# Questions tagged [itos-lemma]

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### Integration and expectation of geometric Brownian motion

Let the stock price S follows the geometric brownian motion: $$dS=\mu Sdt+\sigma Sdz$$ $$\frac{dS}S=\mu dt+\sigma dz$$ where $dz$ is a wiener process. Naively integrating the second equation above ...
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### Different Forms of Geometric Brownian Motion [closed]

If the stock price S follows the geometric brownian motion: $$dS=\mu Sdt+\sigma Sdz$$ $$\frac{dS}S=\mu dt+\sigma dz$$ Where $dz=\epsilon\sqrt{dt}$ is a wiener process. Integrating this to get $S_T$ ...
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### Is it possible to approach finding the risk premium of this derivative using Ito's Lemma?

I understand the author's intended solution to the below problem, but I thought I would see if I could solve this using first principles and Ito's Lemma instead for practice. Let \$V(S(t), t) = e^{rt}\...
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### Worked examples of applying Ito's lemma

In most textbooks Ito's lemma is derived (on different levels of technicality depending on the intended audience) and then only the classic examples of Geometric Brownian motion and the Black-Scholes ...