Stochastic Duration and Fast Coupon Bond Option Pricing in Multi-Factor Models

Abstract

This paper generalizes the stochastic duration concept of Cox, Ingersoll, and Ross (1979) to multi-factor diffusion models of the term structure of interest rates. The stochastic duration has time as its unit and measures the sensitivity of the price of a bond (or portfolio of bonds) with respect to any change of the term structure consistent with the model. Some important general properties of the stochastic duration measure are given. For example, it is proven that, under conditions satisfied by most popular term structure models, the familiar Fisher-Weil duration overestimates the interest rate risk of coupon bonds. The stochastic duration is studied in detail in various well-known models. It is also shown that the price of a European option on a coupon bond can be approximated very accurately by a multiple of the price of a European option on a zero-coupon bond with a time to maturity equal to the stochastic duration of the coupon bond. This provides a fast method for pricing European swaptions in multi-factor models.