Jun 20, 2011 at 10:02 AM
Edited Jun 20, 2011 at 10:18 AM

Hello,
I use Math.NET numerics in order to implement a Monte Carlo simulations pricer. I currently use the MersenneTwister random number source/implementation and I noticed my MC starts to diverge as I generate more that 5 millions simulations.
Is the MersenneTwister the best implementation? Can anyone please advise?
Thanks in advance,
J.
P.S. Here is my code:
using System;
using System.Threading.Tasks;
using MathNet.Numerics.Distributions;
using MathNet.Numerics.Random;
namespace MonteCarlo
{
class VanillaEuropeanCallMonteCarlo
{
static void Main(string[] args)
{
const int NUM_SIMULATIONS = 10000000;
const decimal strike = 50m;
const decimal initialStockPrice = 52m;
const decimal volatility = 0.2m;
const decimal riskFreeRate = 0.05m;
const decimal maturity = 0.5m;
Normal n = new Normal();
n.RandomSource = new MersenneTwister();
VanillaEuropeanCallMonteCarlo vanillaCallMonteCarlo = new VanillaEuropeanCallMonteCarlo();
Task<decimal>[] simulations = new Task<decimal>[NUM_SIMULATIONS];
for (int i = 0; i < simulations.Length; i++)
{
simulations[i] = new Task<decimal>(() => vanillaCallMonteCarlo.RunMonteCarloSimulation(strike, initialStockPrice, volatility, riskFreeRate, maturity, n));
simulations[i].Start();
}
Task.WaitAll(simulations);
decimal total = 0m;
for (int i = 0; i < simulations.Length; i++)
{
total += simulations[i].Result;
}
decimal callPrice = (decimal)(Math.Exp((double)(riskFreeRate * maturity)) * (double)total / (NUM_SIMULATIONS * 2));
Console.WriteLine("Call Price: " + callPrice);
Console.WriteLine("Difference: " + Math.Abs(callPrice  4.744741008m));
}
decimal RunMonteCarloSimulation(decimal strike, decimal initialStockPrice, decimal volatility, decimal riskFreeRate, decimal maturity, Normal n)
{
decimal randGaussian = (decimal)n.Sample();
decimal endStockPriceA = initialStockPrice * (decimal)Math.Exp((double)((riskFreeRate  (decimal)(0.5 * Math.Pow((double)volatility, 2))) * maturity + volatility * (decimal)Math.Sqrt((double)maturity) * randGaussian));
decimal endStockPriceB = initialStockPrice * (decimal)Math.Exp((double)((riskFreeRate  (decimal)(0.5 * Math.Pow((double)volatility, 2))) * maturity + volatility * (decimal)Math.Sqrt((double)maturity) * (randGaussian)));
decimal sumPayoffs = (decimal)(Math.Max(0, endStockPriceA  strike) + Math.Max(0, endStockPriceB  strike));
return sumPayoffs;
}
}
}



Hi,
I'm not sure about the Monte Carlo simulation code itself but as far as using the RNG goes: all RNG's carry a bit of state so when you use them in a parallel context (using Tasks), you have to be careful about locking the RNG. We provider a setting called
MathNet.Numerics.Control.ThreadSafeRandomNumberGenerators which if you set to true will make sure that there are no race issues. I'd try that out first ...
Cheers, Jurgen



Hello Jurgen,
Thanks for your reply. I am new to .NET and I use VisualC# express. Can you please let me know where I need to specify this setting?
Thanks in advance,
J.



As the first line in your program, write
MathNet.Numerics.Control.ThreadSafeRandomNumberGenerators = true;



Thanks!

