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 expressed as a maturity-dependent affine combination of a set of "basis" yields. The authors provide necessary and sufficient conditions for this affine representation and include numerical techniques for solving the model and calculating term-structure derivative prices. The model includes stochastic volatility factors that are specified as linear combinations of yield factors. Discount bond prices at any maturity are given as solutions to Riccati equations, and path-independent derivative prices can be solved using an alternating-direction implicit finite-difference method. The paper also discusses the case of jump diffusions and provides examples of the model's application.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 expressed as a maturity-dependent affine combination of a set of "basis" yields. The authors provide necessary and sufficient conditions for this affine representation and include numerical techniques for solving the model and calculating term-structure derivative prices. The model includes stochastic volatility factors that are specified as linear combinations of yield factors. Discount bond prices at any maturity are given as solutions to Riccati equations, and path-independent derivative prices can be solved using an alternating-direction implicit finite-difference method. The paper also discusses the case of jump diffusions and provides examples of the model's application.