Consider a second risky non-dividend-paying asset with price Z. Assume dZ Z = z dt + z

Consider a second risky non-dividend-paying asset with price Z. Assume dZ Z = μz dt + σz dBz , where Bz is a Brownian motion under the physical probability. Let ρ denote the correlation process of Bz and B.

(a) Define ξt = MtSt = Et[MTST]. Show that dξ

ξ = r dt + σ dB+

dM M .

(b) Prove that

(dBz)

dξ

ξ



=



ρσ − μz − r

σz



dt .

(c) Use Girsanov’s theorem to show that dZ Z = (r + ρσσz)dt + σz dB∗

z , where B∗

z is a Brownian motion under probS

.