Risk management under a two-factor model of the term structure of interest rates

This paper presents several applications to interest rate risk management based on a two-factor continuous-time model of the term structure of interest rates previously presented in Moreno (1996). This model assumes that default free discount bond prices are determined by the time to maturity and two factors, the long-term interest rate and the spread (difference between the long-term rate and the short-term (instantaneous) riskless rate). Several new measures of ``generalized duration" are presented and applied in different situations in order to manage market risk and yield curve risk. By means of these measures, we are able to compute the hedging ratios that allows us to immunize a bond portfolio by means of options on bonds. Focusing on the hedging problem, it is shown that these new measures allow us to immunize a bond portfolio against changes (parallel and/or in the slope) in the yield curve. Finally, a proposal of solution of the limitations of conventional duration by means of these new measures is presented and illustrated numerically.