Duration, factor sensitivities, and interest rate Greeks

Abstract

In this paper, we introduce for interest rate sensitive assets the natural analogs of delta and gamma for equity options by considering the derivatives of asset prices with respect to the directions along which the forward rate curve may evolve. Macaulay duration and convexity, as well as stochastic duration considered in Cox et al. (J Business 52:51–61, 1979) and Munk (Rev Derivat Res 3:157–181, 1999), are easily obtained as special cases of these in which the derivatives are computed along parallel shifts and the direction of the forward rate volatilities, respectively. Moreover, we demonstrate using the example of the Ritchken and Sankarasubramanian (Math Financ 5:55–72, 1995) model that the hedging strategy based on these sensitivity measures provides a superior performance in comparison to the traditional duration based hedging approaches.