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

186 MODELING FINANCIAL SCENARIOSthat equilibrium models are judged to be inferior since traderswill have little confidence in the price of an option if the modelcannot accurately price the underlying asset. Research supportsthis argument. Jegadeesh [31] looks at the pricing ofinterest rate caps and determines that arbitrage-free modelsprice interest rate caps more accurately than equilibrium models.Unfortunately, the pricing accuracy of arbitrage-free termstructure models is based on short pricing horizons; there havebeen no formal comparative tests of the pricing accuracy usinglong-term assets.² Fitton and McNatt [21] comment that arbitrage-free models aremost useful for short-term pricing applications when similarmarket data are readily available. Arbitrage-free models areintractable over long periods of time. With many arbitragefreemodels, the forward rate plays a central role in the expectedpath of interest rates. Forward rates are related to theslope of the term structure and may exhibit strange behaviorthat significantly impacts projections of interest rate paths inarbitrage-free term structure models. For steeply sloped yieldcurves, the forward rate may become very large. For parts ofthe term structure that are downward sloping, the forward ratemay even become negative. Especially for long-term projections,simulation paths may become extreme since the effectsof small fluctuations in the term structure are magnified inlong-term forward rates. For long-term analysis, equilibriummodels are more appropriate.² Arbitrage-free models also suffer from inconsistency acrosstime (see Wilmott [46] and Tuckman [42]). As mentionedabove, many arbitrage-free term structure models assume thatthe risk-free rate is closely related to the forward rate curve.The forward curve is often quite dissimilar at different pointsin time. For example, at time 0, the model uses the existingterm structure to determine forward rates for years into thefuture. If the model were correct, we should be able to restartthe simulation at some subsequent time t using the forward