Same question as in Problem 3 but assume prices follow GBM with the same parameters. Compare the less than 10 values.

Data from in problem 3

(a) Suppose Brownian motion is used to model stock prices (instead of geometric Brownian motion). If S₀ = 10, μ = 0 per year, volatility = 1 per square root year, and T = 1/12 years (about 30 days), what is the probability a stock’s price S_T will be less than 0? less than 1? less than 9? less than 10? 

(b) What is the probability the price went below 0 at some time before t = T and ended above 0? Estimate this by simulation using several difference choices for Δt.