public void ImpliedVolFacts()
{
var t = 1.0;
var k = 120;
var f = 100;
var vol = 0.32;
var rf = 0.05;
var cp = OptionType.P;
var PV = BlackFunctions.BlackPV(f, k, rf, t, vol, cp);
var impliedVol = BlackFunctions.BlackImpliedVol(f, k, rf, t, PV, cp);
Assert.Equal(vol, impliedVol, 10);
}
public void CanRunPV()
{
var sut = GetSut();
var zar = TestProviderHelper.CurrencyProvider["ZAR"];
var pvCube = sut.PV(zar);
var expiryDates = sut.Portfolio.Instruments
.Select(x => x as AsianOption)
.OrderBy(x => x.AverageEndDate)
.Select(x => x.AverageEndDate);
var expiryTimes = expiryDates.Select(d => sut.OriginDate.CalculateYearFraction(d, DayCountBasis.Act365F)).ToArray();
var pvs = pvCube.GetAllRows().Select(x => x.Value).ToArray();
var vols = pvs.Select((x, ix) => BlackFunctions.BlackImpliedVol(1400, 1400, 0.0, expiryTimes[ix], x, OptionType.C)).ToArray();
var volsCl = expiryDates.Select(d => sut.VanillaModel.GetVolSurface("CL").GetVolForDeltaStrike(0.5, d, 100)).ToArray();
var volsFx = expiryDates.Select(d => sut.VanillaModel.GetVolSurface("USD/ZAR").GetVolForDeltaStrike(0.5, d, 100)).ToArray();
var expectedVols = volsCl.Select((x, ix) => System.Math.Sqrt(x * x + volsFx[ix] * volsFx[ix] + 2 * _correls[ix + 1] * volsFx[ix] * x)).ToArray();
for (var i = 0; i < expiryTimes.Length; i++)
{
Assert.Equal(expectedVols[i], vols[i], 1);
}
}
public static void ImplyVols(List <ListedOptionSettlementRecord> optionSettlements, Dictionary <string, double> futuresPrices, IIrCurve discountCurve = null)
{
var o = new Dictionary <DateTime, IInterpolator1D>();
foreach (var s in optionSettlements)
{
if (!futuresPrices.TryGetValue(s.UnderlyingFuturesCode, out var fut))
{
throw new Exception($"No future price found for contract {s}");
}
var t = s.ValDate.CalculateYearFraction(s.ExpiryDate, DayCountBasis.ACT365F);
var r = 0.0;
if (s.MarginType == OptionMarginingType.Regular)
{
if (discountCurve == null)
{
throw new Exception("To strip vols from options with regular margining, a discount curve must be supplied");
}
r = discountCurve.GetRate(s.ExpiryDate);
}
if (s.ExerciseType == OptionExerciseType.European || s.MarginType == OptionMarginingType.FuturesStyle)
{
s.ImpliedVol = BlackFunctions.BlackImpliedVol(fut, s.Strike, r, t, s.PV, s.CallPut);
}
else if (s.ExerciseType == OptionExerciseType.American)
{
s.ImpliedVol = BinomialTree.AmericanFuturesOptionImpliedVol(fut, s.Strike, r, t, s.PV, s.CallPut);
}
else
{
throw new Exception("Unable to handle option in stripper");
}
}
}
public void CompositeSmimleFacts_LocalVol()
{
var origin = new DateTime(2017, 02, 07);
var expiry = origin.AddMonths(2);
var tExp = origin.CalculateYearFraction(expiry, DayCountBasis.Act365F);
var fwdCurveAsset = new Func <double, double>(t => { return(100); });
var fwdCurveFx = new Func <double, double>(t => { return(15); });
var volAsset = 0.32;
var volFx = 0.16;
var correl = 0.25;
var surfaceAsset = new RiskyFlySurface(origin, new[] { volAsset }, new[] { expiry }, new[] { 0.25, 0.1 }, new[] { new[] { 0.02, 0.03 } }, new[] { new[] { 0.005, 0.007 } }, new[] { 100.0 }, WingQuoteType.Arithmatic, AtmVolType.ZeroDeltaStraddle, Interpolator1DType.GaussianKernel, Interpolator1DType.Linear)
