public GaussianKernel(double average, double sigma)
{
nd_ = new NormalDistribution(average, sigma);
cnd_ = new CumulativeNormalDistribution(average, sigma);
// normFact is \sqrt{2*\pi}.
normFact_ = Const.M_SQRT2 * Const.M_SQRTPI;
}
/// <summary>
/// Shortfall.
/// </summary>
/// <param name="target"></param>
/// <param name="mean"></param>
/// <param name="std"></param>
/// <returns></returns>
public static double Shortfall(double target, double mean, double std)
{
var gIntegral =
new CumulativeNormalDistribution(mean, std);
return(gIntegral.Value(target));
}
public void SmallSampleCheck()
{
CumulativeNormalDistribution cnd = new CumulativeNormalDistribution();
Assert.AreEqual(0.5, cnd.ValueOf(0.0), 1e-6);
Assert.AreEqual(1.0, cnd.ValueOf(double.PositiveInfinity));
Assert.AreEqual(0.0, cnd.ValueOf(double.NegativeInfinity));
// values obtained with Maple 9.01
Assert.AreEqual(.6914624613, cnd.ValueOf(0.5), 1e-6);
Assert.AreEqual(.3085375387, cnd.ValueOf(-0.5), 1e-6);
Assert.AreEqual(.9331927987, cnd.ValueOf(1.5), 1e-6);
Assert.AreEqual(.06680720127, cnd.ValueOf(-1.5), 1e-6);
cnd = new CumulativeNormalDistribution(1.0, 2.0);
Assert.AreEqual(0.0, cnd.ValueOf(1.0), 0.5);
Assert.AreEqual(1.0, cnd.ValueOf(double.PositiveInfinity));
Assert.AreEqual(0.0, cnd.ValueOf(double.NegativeInfinity));
// values obtained with Maple 9.01
Assert.AreEqual(.4012936743, cnd.ValueOf(0.5), 1e-6);
Assert.AreEqual(.2266273524, cnd.ValueOf(-0.5), 1e-6);
Assert.AreEqual(.5987063257, cnd.ValueOf(1.5), 1e-6);
Assert.AreEqual(.1056497737, cnd.ValueOf(-1.5), 1e-6);
}
/// <summary>
/// Average shortfall.
/// </summary>
/// <param name="target"></param>
/// <param name="mean"></param>
/// <param name="std"></param>
/// <returns></returns>
public static double AverageShortfall(double target, double mean, double std)
{
var gIntegral =
new CumulativeNormalDistribution(mean, std);
var g = new NormalDistribution(mean, std);
return((target - mean) * gIntegral.Value(target) +
std * std * g.Value(target));
}
public static double Greeks([ExcelArgument("Spot Price of Underlying")] double spot, [ExcelArgument("Strike Price")] double strike,
[ExcelArgument("Risk-Free Rate")] double rfr, [ExcelArgument("Annualised Volatility")] double vol, [ExcelArgument("Time to Maturity")] double tenor,
[ExcelArgument("Option Type")] string opt_type, [ExcelArgument("Option Type")] string greeks_type)
{
var d_1 = (Math.Log(spot / strike) + (rfr + Math.Pow(vol, 2) / 2) * (tenor)) / (vol * Math.Sqrt(tenor));
var d_2 = (d_1 - vol * Math.Sqrt(tenor));
var NormINV = new CumulativeNormalDistribution(0, 1);
if (opt_type == "Put")
{
if (greeks_type == "Delta")
{
return(-Math.Pow(Math.E, -rfr * tenor) * NormINV.value(d_1));
}
else if (greeks_type == "Gamma")
{
return((Math.Pow(Math.E, -rfr * tenor) * NormINV.value(d_1)) / spot * vol * Math.Sqrt(tenor));
}
else
{
return(0);
}
}
else if (opt_type == "Call")
{
if (greeks_type == "Delta")
{
return(Math.Pow(Math.E, -rfr * tenor) * NormINV.value(d_1));
}
else if (greeks_type == "Gamma")
{
return((Math.Pow(Math.E, -rfr * tenor) * NormINV.value(d_1)) / spot * vol * Math.Sqrt(tenor));
}
else
{
return(0);
}
}
else
{
return(0);
}
}
public void RiskStatisticsTest()
{
// ("Testing risk measures...");
IncrementalGaussianStatistics igs = new IncrementalGaussianStatistics();
RiskStatistics s = new RiskStatistics();
double[] averages = { -100.0, -1.0, 0.0, 1.0, 100.0 };
double[] sigmas = { 0.1, 1.0, 100.0 };
int i, j, k, N;
N = (int)Math.Pow(2, 16) - 1;
double dataMin, dataMax;
List <double> data = new InitializedList <double>(N), weights = new InitializedList <double>(N);
for (i = 0; i < averages.Length; i++)
{
for (j = 0; j < sigmas.Length; j++)
{
NormalDistribution normal = new NormalDistribution(averages[i], sigmas[j]);
CumulativeNormalDistribution cumulative = new CumulativeNormalDistribution(averages[i], sigmas[j]);
InverseCumulativeNormal inverseCum = new InverseCumulativeNormal(averages[i], sigmas[j]);
SobolRsg rng = new SobolRsg(1);
dataMin = double.MaxValue;
dataMax = double.MinValue;
for (k = 0; k < N; k++)
{
data[k] = inverseCum.value(rng.nextSequence().value[0]);
dataMin = Math.Min(dataMin, data[k]);
dataMax = Math.Max(dataMax, data[k]);
