Extended yield-curve-based interest rate contigent claim pricing models

Arbitrage-based interest rate contingent claim pricing models are constructed upon the assumption that claim prices are functions of a small number of stochastic variables and payoff patterns can be dynamically replicated by trading securities that are sensitive to those variables. A pricing function is derived based on this possibility of replication and a no-arbitrage restriction. The parameters of extended yield-curve-based interest rate pricing models are implied from a set of market observables, e.g., the observed par-yield curve, the term structure of yield volatilities, the term structure of interest rate cap prices, etc;Essay 1 examines the accuracy of interest rate hedges constructed under the prescriptions of the Black/Derman/Toy (BDT) and yield-curve-fitting extensions of the Cox/Ingersoll/Ross (CIR) and Brennan/Schwartz (BS) models. Those models are calibrated to fit an arbitrary set of market observables. We find the 2-factor bond replicating strategies to be more accurate. The one-factor models perform poorly in simultaneously accommodating the movements of the short and long end of the yield curve. Principal components analysis shows that there is still a dominant factor (slope) associated with the hedging errors in the BDT and CIR model. There is no dominant factor in the BS hedging errors.;Essay 2 examines the accuracy of extended yield-curve-based one-factor interest rate models in pricing and hedging various types of interest rate derivatives (interest rate caps, options on zero-coupon bonds, embedded options on coupon bonds and spread options). The one-factor models examined are the extended Cox/Ingersoll/Ross and the Black/Derman/Toy models. The models are calibrated to fit the term structures of interest rates and interest rate cap prices. We find the fitted one-factor models to be reasonably accurate for pricing derivatives except those claims whose values are contingent on differential movements across sectors of the yield curve (e.g., spread options). They are not accurate for hedging, though. This is particularly the case in an interest rate environment driven by two factors where the second factor is relatively important.;Essay 3 presents a two-factor model to price employee stock options. The two factors are the market value of the firm's stock and the short-term interest rate. The explicit modelling of the stochastic evolution of the term structure of interest rates is desirable because of the typical long lives of those options. The model explicitly takes into account the vesting schedule of the option and the probability of the employee leaving the firm before the option expiration. It also considers the fact that, under the current tax legislation, the effective cost of the option to the firm is reduced by the tax savings created by the deduction of its value upon exercise. We let the probability of the employee leaving the firm and the tax rate be functions of both state variables and time allowing the model's user to express his/her views about the future values of those parameters. For example: (1) the probability of the employee leaving might be contingent on the success of the business (as reflected in the market value of the stock) and might also depend on his/her tenure in the firm; (2) the tax rate might be expected to change over time. The model is solved numerically using the hopscotch method and can be readily implemented in a personal computer or workstation. An alternative application of the model to equity-index swaps and swaptions is also discussed in detail.