public void DeltaStrikeMappingFacts()
{
var today = DateTime.Parse("2017-02-07");
var expiry = DateTime.Parse("2017-12-06");
var delivery = DateTime.Parse("2017-12-20");
var tExp = DayCountBasis.Act_365F.CalculateYearFraction(today, expiry);
var tDel = DayCountBasis.Act_365F.CalculateYearFraction(today, delivery);
var k = 100;
var f = 100;
var vol = 0.32;
var cp = OptionType.P;
//black forward delta matches
var delta = LMEFunctions.LMEBlackDelta(f, k, tExp, vol, cp);
var absolute = LMEFunctions.AbsoluteStrikefromDeltaKAnalytic(f, delta, tExp, vol);
Assert.Equal(k, absolute, 10);
}
public void DeltaGammaFacts()
{
var today = DateTime.Parse("2017-02-07");
var expiry = DateTime.Parse("2017-12-06");
var delivery = DateTime.Parse("2017-12-20");
var tExp = DayCountBasis.Act_365F.CalculateYearFraction(today, expiry);
var tDel = DayCountBasis.Act_365F.CalculateYearFraction(today, delivery);
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 = LMEFunctions.LMEBlackPV(f + 0.000005, k, rf, tExp, tDel, vol, cp);
var PV2 = LMEFunctions.LMEBlackPV(f - 0.000005, k, rf, tExp, tDel, vol, cp);
var deltaEst = System.Math.Exp(tDel * rf) * (PV1 - PV2) / 0.00001; //undiscount the delta
var delta = LMEFunctions.LMEBlackDelta(f, k, tExp, vol, cp);
Assert.Equal(deltaEst, delta, 6);
//zero-strike call has fwd delta of 1.0
k = 0;
cp = OptionType.C;
delta = LMEFunctions.LMEBlackDelta(f, k, tExp, vol, cp);
Assert.Equal(1.0, delta, 10);
//put-call parity
k = 100;
var deltaCall = LMEFunctions.LMEBlackDelta(f, k, tExp, vol, OptionType.C);
var deltaPut = LMEFunctions.LMEBlackDelta(f, k, tExp, vol, OptionType.P);
var syntheticFwdDelta = deltaCall - deltaPut;
Assert.Equal(1.0, syntheticFwdDelta, 10);
//gamma closely matches numerical estimate
var delta1 = LMEFunctions.LMEBlackDelta(f + 0.000005, k, tExp, vol, cp);
var delta2 = LMEFunctions.LMEBlackDelta(f - 0.000005, k, tExp, vol, cp);
var gammaEst = (delta1 - delta2) / 0.00001;
var gamma = LMEFunctions.LMEBlackGamma(f, k, tExp, vol);
Assert.Equal(gammaEst, gamma, 6);
}