This thesis provides a deep overview of a research conducted on short rate interest models and asset pricing methods to help in pricing bonds and related assets. We shall consider a continuous market setup and by use of available data in the market, we shall test the functionality of Vasicek Model of interest rate models for various interesting properties. We shall use Monte Carlo simulation to make some predictions and conclusions. The main result expected is the term structure or the yield curve of the interest rates and a fair price of a given bond considered in any bond market. We shall investigate bond option pricing as well.