Volatility Models of the Yield Curve

Models of forward interest rates often use high-dimensional Brownian motions to capture imperfect correlations between near term and long term rates. Several statistical analyses suggest the practicality of using a simpler model. Principal component analyses reveal a pattern of correlations which can be essentially explained with a properly chosen three-dimensional Brownian motion.We describe the well known mathematical difficulties in implementing this approach, and we provide a substantial resolution of these obstacles. By focusing on no-arbitrage models using a long bond as a numeraire, we avoid problems with infinities which appeared in conventional risk-neutral models