Duration for bonds with default risk

Does approximating duration estimates by ignoring default risk lead to error in the two major duration applications - measuring interest - rate price elasticity and immunization? We derive a general expression for duration in the presence of default risk based on Jonkhart's term structure model (On the term structure of interest rates and the risk of default, Journal of Banking and Finance 3, 253-262, 1979) extended to encompass risk aversion. The model includes terms for default probabilities and default payoffs in each period as well as for a delay between the occurrence of default and the final default payoff. Our main conclusion is that practical duration applications involving bonds with default risk must employ duration measures adjusted for default risk.