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(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);
//derivs
k = 100;
delta = BlackFunctions.BlackDelta(f, k, rf, t, vol, cp);
var derivs = BlackFunctions.BlackDerivs(f, k, rf, t, vol, cp);
Assert.Equal(delta, derivs[0]);
cp = OptionType.C;
delta = BlackFunctions.BlackDelta(f, k, rf, t, vol, cp);
derivs = BlackFunctions.BlackDerivs(f, k, rf, t, vol, cp);
Assert.Equal(delta, derivs[0]);
}
