Building and Testing Yield Curve Generators for P&C Insurance

Abstract

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. Typically regulators, security analysts, and customers focus on one to three-year timeframes for capital risk. This is much different than risk-management in other financial institutions, where the focus is on how much markets can move from one day's close to the next day's opening. Those institutions trade continuously when the markets are open, and manage risk with derivatives. P&C insurers, on the other hand, 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. We do try to make the modeling more accessible to actuarial modelers, compared to our source papers in the financial literature. Code for MCMC estimation is included at the CAS GitHub site. Model estimation is getting easier as the software advances, and interested actuaries, who often have a better feel for the application needs than do financial modelers, can use this to fit their own yield-curve generators.