I would like to ask a question related to Geometric Brownian Motion again. Thanks in advance.
Question:
Suppose that $S(t)$ follows a geometric Brownian Process:
dS(t) = μS(t)dt + σS(t)dW(t)
What is the process ( that is, $dY(t)$) followed by $$Y(t) = \frac{e^{r(T-t)}}{S(t)}$$
Hint
You will need Ito's Lemma:
$$dY=\left(Y_{t}+\mu S Y_{S}+\frac{1}{2} \sigma^2 S^2Y_{SS} \right)dt+(\sigma SY_{S})dW$$
You just have to calculate the derivatives: $Y_{t}, Y_{S}, Y_{SS}$.
Can you finish?