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

question 14

Multiple Choice

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) \(b X _ { t } \left[ \frac { 1 } { 2 } b d t + d W _ { t } \right]\)

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