public void VegaFacts()
{
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;
//vega closely matches numerical estimate
var PV1 = LMEFunctions.LMEBlackPV(f, k, rf, tExp, tDel, vol - 0.00005, cp);
var PV2 = LMEFunctions.LMEBlackPV(f, k, rf, tExp, tDel, vol + 0.00005, cp);
var vegaEst = (PV2 - PV1) / 0.0001 * 0.01;
var vega = LMEFunctions.LMEBlackVega(f, k, rf, tExp, tDel, vol);
Assert.Equal(vegaEst, vega, 6);
//cases for zero vega
vega = LMEFunctions.LMEBlackVega(f, 0, rf, tExp, tDel, vol);
Assert.Equal(0, vega, 8);
vega = LMEFunctions.LMEBlackVega(f, 1e6, rf, tExp, tDel, vol);
Assert.Equal(0, vega, 8);
}
public void ImpliedVolFacts()
{
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 = 120;
var f = 100;
var vol = 0.32;
var rf = 0.05;
var cp = OptionType.P;
var PV = LMEFunctions.LMEBlackPV(f, k, rf, tExp, tDel, vol, cp);
var impliedVol = LMEFunctions.LMEBlackImpliedVol(f, k, rf, tExp, tDel, PV, cp);
Assert.Equal(vol, impliedVol, 10);
}
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);
}
public void PVFacts()
{
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 = 0;
var f = 100;
var vol = 0.32;
var rf = 0.05;
var cp = OptionType.P;
//zero strike put is worthless
var PV = LMEFunctions.LMEBlackPV(f, k, rf, tExp, tDel, vol, cp);
Assert.Equal(0, PV, 10);
//zero strike call is worth discounted fwd
cp = OptionType.C;
PV = LMEFunctions.LMEBlackPV(f, k, rf, tExp, tDel, vol, cp);
Assert.Equal(System.Math.Exp(-rf * tDel) * f, PV, 10);
//OTM option with zero vol is worthless
vol = 0.0;
k = f + 1;
PV = LMEFunctions.LMEBlackPV(f, k, rf, tExp, tDel, vol, cp);
Assert.Equal(0, PV, 10);
//put-call parity at f==k
k = f;
vol = 0.32;
var PVcall = LMEFunctions.LMEBlackPV(f, k, rf, tExp, tDel, vol, OptionType.C);
var PVput = LMEFunctions.LMEBlackPV(f, k, rf, tExp, tDel, vol, OptionType.P);
Assert.Equal(PVcall, PVput, 10);
}
public void BlackImpliedVol_Facts()
{
Assert.Equal("Could not parse call or put flag - blah", LMEFunctions.QOpt_LMEBlackImpliedVol(DateTime.Today, DateTime.Today, DateTime.Today, 1.0, 1.0, 1, 1, "blah"));
Assert.Equal(1e-9, LMEFunctions.QOpt_LMEBlackImpliedVol(DateTime.Today, DateTime.Today.AddDays(1), DateTime.Today.AddDays(1), 1.0, 0.5, 0.0, 0.0, "C"));
}
public void BlackGammaVega_Facts()
{
Assert.Equal(0.0, LMEFunctions.QOpt_LMEBlackGamma(DateTime.Today, DateTime.Today.AddDays(1), 1.0, 0.5, 0.001));
Assert.Equal(0.0, LMEFunctions.QOpt_LMEBlackVega(DateTime.Today, DateTime.Today.AddDays(1), DateTime.Today.AddDays(1), 1.0, 0.5, 0.0, 0.001));
}
public void BlackDelta_Facts()
{
Assert.Equal("Could not parse call or put flag - blah", LMEFunctions.QOpt_LMEBlackDelta(DateTime.Today, DateTime.Today, 1.0, 1, 1, "blah"));
Assert.Equal(0.0, LMEFunctions.QOpt_LMEBlackDelta(DateTime.Today, DateTime.Today, 1.0, 1, 1, "C"));
}