{
FlatDeltaSmileInExtreme = true
};
var surfaceFx = new RiskyFlySurface(origin, new[] { volFx }, new[] { expiry }, new[] { 0.25, 0.1 }, new[] { new[] { 0.015, 0.025 } }, new[] { new[] { 0.005, 0.007 } }, new[] { 0.1 }, WingQuoteType.Arithmatic, AtmVolType.ZeroDeltaStraddle, Interpolator1DType.GaussianKernel, Interpolator1DType.Linear)
{
FlatDeltaSmileInExtreme = true
};
//var surfaceAsset = new SabrVolSurface(origin, new[] { volAsset }, new[] { expiry }, new[] { 0.25, 0.1 }, new[] { new[] { 0.02, 0.03 } }, new[] { new[] { 0.005, 0.007 } }, new[] { 100.0 }, WingQuoteType.Arithmatic, AtmVolType.ZeroDeltaStraddle, Interpolator1DType.Linear);
//var surfaceFx = new SabrVolSurface(origin, new[] { volFx }, new[] { expiry }, new[] { 0.25, 0.1 }, new[] { new[] { 0.015, 0.025 } }, new[] { new[] { 0.005, 0.007 } }, new[] { 0.1 }, WingQuoteType.Arithmatic, AtmVolType.ZeroDeltaStraddle, Interpolator1DType.Linear);
//var surfaceAsset = new SVIVolSurface(origin, new[] { volAsset }, new[] { expiry }, new[] { 0.25, 0.1 }, new[] { new[] { 0.02, 0.03 } }, new[] { new[] { 0.005, 0.007 } }, new[] { 100.0 }, WingQuoteType.Arithmatic, AtmVolType.ZeroDeltaStraddle, Interpolator1DType.Linear);
//var surfaceFx = new SVIVolSurface(origin, new[] { volFx }, new[] { expiry }, new[] { 0.25, 0.1 }, new[] { new[] { 0.015, 0.025 } }, new[] { new[] { 0.005, 0.007 } }, new[] { 0.1 }, WingQuoteType.Arithmatic, AtmVolType.ZeroDeltaStraddle, Interpolator1DType.Linear);
var invFx = new InverseFxSurface("inv", surfaceFx, TestProviderHelper.CurrencyProvider);
var surfaceCompo = surfaceAsset.GenerateCompositeSmile(invFx, 200, expiry, 100, 1.0 / 15, correl);
//setup MC
using var engine = new PathEngine(2.IntPow(IsCoverageOnly?5:15));
engine.AddPathProcess(
new Qwack.Random.MersenneTwister.MersenneTwister64
{
UseNormalInverse = true
});
var correlMatrix = new double[][]
{
new double[] { 1.0, correl },
new double[] { correl, 1.0 },
};
engine.AddPathProcess(new Cholesky(correlMatrix));
var asset1 = new TurboSkewSingleAsset
(
startDate: origin,
expiryDate: expiry,
volSurface: surfaceAsset,
forwardCurve: fwdCurveAsset,
nTimeSteps: 1,
name: "Asset"
);
var asset2 = new TurboSkewSingleAsset
(
startDate: origin,
expiryDate: expiry,
volSurface: surfaceFx,
forwardCurve: fwdCurveFx,
nTimeSteps: 1,
name: "USD/ZAR"
);
engine.AddPathProcess(asset1);
engine.AddPathProcess(asset2);
var strike = 1500;
var product = new EuropeanOption
{
AssetId = "Asset",
CallPut = OptionType.C,
ExpiryDate = expiry,
PaymentCurrency = TestProviderHelper.CurrencyProvider["ZAR"],
PaymentDate = expiry,
Notional = 1.0,
SpotLag = new Frequency("0b"),
Strike = strike,
FxConversionType = FxConversionType.ConvertThenAverage
};
var productAsset = new EuropeanOption
{
AssetId = "Asset",
CallPut = OptionType.C,
ExpiryDate = expiry,
PaymentCurrency = TestProviderHelper.CurrencyProvider["USD"],
PaymentDate = expiry,
Notional = 1.0,
SpotLag = new Frequency("0b"),
Strike = 100,
FxConversionType = FxConversionType.None
};
var productFx = new EuropeanOption
{
AssetId = "USD/ZAR",
CallPut = OptionType.C,
ExpiryDate = expiry,
PaymentCurrency = TestProviderHelper.CurrencyProvider["ZAR"],
PaymentDate = expiry,
