Generalized duration measures in a risk immunization setting. Implementation of the Heath–Jarrow–Morton model
The aim of this paper is to set different lower bounds on the change of the expected net cash flow value at time $H>0$ in general term structure models, referring to the studies of Fong and Vasiček (1984), Nawalkha and Chambers (1996), and Balbás and Ibáñez (1998) among others. New immunization strategies are derived with new risk measures: generalized duration and generalized $M$-absolute of Nawalkha and Chambers, and exponential risk measure. Furthermore, examples of specific one-factor HJM models are provided and the problem of immunization is discussed.