Therefore the drift adjustment for forward rate fk+1 is given by

or after using Ito's lemma again, ak+1 ajfJ^+lfjrj

Extending and generalising the reasoning, in Chapter 18 for the drift adjustment to forward f k+s we shall obtain the expression

Vk+s ajPj,k+sfjrJ

The crucial importance of these equations in the context of discrete-time implementations of the HJM and BGM frameworks will be explored later on. Expressions of this type have now been published in several papers (see, e.g., Jamshidian (1996, 1997)), although the derivation follows different lines of argument (and is often considerably more complex). Whilst establishing priority in these matters is always difficult and often futile (since results are often simultaneously obtained by different researchers), to the best knowledge of the writer expression (7.102) had been obtained as far back as 1994 by Mike Sherring.

0 0

Post a comment