Faster geometric brownian motion

gbm.jl

function genS_jl(I)
    s0 = 600.0
    r = 0.02
    sigma = 2.0
    T = 1.0
    M = 100
    dt = T/M
    a = (r - 0.5*sigma^2)*dt
    b = sigma*sqrt(dt)

    paths = zeros(Float64, M, I)

    for i in 1:I
        paths[1, i] = st = s0
        for j in 2:M
            st *= exp(a + b*randn())
            paths[j, i] = st
        end
    end
    return paths
end

genS_jl(10) # Warm up JIT

@elapsed genS_jl(100000) # Outputs 0.538962298