linguist/samples/Julia/stockcorr.jl

## Test case from Issue #445

#STOCKCORR - The original, unoptimised code that simulates two correlated assets
function stockcorr()

    ## Correlated asset information
    CurrentPrice = [78. 102.]     # Initial Prices of the two stocks
    Corr = [1. 0.4; 0.4 1.]       # Correlation Matrix
    T = 500                       # Number of days to simulate = 2years = 500days
    n = 100000                    # Number of simulations
    dt = 1/250                    # Time step (1year = 250days)
    Div=[0.01 0.01]               # Dividend
    Vol=[0.2 0.3]                 # Volatility

    ## Market Information
    r = 0.03                      # Risk-free rate

    ## Define storages
    SimulPriceA = zeros(T,n)      # Simulated Price of Asset A
    SimulPriceA[1,:] = CurrentPrice[1]
    SimulPriceB = zeros(T,n)      # Simulated Price of Asset B
    SimulPriceB[1,:] = CurrentPrice[2]

    ## Generating the paths of stock prices by Geometric Brownian Motion
    UpperTriangle=chol(Corr)      # UpperTriangle Matrix by Cholesky decomposition

    for i = 1:n
       Wiener = randn(T-1,2)
       CorrWiener = Wiener*UpperTriangle
       for j = 2:T
          SimulPriceA[j,i] = SimulPriceA[j-1,i]*exp((r-Div[1]-Vol[1]^2/2)*dt+Vol[1]*sqrt(dt)*CorrWiener[j-1,1])
          SimulPriceB[j,i] = SimulPriceB[j-1,i]*exp((r-Div[2]-Vol[2]^2/2)*dt+Vol[2]*sqrt(dt)*CorrWiener[j-1,2])
       end
    end

    return (SimulPriceA, SimulPriceB)
end