public void DeltaGammaFacts()
{
var t = 1.0;
var k = 100;
var f = 100;
var vol = 0.32;
var rf = 0.05;
var cp = OptionType.P;
//delta closely matches numerical estimate
var PV1 = BlackFunctions.BlackPV(f + 0.000005, k, rf, t, vol, cp);
var PV2 = BlackFunctions.BlackPV(f - 0.000005, k, rf, t, vol, cp);
var deltaEst = (PV1 - PV2) / 0.00001;
var delta = BlackFunctions.BlackDelta(f, k, rf, t, vol, cp);
Assert.Equal(deltaEst, delta, 6);
//all else the same, more time for OTM option == more delta
k = 150;
var deltaNear = BlackFunctions.BlackDelta(f, k, rf, t, vol, cp);
var deltaFar = BlackFunctions.BlackDelta(f, k, rf, t * 2, vol, cp);
Assert.True(deltaFar > deltaNear);
//put-call parity
var deltaCall = BlackFunctions.BlackDelta(f, k, rf, t, vol, OptionType.C);
var deltaPut = BlackFunctions.BlackDelta(f, k, rf, t, vol, OptionType.P);
var syntheticFwdDelta = deltaCall - deltaPut;
Assert.Equal(System.Math.Exp(-rf * t), syntheticFwdDelta, 10);
//gamma closely matches numerical estimate
var delta1 = BlackFunctions.BlackDelta(f + 0.000005, k, rf, t, vol, cp);
var delta2 = BlackFunctions.BlackDelta(f - 0.000005, k, rf, t, vol, cp);
var gammaEst = (delta1 - delta2) / 0.00001;
var gamma = BlackFunctions.BlackGamma(f, k, rf, t, vol);
Assert.Equal(gammaEst, gamma, 6);
//cases for zero delta / gamma
delta = BlackFunctions.BlackDelta(f, 0, rf, t, vol, OptionType.P);
Assert.Equal(0, delta, 8);
delta = BlackFunctions.BlackDelta(f, 1e6, rf, t, vol, OptionType.C);
Assert.Equal(0, delta, 8);
gamma = BlackFunctions.BlackGamma(f, 0, rf, t, vol);
Assert.Equal(0, gamma, 8);
gamma = BlackFunctions.BlackGamma(f, 1e6, rf, t, vol);
Assert.Equal(0, gamma, 8);
}
public double Dvdk(double strike, DateTime expiry, double fwd)
{
if (StrikeType == StrikeType.ForwardDelta)
{
var t = TimeBasis.CalculateYearFraction(OriginDate, expiry);
var pillarIx = Array.BinarySearch(Expiries, expiry);
var interpForMaturity = pillarIx > 0 ?
_interpolators[pillarIx] :
InterpolatorFactory.GetInterpolator(Strikes, Strikes.Select(k => GetVolForDeltaStrike(k, expiry, fwd)).ToArray(), StrikeInterpolatorType);
var deltaK = GetDeltaStrikeForAbs(fwd, strike, t);
var vol = GetVolForAbsoluteStrike(strike, expiry, fwd);
var gamma = BlackFunctions.BlackGamma(fwd, strike, 0.0, t, vol);
return(interpForMaturity.FirstDerivative(deltaK) * gamma);
}
else
{
var interpForMaturity = InterpolatorFactory.GetInterpolator(Strikes,
Strikes.Select(k => GetVolForAbsoluteStrike(k, expiry, fwd)).ToArray(),
StrikeInterpolatorType);
return(interpForMaturity.FirstDerivative(strike));
}
}
public void BlackGammaVega_Facts()
{
Assert.Equal(0.0, BlackFunctions.BlackGamma(0.1, 1.0, 0.5, 0.0, 0.001));
Assert.Equal(0.0, BlackFunctions.BlackVega(0.1, 1.0, 0.5, 0.0, 0.001));
}
