The duration vector: A continuous-time extension to default-free interest rate contingent claims

This paper presents a continuous-time contingent claims framework for the traditional duration vector models of Chambers et al. (Journal of Financial and Quantitative Analysis (March 1988) 89–104), Prisman and Shores (Journal of Banking and Finance 12 (1988) 493–504), and others, by embedding these into the Merton (The Bell Journal of Economics and Management Science 4 (1973) 141–183) stochastic interest rate option pricing model. Using this framework, we analyze the interest rate risk characteristics of bond options and callable bonds. We derive duration measures that are significantly different from the ones reported previously in the literature by Garman (Journal of Financial Economics 14 (1985) 309–315), Jamshidian and Zhu (Advances in Futures and Options Research 3 (1988) 63–95) and others. The upper and lower bounds of the duration vectors of bond options and callable bonds are investigated. An empirical technique based on the implied volatility methodology is suggested for the computation of the duration vectors of bond options and callable bonds.