Assume that the financial variable $x$ follows the process:

$\frac{d{x}_t}{x_t}=dt+d{W}_t$

where $W$ is a Wiener process.

a$)$ Using Ito's Lemma, find the process followed by variable $y_t$ defined as follows:

$y_t=ln(x_t)$

Compare it with the process defined in $(1)$ and comment on your results.

$[3$ Marks$]$

Suppose that the price of a stock follows a geometric Brownian motion, and the price is initially $S_0=1.$ The rate of return is $3\%$ per month and the variance rate is $9\%$