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