Term structure modeling and the pricing of interest rate derivative securities
This dissertation uses the trinomial lattice modeling approach of Hull and White (1993) to implement several one-factor term structure models which have been proposed in the literature. The objective is to determine which model gives the most accurate prices for interest rate derivative securities; specifically, Eurodollar Futures Options.^ The Hull and White approach is designed to allow the testing of "perfect replication" term structure models. With perfect replication models, the short-term, riskless nominal rate is modeled to match the current term structure and evolve over time in an arbitrage-free manner. There is no attempt to model risk preferences; the use of time-dependent parameters eliminates risk preferences from the prices of bonds and interest-rate derivative securities. This is a significant departure from previous approaches, which took the form of general or partial equilibrium models.^ For the purpose of pricing interest rate derivatives, the perfect replication approach may be preferable because: (a) risk preferences are unobservable and therefore difficult to model and (b) an equilibrium model does not necessarily match the currently observed term structure. In this case, bond and derivative prices would not be discounted correctly, leading to inaccuracies.^ The Hull and White approach enables any equilibrium model to be converted into a perfect replication model with the introduction of time-dependent parameters. In this way, these "extended" models may be tested within a consistent framework. ^
Anderson, Alan, "Term structure modeling and the pricing of interest rate derivative securities" (1995). ETD Collection for Fordham University. AAI9530017.