Let the Geometric Brownian motion be:

âˆ†S/S=Âµâˆ†t + ÏƒÏµsqrt(âˆ†t)

âˆ†S = change in stock price (s)

Âµ = expected rate of return

Ïƒ = volatility of shock

Ïµ has standard normal N(0,1) distribution

ÏƒÏµsqrt(âˆ†t) = stochastic companion

i) Derive the Ito process with a drift for the above

ii) Given that the option price at time t is f(s,t), derive the process with Ito's lemma. Give an example.