This paper presents a consistent and arbitrage-free multifactor model of the term structure of interest rates, where yields at selected fixed maturities follow a parametric multivariate Markov diffusion process with stochastic volatility. The yield of any zero-coupon bond is an affine combination of a selected set of yields. The model includes numerical techniques for solving the model and calculating the prices of term-structure derivatives. The case of jump diffusions is also considered. The model is "affine" in that for each maturity, there is an affine function relating the yield to the state variables. The model is shown to be equivalent to the Heath, Jarrow, and Morton (HJM) model. The paper discusses the conditions for existence and uniqueness of solutions to the associated stochastic differential equation. It also presents examples of constant and stochastic volatility versions of the yield-factor model, and provides a finite-difference algorithm for solving the PDE for derivative prices. The paper also discusses the conditions for the existence of a unique solution to the stochastic differential equation, and presents an example of a two-factor stochastic volatility model. The paper concludes with an example of a deterministic volatility bond option pricing model, where the short rate process is a component of a multivariate Gaussian process. The paper shows that the model can be used to price bond options and other derivatives, and that the model is computationally tractable and consistent with the absence of arbitrage.This paper presents a consistent and arbitrage-free multifactor model of the term structure of interest rates, where yields at selected fixed maturities follow a parametric multivariate Markov diffusion process with stochastic volatility. The yield of any zero-coupon bond is an affine combination of a selected set of yields. The model includes numerical techniques for solving the model and calculating the prices of term-structure derivatives. The case of jump diffusions is also considered. The model is "affine" in that for each maturity, there is an affine function relating the yield to the state variables. The model is shown to be equivalent to the Heath, Jarrow, and Morton (HJM) model. The paper discusses the conditions for existence and uniqueness of solutions to the associated stochastic differential equation. It also presents examples of constant and stochastic volatility versions of the yield-factor model, and provides a finite-difference algorithm for solving the PDE for derivative prices. The paper also discusses the conditions for the existence of a unique solution to the stochastic differential equation, and presents an example of a two-factor stochastic volatility model. The paper concludes with an example of a deterministic volatility bond option pricing model, where the short rate process is a component of a multivariate Gaussian process. The paper shows that the model can be used to price bond options and other derivatives, and that the model is computationally tractable and consistent with the absence of arbitrage.