has used a fixed parameter for mean reversion. This is
because an analysis suggests that using the limited available data would overestimate the rate of mean reversion. Moody’s has used the
same fixed parameter for mean reversion when calculating refinancing margins for each rating category of each major asset class.
18 • Moody’s Investors Service European Covered Bond Rating Methodology