Tractable forms of the bond pricing equation

A key area of study in the world of financial derivatives is the modelling of the short-term interest rate with a view to finding theoretically fair prices for financial instruments. We consider a second order linear partial differential equation of parabolic type which has the spot-rate (otherwise known as the short-term interest rate) and time as independent variables, and which can be used to model various financial instruments such as fixed-income products. In this thesis we have concentrated on finding analytic solutions to this equation for pricing simple bonds and hence refer to this equation as the Bond Pricing Equation (BPE). The non-constant coefficients of this equation originate from the drift coefficients and variable volatility in the underlying stochastic dynamics for the interest rate, as well as the market price for risk.