If a variable x follows the process dx = b dz where dz is a Wiener process, which of the following is the process followed by y = exp(x)
A. dy = by dz
B. dy = 0.5b2y dt+by dz
C. dy = (y+0.5b2y) dt+by dz
D. dy = 0.5b2y dt+b dz
B
Ito's lemma shows that the process followed by y is dy = 0.5b2exp(x) dt +bexp(x) dz. Substituting y = exp(x) we get the answer in B.
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