PROCEEDINGS May 15, 16, 17, 18, 2005 - Casualty Actuarial Society

190 MODELING FINANCIAL SCENARIOSavailable, this allows users of the term structure model to trackall interest rates on the yield curve during a simulation, not alimited few. For example, users of a term structure model whoare interested in mortgage prepayment rates will be interested inthe refinancing rate, which may be closely related to bond yieldsof specific maturities (such as 10 years). Other users may beconcerned about crediting rates that are a function of historical5-year interest rates. Without some explicit closed-form solution,the modeler has no foundation to imply yields of different maturitiesfrom a limited set of stochastic factors. The two-factorequilibrium model selected for the financial scenario model isdescribedinthethirdsectionofthispaper.Equity ReturnsSimilar to interest rates, there have been many studies thathave looked at the behavior of equity returns. Shiller [39] andSiegel [38] analyze long-term patterns in stock returns and providehelpful analyses of long-term trends. Sornette [40] examinesthe behavior of stock markets, investigating why complexsystemssuchasstockmarketscrash.Often equity returns are assumed to follow a normal distribution.For example, in the development of their famous optionpricing formula, Black and Scholes [7] assume that (continuouslycompounded) returns for stocks are normally distributed.However, historical observation of equity returns reveals that thedistribution has “fatter tails” than predicted by the assumption ofnormality (Campbell, Lo, and MacKinlay [8]).A number of alternative assumptions have been proposedfor stock movements. Alexander [4] summarizes a variety ofsubstitutes, including generalized autoregressive conditional heteroskedasticity(GARCH) processes and principal componentanalysis. Hardy [22] uses a regime-switching model for stock returnsand concludes that the performance of the regime-switchingmodel is favorable relative to competing models. To understandthe rationale for Hardy’s model, consider the severe decline of