weights[k] = 1.0;
}
igs.addSequence(data, weights);
s.addSequence(data, weights);
// checks
double calculated, expected;
double tolerance;
if (igs.samples() != N)
{
QAssert.Fail("IncrementalGaussianStatistics: "
+ "wrong number of samples\n"
+ " calculated: " + igs.samples() + "\n"
+ " expected: " + N);
}
if (s.samples() != N)
{
QAssert.Fail("RiskStatistics: wrong number of samples\n"
+ " calculated: " + s.samples() + "\n"
+ " expected: " + N);
}
// weightSum()
tolerance = 1e-10;
expected = weights.Sum();
calculated = igs.weightSum();
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("IncrementalGaussianStatistics: "
+ "wrong sum of weights\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.weightSum();
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: wrong sum of weights\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
// min
tolerance = 1e-12;
expected = dataMin;
calculated = igs.min();
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("IncrementalGaussianStatistics: "
+ "wrong minimum value\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.min();
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: "
+ "wrong minimum value\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
// max
expected = dataMax;
calculated = igs.max();
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("IncrementalGaussianStatistics: "
+ "wrong maximum value\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.max();
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: "
+ "wrong maximum value\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
// mean
expected = averages[i];
tolerance = (expected == 0.0 ? 1.0e-13 :
Math.Abs(expected) * 1.0e-13);
calculated = igs.mean();
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("IncrementalGaussianStatistics: "
+ "wrong mean value"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.mean();
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: wrong mean value"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
// variance
expected = sigmas[j] * sigmas[j];
tolerance = expected * 1.0e-1;
calculated = igs.variance();
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("IncrementalGaussianStatistics: "
+ "wrong variance"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.variance();
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: wrong variance"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
// standardDeviation
expected = sigmas[j];
tolerance = expected * 1.0e-1;
calculated = igs.standardDeviation();
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("IncrementalGaussianStatistics: "
+ "wrong standard deviation"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.standardDeviation();
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: wrong standard deviation"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
// missing errorEstimate() test
// skewness
expected = 0.0;
tolerance = 1.0e-4;
calculated = igs.skewness();
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("IncrementalGaussianStatistics: "
+ "wrong skewness"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.skewness();
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: wrong skewness"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
// kurtosis
expected = 0.0;
tolerance = 1.0e-1;
calculated = igs.kurtosis();
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("IncrementalGaussianStatistics: "
+ "wrong kurtosis"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.kurtosis();
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: wrong kurtosis"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
// percentile
expected = averages[i];
tolerance = (expected == 0.0 ? 1.0e-3 :
Math.Abs(expected * 1.0e-3));
calculated = igs.gaussianPercentile(0.5);
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("IncrementalGaussianStatistics: "
+ "wrong Gaussian percentile"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.gaussianPercentile(0.5);
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: wrong Gaussian percentile"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.percentile(0.5);
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: wrong percentile"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
