@rawrjustin's bitcoin simulation

final.jl

# some further optimizations

# Parameters
const S0 = 600; # current bitcoin price
const r = 0.02; # risk neutral payoff, assumed 2% for this exercise, in reality probably less.
const sigma = 2; # extremely high sigma due to spike in bitcoin prices late last year
const T = 1.0; # 1 Time cycle
const M = 100; # 100 steps
const dt = T / M # dt

# Simulating I paths with M time steps
function genS_jl_mine(I::Int)
    const a = (r - 0.5 * ^(sigma,2)) * dt
    const b = sigma * sqrt(dt)
    # allocate M by I array in which to store results
    S = Array(Float32, I, M)
    # value at t =1 in each path is 600
    S[:,1] = 600.0
    for i in 1:I
        for t in 2:M
            z = randn()
            S[i,t] = S[i,t-1] * exp(a + b * z)
        end
    end
    return S
end


# run once so we don't measure compilation time
genS_jl(10)

# now measure
@elapsed genS_jl(100_000)
# => 0.312882383

original.jl

#
# Simulating Geometric Brownian Motion with Julia
#

# Parameters
S0 = 600; # current bitcoin price
r = 0.02; # risk neutral payoff, assumed 2% for this exercise, in reality probably less.
sigma = 2; # extremely high sigma due to spike in bitcoin prices late last year
T = 1.0; # 1 Time cycle
M = 100; # 100 steps
dt = T / M # dt

# Simulating I paths with M time steps
function genS_jl(i::Int64)
    S = {}
    for i in 1:i
        path = Float32[]
        for t in 1:(M + 1)
            if t == 1
                push!(path, S0)
            else
                z = randn()
                st = path[t - 1] * exp((r - 0.5 * ^(sigma,2)) * dt + sigma * sqrt(dt) * z)
                push!(path, st)
            end
        end
        push!(S,path)
    end
    return S
end

# run once so we don't measure compilation time
genS_jl(10)

# now measure
@elapsed genS_jl(100_000)
# => 10.584006556

with_consts.jl

# watch what happens when we declare the parameters as const

# Parameters
const S0 = 600; # current bitcoin price
const r = 0.02; # risk neutral payoff, assumed 2% for this exercise, in reality probably less.
const sigma = 2; # extremely high sigma due to spike in bitcoin prices late last year
const T = 1.0; # 1 Time cycle
const M = 100; # 100 steps
const dt = T / M # dt

# Simulating I paths with M time steps
function genS_jl(i::Int64)
    S = {}
    for i in 1:i
        path = Float32[]
        for t in 1:(M + 1)
            if t == 1
                push!(path, S0)
            else
                z = randn()
                st = path[t - 1] * exp((r - 0.5 * ^(sigma,2)) * dt + sigma * sqrt(dt) * z)
                push!(path, st)
            end
        end
        push!(S,path)
    end
    return S
end

# run once so we don't measure compilation time
genS_jl(10)

# now measure
@elapsed genS_jl(100_000)
# => 1.238375246
# 10x speedup! global variables are not optimized, performance gotcha