Divergence issue with my monte carlo pricer...

[[email protected]]

Hello,

I am trying to implement a vanilla European option pricer with Monte Carlo and compare its result to the BS analytical formula's result.

I noticed that as I increase (from 1 million to 10 millions) the number of simulations, the MC result starts to diverge...

Note that I deliberately only use only one variance reduction technique: antithetic variables. I was hoping that by merely increasing the number of simulations, I would manage to increase the precision.

Can anyone please give me clues or pointers as to why my result diverges?

Thanks in advance,

J.

P.S. Included below is the C# code for the pricer:


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 = new Task<decimal>(() => vanillaCallMonteCarlo.RunMonteCarloSimulation(strike, initialStockPrice, volatility, riskFreeRate, maturity, n));
simulations.Start();
}

Task.WaitAll(simulations);

decimal total = 0m;

for (int i = 0; i < simulations.Length; i++)
{
total += simulations.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;
}
}
}