// potential upside
double upper_tail = averages[i] + 2.0 * sigmas[j],
lower_tail = averages[i] - 2.0 * sigmas[j];
double twoSigma = cumulative.value(upper_tail);
expected = Math.Max(upper_tail, 0.0);
tolerance = (expected == 0.0 ? 1.0e-3 :
Math.Abs(expected * 1.0e-3));
calculated = igs.gaussianPotentialUpside(twoSigma);
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("IncrementalGaussianStatistics: "
+ "wrong Gaussian potential upside"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.gaussianPotentialUpside(twoSigma);
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: wrong Gaussian potential upside"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.potentialUpside(twoSigma);
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: wrong potential upside"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
// just to check that GaussianStatistics<StatsHolder> does work
StatsHolder h = new StatsHolder(s.mean(), s.standardDeviation());
GenericGaussianStatistics <StatsHolder> test = new GenericGaussianStatistics <StatsHolder>(h);
expected = s.gaussianPotentialUpside(twoSigma);
calculated = test.gaussianPotentialUpside(twoSigma);
if (calculated != expected)
{
QAssert.Fail("GenericGaussianStatistics<StatsHolder> fails"
+ "\n calculated: " + calculated
+ "\n expected: " + expected);
}
// value-at-risk
expected = -Math.Min(lower_tail, 0.0);
tolerance = (expected == 0.0 ? 1.0e-3 :
Math.Abs(expected * 1.0e-3));
calculated = igs.gaussianValueAtRisk(twoSigma);
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("IncrementalGaussianStatistics: "
+ "wrong Gaussian value-at-risk"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.gaussianValueAtRisk(twoSigma);
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: wrong Gaussian value-at-risk"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.valueAtRisk(twoSigma);
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: wrong value-at-risk"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
if (averages[i] > 0.0 && sigmas[j] < averages[i])
{
// no data will miss the targets:
// skip the rest of this iteration
igs.reset();
s.reset();
continue;
}
// expected shortfall
expected = -Math.Min(averages[i]
- sigmas[j] * sigmas[j]
* normal.value(lower_tail) / (1.0 - twoSigma),
0.0);
tolerance = (expected == 0.0 ? 1.0e-4
: Math.Abs(expected) * 1.0e-2);
calculated = igs.gaussianExpectedShortfall(twoSigma);
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("IncrementalGaussianStatistics: "
+ "wrong Gaussian expected shortfall"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.gaussianExpectedShortfall(twoSigma);
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: wrong Gaussian expected shortfall"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.expectedShortfall(twoSigma);
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: wrong expected shortfall"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
// shortfall
expected = 0.5;
tolerance = (expected == 0.0 ? 1.0e-3 :
Math.Abs(expected * 1.0e-3));
calculated = igs.gaussianShortfall(averages[i]);
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("IncrementalGaussianStatistics: "
+ "wrong Gaussian shortfall"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.gaussianShortfall(averages[i]);
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: wrong Gaussian shortfall"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.shortfall(averages[i]);
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: wrong shortfall"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
// average shortfall
expected = sigmas[j] / Math.Sqrt(2.0 * Const.M_PI) * 2.0;
tolerance = expected * 1.0e-3;
calculated = igs.gaussianAverageShortfall(averages[i]);
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("IncrementalGaussianStatistics: "
+ "wrong Gaussian average shortfall"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.gaussianAverageShortfall(averages[i]);
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: wrong Gaussian average shortfall"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.averageShortfall(averages[i]);
