simplified Libor in arrears payoff: pay at time 1 1-year Libor reset at time 1 F(1)
where is measure with numeraire
change measure from time 0 to time 1 (time while F(t) is changing)
with girsanov formula :
so we get
under F(1) is martingale i.e.
to calculate we must introduce dynamics for F(1)
for example black-scholes where under :
so and therefore
for CMS convexity adjustment use linear model i.e.