ABSTRACT
The previous chapters show that BGM, swaprate models and market models in general are in many ways plays on measures ; just find the right measures to make the variables of interest lognormal! In this chapter we try to capture the essentials of the different measures available. First note from Geman et al [43] that in general measure changes are gov-
erned by:
LEMMA 5.1
If P and Q are equivalent measures induced by the numeraires Mt and Nt respectively, then for 0 < t ≤ T and f (·) measurable FT
EQ {f (T )| Ft} = EP ½
f (T )
¯¯¯¯ Ft ¾ .
