public void CallNaiveImplemXCheck()
{
var maturities = GridUtils.RegularGrid(0.1, 5.0, 100);
var vols = GridUtils.RegularGrid(0.001, 0.015, 10);
var volMoneynesses = GridUtils.RegularGrid(-3, 3, 100);
foreach (var mat in maturities)
{
foreach (var vol in vols)
{
var sigma = Math.Sqrt(mat) * vol;
foreach (var vm in volMoneynesses)
{
var strike = vm * sigma;
var call = BachelierOption.Price(0.0, strike, vol, mat, 1);
//Naive implementation of bachelier formulae
var d = strike / sigma;
var call_xcheck = -strike *NormalDistribution.Cumulative(-d) + sigma * NormalDistribution.Density(d);
if (DoubleUtils.EqualZero(call))
{
Assert.IsTrue(DoubleUtils.EqualZero(call_xcheck));
}
else
{
var errRelative = (call - call_xcheck) / call_xcheck;
Assert.IsTrue(Math.Abs(errRelative) < 1.0e-13);
}
}
}
}
}
public void TestCallBachelier(int dim, SobolDirection direction)
{
var gaussianGen = RandomGenerators.GaussianSobol(direction).Build(dim);
var chrono = new Stopwatch();
chrono.Start();
var atmCalls = new double[dim];
var strikeCall1 = new double[dim];
var strikeCall2 = new double[dim];
var strikePut1 = new double[dim];
var strikePut2 = new double[dim];
const int nbPaths = 1000000;
for (int index = 0; index < nbPaths; index++)
{
var sample = gaussianGen.Next();
for (int i = 0; i < dim; i++)
{
var gaussian = sample[i];
atmCalls[i] += Math.Max(0.0, gaussian);
strikeCall1[i] += Math.Max(0.0, gaussian - 1.0);
strikeCall2[i] += Math.Max(0.0, gaussian - 2.0);
strikePut1[i] += Math.Max(0.0, -1.0 - gaussian);
strikePut2[i] += Math.Max(0.0, -2.0 - gaussian);
}
}
for (int i = 0; i < dim; i++)
{
atmCalls[i] /= nbPaths;
strikeCall1[i] /= nbPaths;
strikeCall2[i] /= nbPaths;
strikePut1[i] /= nbPaths;
strikePut2[i] /= nbPaths;
}
chrono.Stop();
Console.WriteLine("Elapsed " + chrono.Elapsed);
var refAtmCalls = atmCalls.Select(c => BachelierOption.Price(0.0, 0.0, 1.0, 1.0, 1)).ToArray();
var refStrikeCall1 = atmCalls.Select(c => BachelierOption.Price(0.0, 1.0, 1.0, 1.0, 1)).ToArray();
var refStrikeCall2 = atmCalls.Select(c => BachelierOption.Price(0.0, 2.0, 1.0, 1.0, 1)).ToArray();
var refStrikePut1 = atmCalls.Select(c => BachelierOption.Price(0.0, -1.0, 1.0, 1.0, -1)).ToArray();
var refStrikePut2 = atmCalls.Select(c => BachelierOption.Price(0.0, -2.0, 1.0, 1.0, -1)).ToArray();
UnitTestUtils.EqualDoubleArray(atmCalls, refAtmCalls, 2.0e-5, true);
UnitTestUtils.EqualDoubleArray(strikeCall1, refStrikeCall1, 8.0e-5, true);
UnitTestUtils.EqualDoubleArray(strikeCall2, refStrikeCall2, 6.0e-4, true);
UnitTestUtils.EqualDoubleArray(strikePut1, refStrikePut1, 8.0e-5, true);
UnitTestUtils.EqualDoubleArray(strikePut2, refStrikePut2, 6.0e-4, true);
}
public void ImpliedVol_HighRegion_Test()
{
const double mat = 0.5;
const double vol = 0.070;
var moneynesses = GridUtils.RegularGrid(5.5, 15.0, 10000);
foreach (double m in moneynesses)
{
var strike = m * vol * Math.Sqrt(mat);
var option = BachelierOption.Price(0.0, strike, vol, mat, m > 0 ? 1 : -1);
var impliedVol = BachelierOption.ImpliedVol(option, 0.0, strike, mat, m > 0 ? 1 : -1);
var errRelative = (impliedVol - vol) / vol;
Assert.IsTrue(Math.Abs(errRelative) < 5.5e-11);
}
}
