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June 15th, 2019, 10:47 PM   #1
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Deriving Ito process with a drift from geometric Brownian motion.

Please help me solve this question. Thank you.
Let the Geometric Brownian motion be:

∆S/S=µ∆t + σϵsqrt(∆t)

∆S = change in stock price (s)
µ = expected rate of return
σ = volatility of shock
ϵ has standard normal N(0,1) distribution
σϵsqrt(∆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.
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