Options (Finance)

The purpose of this thesis is to compare the effectiveness of several interest
rate models in fitting the true value of interest rates. Up until 1990, the universally
accepted models were the equilibrium models, namely the Rendleman-Bartter model,
the Vasicek model, and the Cox-Ingersoll-Ross (CIR) model. While these models
were probably considered relatively accurate around the time of their discovery, they
do not provide a good fit to the initial term structure of interest rates, making them
substandard for use by traders in pricing interest rate options. The fourth model
we consider is the Hull-White one-factor model, which does provide this fit. After
calibrating, simulating, and comparing these four models, we find that the Hull-White
model gives the best fit to our data sets.

Lookback options are path dependent contingent claims whose payoff depend on the extrema of a given security's price over a given period. Some of these options are already traded on specialized markets (such as foreign exchange) and mostly in over-the-counter market alongside with other path dependent options (knock-ins, knock-outs, etc.). This thesis examines the existing pricing models of conventional options as well as standard European lookback options and provides some results about early exercise of their American counterparts with the use of notions from the theory of optimal stopping.