Given That $d Y _ { t } = b d W _ { t }$

Given that $d Y _ { t } = b d W _ { t }$ and $X _ { t } = \ln \left( Y _ { t } \right)$ ,what is $d X _ { t }$ ?

A) $X _ { t } e ^ { b ^ { 2 } dt + Y _ { t } d W _ { t } }$
B) $\ln \left( X _ { t } \right) \left[ \frac { 1 } { 2 } b ^ { 2 } d t + b d W _ { t } \right]$
C) $- \frac { 1 } { 2 } b ^ { 2 } e ^ { 2 X _ { t } } d t + b e ^ { - x _ { t } } d W _ { t }$
)
D) $b X _ { t } \left[ \frac { 1 } { 2 } b d t + d W _ { t } \right]$

Correct Answer:

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