Global insurance market report [gimar]

Figure 3.2d:
Life insurers’ interest rate sensitivity (2014–2019)
Source: Hartley et al.

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principal component analysis. Using this method, 
the time series of risk-free interest rates of different 
maturities and the yields of corporate bonds 
from different rating classes
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are broken down 
(decomposed) into factors.
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These factors have 
smaller dimensions than that of the time series
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in 
question and are able to perfectly predict the time 
series that have been decomposed.
The principal component analysis method is 
designed to provide 100% accurate in-sample 
forecasts that reproduce the decomposed time 
series. At the same time, these factors can 
be treated as random variables and projected 
forward. Once these factors are projected, they 
can be recomposed to produce forecasts about 
the time series from which they were created. 
In the BMA model, the factors are fitted with a 
vector autoregression model, which accounts 
for correlation between factors. Once the vector 
autoregression model has been estimated, it is 
simulated forward for 12 months. At the end of 
this period, the factors are recomposed back into 
risk-free interest rates and corporate bond yields 
for different rating classes.
Because risk-free rates are given in discrete 
maturities, a set of techniques is used to create 
smooth curves for all maturities. Initially, for 
maturities of 20 years, for example, new data 
points are added (interpolation) between the 15th 
and 30th year to close an important gap in the 
US yield curve.
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The end product is a collection 
of risk-free curves and corporate bond yield 
forecasts for rating classes from AAA to non-
investment grade. Figure 3.2e shows 100 sample 
US risk-free curves, produced by the BMA model.
The model produces multiple curves, from 
regular increasing curves to inverted ones. The 
relative frequency of each curve is based on 
historical data and, as can be seen in Figure 
3.2f, most curves increase with an inversion at 
shorter maturities. Based on the 10,000 curves 
produced, the mean curve, the median curve, 
the 10th percentile curve and the 95th percentile 
curve can be estimated. These are the four main 
scenario curves. In addition, the same mean, 
median, 10th percentile and 95th percentile yields 
for corporate bonds are produced for different 
rating classes. Since there isn’t a curve with 
different maturities of corporate bond yields for 
each rating category, the assumption is that shifts 
in the yield curves of corporate bonds are parallel 
for all maturities.
The mean risk-free curve is produced by 
averaging 10,000 projected risk-free rates for 
every maturity. The median curve is produced by 
taking the median of 10,000 projected risk-free 
rates for every maturity. Similarly, the 10th and 
95th percentile curves are respectively the 10th