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

MODELING FINANCIAL SCENARIOS 189stochastic factor is to allow movements at opposite ends of theyield curve. Any correlation between short and long rates is accountedfor in the correlation of the Brownian motion componentsof Formula (2.8).Summary of Term Structure IssuesThe final choice of term structure model is a decision thatfrequently elicits passionate debate. Decisions are needed to selectamong the various kinds of assumptions including matchingthe existing term structure (equilibrium vs. arbitrage-free model),the number of parameters employed, and so on. In making thesedecisions, it is vital to bear in mind the application of the model.The choice of a term structure model is likely to be differentfor short-term applications that require precision and comparabilityto traded securities than for long-term strategic planningexercises.Forthisresearch,itisnot intended that our model will beused for trading purposes. Rather, it is meant to give insurersa range of potential interest rate scenarios that are possible inthe future. In selecting a term structure model for the financialscenario generator, we attempted to balance three important (andoften opposing) goals: (1) mimicking the key historical characteristicsof term structure movements, (2) generating the entireterm structure for any future projection date, and (3) recognizingthe desire for parsimony.The first concern led us to a multifactor model that allowsfor some flexibility in yield curve shapes. While single-factormodels are often easier to describe and use, their restricted yielddynamics are too important for insurers to ignore. The secondissue highlights the importance of interest rates of all time horizons,not of any specific key rates on the curve. Based on therealizations of the limited number of stochastic factors, we preferredterm structure models that have closed-form solutions forbond prices so that the entire term structure can be quickly andeasily retrieved. When closed-form solutions for bond yields are