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: wrong average shortfall"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
// regret
expected = sigmas[j] * sigmas[j];
tolerance = expected * 1.0e-1;
calculated = igs.gaussianRegret(averages[i]);
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("IncrementalGaussianStatistics: "
+ "wrong Gaussian regret(" + averages[i] + ") "
+ "for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.gaussianRegret(averages[i]);
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: "
+ "wrong Gaussian regret(" + averages[i] + ") "
+ "for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.regret(averages[i]);
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: "
+ "wrong regret(" + averages[i] + ") "
+ "for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
// downsideVariance
expected = s.downsideVariance();
tolerance = (expected == 0.0 ? 1.0e-3 :
Math.Abs(expected * 1.0e-3));
calculated = igs.downsideVariance();
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("IncrementalGaussianStatistics: "
+ "wrong downside variance"
+ "for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = igs.gaussianDownsideVariance();
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("IncrementalGaussianStatistics: "
+ "wrong Gaussian downside variance"
+ "for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
// downsideVariance
if (averages[i] == 0.0)
{
expected = sigmas[j] * sigmas[j];
tolerance = expected * 1.0e-3;
calculated = igs.downsideVariance();
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("IncrementalGaussianStatistics: "
+ "wrong downside variance"
+ "for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = igs.gaussianDownsideVariance();
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("IncrementalGaussianStatistics: "
+ "wrong Gaussian downside variance"
+ "for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.downsideVariance();
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: wrong downside variance"
+ "for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.gaussianDownsideVariance();
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: wrong Gaussian downside variance"
+ "for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
}
igs.reset();
s.reset();
}
}
}
internal static global::System.Runtime.InteropServices.HandleRef getCPtr(CumulativeNormalDistribution obj)
{
return((obj == null) ? new global::System.Runtime.InteropServices.HandleRef(null, global::System.IntPtr.Zero) : obj.swigCPtr);
}
public void testOperatorConsistency()
{
//("Testing differential operators...");
NormalDistribution normal = new NormalDistribution(average, sigma);
CumulativeNormalDistribution cum = new CumulativeNormalDistribution(average, sigma);
double xMin = average - 4 * sigma,
xMax = average + 4 * sigma;
int N = 10001;
double h = (xMax - xMin) / (N - 1);
Vector x = new Vector(N),
y = new Vector(N),
yi = new Vector(N),
yd = new Vector(N),
temp = new Vector(N),
diff = new Vector(N);
for (int i = 0; i < N; i++)
{
x[i] = xMin + h * i;
}
for (int i = 0; i < x.Count; i++)
{
y[i] = normal.value(x[i]);
}
for (int i = 0; i < x.Count; i++)
{
yi[i] = cum.value(x[i]);
}
for (int i = 0; i < x.size(); i++)
{
yd[i] = normal.derivative(x[i]);
}
// define the differential operators
DZero D = new DZero(N, h);
DPlusDMinus D2 = new DPlusDMinus(N, h);
// check that the derivative of cum is Gaussian
temp = D.applyTo(yi);
for (int i = 0; i < y.Count; i++)
{
diff[i] = y[i] - temp[i];
}
double e = Utilities.norm(diff, diff.size(), h);
if (e > 1.0e-6)
{
Assert.Fail("norm of 1st derivative of cum minus Gaussian: " + e + "\ntolerance exceeded");
}
// check that the second derivative of cum is normal.derivative
temp = D2.applyTo(yi);
for (int i = 0; i < yd.Count; i++)
{
diff[i] = yd[i] - temp[i];
}
e = Utilities.norm(diff, diff.size(), h);
if (e > 1.0e-4)
{
Assert.Fail("norm of 2nd derivative of cum minus Gaussian derivative: " + e + "\ntolerance exceeded");
}
}
internal static global::System.Runtime.InteropServices.HandleRef getCPtr(CumulativeNormalDistribution obj) {
return (obj == null) ? new global::System.Runtime.InteropServices.HandleRef(null, global::System.IntPtr.Zero) : obj.swigCPtr;
}
