The uncertainty attached to the future movements of interest rates is an important part of the theory of financial decision making. Most investors are risk averse and risk is linked in particular to interest rates. It is thus important to understand the factors that drive interest rates and the models associated with it. The issue of pricing interest rate derivatives
has been addressed by the financial literature in a number of different ways.
One of the oldest approaches is based on modelling the evaluation of the instantaneous short interest rate. This is still quite popular for pricing interest rate derivatives and for risk management purposes, and represents the most commonly used type of dynamical stochastic model for interest rates. More over, in literature there are many models on the instantaneous short interest rate, but despite bewildering number of models, little is known about how these models compare in terms of their ability to capture the actual behavior of the short rate. Therefore, one of the aim of this study is to give information about these models and allow readers to compare them. We can separate these models into two category, which are Equilibrium models and No-arbitrage models. Vasicek (1977), Dothan (1978), Courtadon (1982), CIR (1985), Ho-Lee (1986), Black-Karasinski (1991), Hull-White (Extended Vasicek) (1993), Hull-White (Extended CIR)(1993), Ait-Sahalia (1996), Mercurio- Moraleda (2000), etc., is a list of one-factor short rate models investigated in the thesis.

Many books contain analytic solutions to some of these models, though no specific book contains all solutions. In the work, we united various solutions and, in addition we derived the analytic expression of the Courtadon Model. We solve these models analytically by using stochastic differential methods. For further reading about mathematical methods, Kloedan-Platen (1992) is recommended. Then, we deal with parameter estimation of some of these models using Turkey’s treasury zero coupon bond data. For estimating parameters we use different kinds of discretization methods and compare the results. Moreover, by this work we cope with the missing data problem. Indeed, we can observe the limited number of price of bonds which have different time to maturity since the Turkey’s finance market is not deep. But, in parameter estimation we need the time series for the one day interest rate and so we develop a methodology for forming the time series data.