... , 2 T T + B T Z1 b2 = p1 T + b expf,b , 2 T g exp , 2T db 2 T ,1 Z T + b exp , b + T 2 db =p 2T 2 T ,1 2 Z1 y exp , y2 dy (Substitute y = T + b) y = T + b = p 2 T ... we use the Girsanov Theorem to change the probability measure, means change but variances not Martingales may be destroyed or created Volatilities, quadratic variations and cross variations are ... because Z t; t T , is a martingale under IP 1 92 Lemma 1.54 (Baye s Rule) If X is F t-measurable and s t T , then f IE X jF s = Z s IE XZ tjF s : Proof: It is clear that Z 1s ...