Convexity Analysis of Option Embedded Bonds

Abstract

Interest rate risk hedge strategies usually assume that term structure of interest rates in moving under a specific way. If a real term structure is moving differently from the assumed term structure movement, the interest rate risk hedge strategies assuming the special term structure movement may incur unexpected large loss for a bond portfolio manager. Hence an interest rate risk hedge strategy which could be effective under various types of term structure movements has been strongly needed by bond portfolio managers. Duration vector strategies have been developed to satisfy this practical need. To allow various types of term structure movements, duration vector strategies assume multi-factor models for the term structure movement. When a duration vector strategy is considered as a generalization of a duration strategy which is a single factor model for the term structure movement, there will be a generalized concept which measures convexity of a bond under the duration vector model. This study identifies the convexity property of an option embedded bond portfolio under ‘key rate duration model‘ which is a kind of duration vector model suggested by Ho (1992).