Stochastic Models for Interest Rates

We show how a term structure reflected in published bond prices may be used to calibrate the annualised risk-free rate of interest for a Black-Scholes asset model. Then we review the theory of risk-neutral pricing of bonds and interest rate derivatives. We study stochastic interest rate models as SDEs, their dynamics, and the implications for bond pricing for each. Finally we demonstrate techniques for exact sampling from the bivariate distribution of the Vasicek model and associated discount factor with application to the valuation of interest rate derivatives, and the use of the forward risk-neutral measure for pricing.