  Interest-rate risk is a key factor for property-casualty insurer capital. P&C
companies tend to be highly leveraged, with bond holdings much greater than
capital. For GAAP capital, bonds are marked to market but liabilities are not,
so shifts in the yield curve can have a significant impact on capital.
Yield-curve scenario generators are one approach to quantifying this risk. They
produce many future simulated evolutions of the yield curve, which can be used
to quantify the probabilities of bond-value changes that would result from
various maturity-mix strategies. Some of these generators are provided as
black-box models where the user gets only the projected scenarios. One focus of
this paper is to provide methods for testing generated scenarios from such
models by comparing to known distributional properties of yield curves.
  P&C insurers hold bonds to maturity and manage cash-flow risk by matching
asset and liability flows. Derivative pricing and stochastic volatility are of
little concern over the relevant time frames. This requires different models
and model testing than what is common in the broader financial markets.
  To complicate things further, interest rates for the last decade have not
been following the patterns established in the sixty years following WWII. We
are now coming out of the period of very low rates, yet are still not returning
to what had been thought of as normal before that. Modeling and model testing
are in an evolving state while new patterns emerge.
  Our analysis starts with a review of the literature on interest-rate model
testing, with a P&C focus, and an update of the tests for current market
behavior. We then discuss models, and use them to illustrate the fitting and
testing methods. The testing discussion does not require the model-building
section.
