A New Stochastic Duration Measure by the Vasicek and Cir Term Structure Theories
City University of Hong Kong Working Paper No. 89
Posted: 13 Nov 1996
Date Written: May 1996
Ingersoll, Skelton and Weil (1978) and Cox, Ingersoll and Ross (1979) put forward a stochastic duration measure (ISW/CIR's duration) that is theoretically much sounder than Macaulay's duration. However, empirical tests on immunization performance, so far, have not been able to show its superiority at all. ISW/CIR's duration measure takes the change in the single underlying instantaneous interest rate as the risk factor of interest rates, but it seems to understate price sensitivities of long (coupon) bonds relative to short bonds. This paper proposes a new bond price sensitivity measure that accommodates the change in a bond-specific zero-curve yield as a risk factor. Like ISW/CIR's duration, the new measure is derived from the (one-factor) Vasicek and CIR term structure theories and can preserve the theoretical and empirical tractability of the term structure models. We prove that the new approach magnifies, more for long bonds than for short bonds, ISW/CIR's duration measure. The empirical tests using the Belgian Government bond data show that the immunization performance of the new stochastic duration measure improves dramatically and is better than that of Macaulay's duration.
JEL Classification: H63, G12
Suggested Citation: Suggested Citation