public EuropeanPutResult Calculate(double K, double S, double r, double t, double sigma)
{
EuropeanPutResult ePut = new EuropeanPutResult();
ePut.IntegralPointD1 = _integralPoints.CalculateIntegralPointD1(S, K, r, sigma, t);
ePut.IntegralPointD2 = _integralPoints.CalculateIntegralPointD2(ePut.IntegralPointD1, sigma, t);
ePut.Distribution1 = _distribution.CumulativeDistribution(-ePut.IntegralPointD1.Result.Value);
ePut.Distribution2 = _distribution.CumulativeDistribution(-ePut.IntegralPointD2.Result.Value);
ePut.Result.Value = CalculateValue(K, S, r, t, ePut);
return(ePut);
}
public BtResult CalculateBtK1(double r, double sigma, double t, double K, double S, int n, double T)
{
BtResult bt = new BtResult();
bt.IntegralPointD1 = _integralPoints.CalculateIntegralPointD1(K, K, r, sigma, t);
bt.IntegralPointD2 = _integralPoints.CalculateIntegralPointD2(bt.IntegralPointD1, sigma, t);
bt.Distribution = _distribution.CumulativeDistribution(bt.IntegralPointD1.Result.Value);
bt.a = CalculateAValue(sigma, t);
bt.Result.Value = CalculateBtK1(sigma, K, r, t, bt);
return(bt);
}
public async Task <IntegralFunction> CalculateAsync(int n, double T, double r, double sigma, double t, double S, double K, BtResult Btksi)
{
IntegralFunction integralFunction = new IntegralFunction();
UnderIntegral[] underIntegral = new UnderIntegral[n];
for (int i = 0; i < n; i++)
{
UnderIntegral ui = new UnderIntegral();
ui.h = (T / n);
ui.ksi = i * ui.h;
ui.IntegralPointD1 = _integralPoints.CalculateIntegralPointD1(S, Btksi.Result.Value, r, sigma, t - ui.ksi);
ui.IntegralPointD2 = _integralPoints.CalculateIntegralPointD2(ui.IntegralPointD1, sigma, t - ui.ksi);
ui.Distribution = _distribution.CumulativeDistribution(-ui.IntegralPointD2.Result.Value);
ui.Result.Value = CalculateUnderIntegral(r, K, t, ui.ksi, ui.Distribution) * ui.h;
underIntegral[i] = ui;
integralFunction.Result.Value += ui.Result.Value;
}
integralFunction.UnderIntegral = underIntegral;
return(integralFunction);
}
/// <summary>
/// Vapnik Chervonenkis test.
/// </summary>
/// <param name="epsilon">The error we are willing to tolerate.</param>
/// <param name="delta">The error probability we are willing to tolerate.</param>
/// <param name="s">The samples to use for testing.</param>
/// <param name="dist">The distribution we are testing.</param>
public static void VapnikChervonenkisTest(double epsilon, double delta, IEnumerable <double> s, IUnivariateDistribution dist)
{
// Using VC-dimension, we can bound the probability of making an error when estimating empirical probability
// distributions. We are using Theorem 2.41 in "All Of Nonparametric Statistics".
// http://books.google.com/books?id=MRFlzQfRg7UC&lpg=PP1&dq=all%20of%20nonparametric%20statistics&pg=PA22#v=onepage&q=%22shatter%20coe%EF%AC%83cients%20do%20not%22&f=false .</para>
// For intervals on the real line the VC-dimension is 2.
double n = s.Count();
Assert.Greater(n, Math.Ceiling(32.0 * Math.Log(16.0 / delta) / epsilon / epsilon));
var histogram = new Histogram(s, NumberOfBuckets);
for (var i = 0; i < NumberOfBuckets; i++)
{
var p = dist.CumulativeDistribution(histogram[i].UpperBound) - dist.CumulativeDistribution(histogram[i].LowerBound);
var pe = histogram[i].Count / n;
Assert.Less(Math.Abs(p - pe), epsilon, dist.ToString());
}
}
private void Recompute(bool getBetaHatOnly)
{
int p = augmentedExplanatory.ColumnCount;
int n = augmentedExplanatory.RowCount;
Matrix <double> xt = augmentedExplanatory.Clone();
xt.Transpose();
Vector <double> xty = ((xt * dependent.ToColumnMatrix())).ToVector();
Matrix <double> xtx = xt * augmentedExplanatory;
Matrix <double> mxty = Matrix <double> .Build.Dense(xty.Count, 1);
for (int i = 0; i < xty.Count; ++i)
{
mxty[i, 0] = xty[i];
}
BetaHat = Vector <double> .Build.Dense(p);
//if (mxty.Norm2()==0)
if (mxty.L2Norm() == 0)
{
return;
}
Matrix <double> bm = xtx.Solve(mxty);
// .SolveRobust(mxty);
for (int i = 0; i < p; ++i)
{
BetaHat[i] = bm[i, 0];
}
if (getBetaHatOnly)
{
return;
}
var fitted = (augmentedExplanatory * BetaHat.ToColumnMatrix()).ToVector();
var resids = dependent - fitted;
// now compute approximate p-values
Sigma = Math.Sqrt(resids.Variance()) * n / (n - p);
BetaHatCovariance = Sigma * Sigma * xtx.Inverse();
PValues = Vector <double> .Build.Dense(augmentedExplanatory.ColumnCount);
for (int i = 0; i < augmentedExplanatory.ColumnCount; ++i)
{
double x = Math.Abs(BetaHat[i]) / Math.Sqrt(BetaHatCovariance[i, i]);
PValues[i] = 2 * (1 - stdNormal.CumulativeDistribution(x));
}
}
public static double TwoTailProbability(this IUnivariateDistribution nd, double value)
{
var result = nd.CumulativeDistribution(value);
if (result > 0.5)
{
result = 1 - result;
}
result *= 2;
return(result);
}
/// <summary>
/// Vapnik Chervonenkis test.
/// </summary>
/// <param name="epsilon">The error we are willing to tolerate.</param>
/// <param name="delta">The error probability we are willing to tolerate.</param>
/// <param name="s">The samples to use for testing.</param>
/// <param name="dist">The distribution we are testing.</param>
public static void VapnikChervonenkisTest(double epsilon, double delta, IEnumerable<double> s, IUnivariateDistribution dist)
{
// Using VC-dimension, we can bound the probability of making an error when estimating empirical probability
// distributions. We are using Theorem 2.41 in "All Of Nonparametric Statistics".
// http://books.google.com/books?id=MRFlzQfRg7UC&lpg=PP1&dq=all%20of%20nonparametric%20statistics&pg=PA22#v=onepage&q=%22shatter%20coe%EF%AC%83cients%20do%20not%22&f=false .</para>
// For intervals on the real line the VC-dimension is 2.
double n = s.Count();
Assert.Greater(n, Math.Ceiling(32.0 * Math.Log(16.0 / delta) / epsilon / epsilon));
var histogram = new Histogram(s, NumberOfBuckets);
for (var i = 0; i < NumberOfBuckets; i++)
{
var p = dist.CumulativeDistribution(histogram[i].UpperBound) - dist.CumulativeDistribution(histogram[i].LowerBound);
var pe = histogram[i].Count / n;
Assert.Less(Math.Abs(p - pe), epsilon, dist.ToString());
}
}
/// <summary> Provide the cumulative probability that a value will be equal to or lower than that supplied </summary>
public static decimal?CumulativeP(IUnivariateDistribution distribution, decimal?val)
{
return(val == null || distribution == null ? null : sanitiseCumulativeP((decimal?)distribution.CumulativeDistribution((double)val)));
}