Notional = 1.0,
SpotLag = new Frequency("0b"),
Strike = 0.1,
FxConversionType = FxConversionType.None
};
var pathProduct = new AssetPathPayoff(product, TestProviderHelper.CurrencyProvider, TestProviderHelper.CalendarProvider, TestProviderHelper.CurrencyProvider["ZAR"]);
var pathProductAsset = new AssetPathPayoff(productAsset, TestProviderHelper.CurrencyProvider, TestProviderHelper.CalendarProvider, TestProviderHelper.CurrencyProvider["ZAR"]);
var pathProductFx = new AssetPathPayoff(productFx, TestProviderHelper.CurrencyProvider, TestProviderHelper.CalendarProvider, TestProviderHelper.CurrencyProvider["ZAR"]);
engine.AddPathProcess(pathProduct);
engine.AddPathProcess(pathProductAsset);
engine.AddPathProcess(pathProductFx);
engine.SetupFeatures();
engine.RunProcess();
var q = pathProduct.ResultsByPath;
var qq = q.Average();
var productIv = BlackFunctions.BlackImpliedVol(1500, strike, 0.0, tExp, pathProduct.AverageResult, OptionType.C);
var productAssetIv = BlackFunctions.BlackImpliedVol(100, 100, 0.0, tExp, pathProductAsset.AverageResult, OptionType.C);
var productFxIv = BlackFunctions.BlackImpliedVol(10, 10, 0.0, tExp, pathProductFx.AverageResult, OptionType.C);
Assert.True(Abs(productIv - surfaceCompo.Interpolate(strike)) < 0.01);
}
public void BlackImpliedVol_Facts()
{
Assert.Equal("Could not parse call or put flag - blah", BlackFunctions.BlackImpliedVol(1.0, 1.0, 1, 1, 1, "blah"));
Assert.Equal(1e-9, BlackFunctions.BlackImpliedVol(0.1, 1.0, 0.5, 0.0, 0.0, "C"));
}
public static IInterpolator1D GenerateCompositeSmileB(this IVolSurface surface, IVolSurface fxSurface, int numSamples, DateTime expiry, double fwdAsset, double fwdFx, double correlation, bool strikesInDeltaSpace = false)
{
var t = surface.OriginDate.CalculateYearFraction(expiry, DayCountBasis.Act365F);
var fxInv = new InverseFxSurface("fxInv", fxSurface as IATMVolSurface, null);
var atmFx = fxSurface.GetVolForDeltaStrike(0.5, t, fwdFx);
var atmA = surface.GetVolForDeltaStrike(0.5, t, fwdAsset);
var compoFwd = fwdAsset * fwdFx;
var atmCompo = Sqrt(atmFx * atmFx + atmA * atmA + 2.0 * correlation * atmA * atmFx);
var lowK = BlackFunctions.AbsoluteStrikefromDeltaKAnalytic(compoFwd, -0.01, 0, t, atmCompo);
var hiK = BlackFunctions.AbsoluteStrikefromDeltaKAnalytic(compoFwd, -0.99, 0, t, atmCompo);
//var cdfInvFx = fxSurface.GenerateCDF2(numSamples * 10, expiry, fwdFx, true);
//var cdfInvAsset = surface.GenerateCDF2(numSamples * 10, expiry, fwdAsset, true);
//var yFx = new Func<double, double>(z => cdfInvFx.Interpolate(Statistics.NormSDist(z)));
//var yAsset = new Func<double, double>(z => cdfInvAsset.Interpolate(Statistics.NormSDist(z)));
var fxCDFCache = new Dictionary <double, double>();
var assetCDFCache = new Dictionary <double, double>();
var yFx = new Func <double, double>(z =>
{
if (fxCDFCache.TryGetValue(z, out var K))
{
return(K);
}
K = fxInv.InverseCDF(expiry, 1.0 / fwdFx, Statistics.NormSDist(z));
fxCDFCache.Add(z, K);
return(K);
});
var yAsset = new Func <double, double>(z =>
{
if (assetCDFCache.TryGetValue(z, out var K))
{
return(K);
}
K = surface.InverseCDF(expiry, fwdAsset, Statistics.NormSDist(z));
assetCDFCache.Add(z, K);
return(K);
});
//var fxCDFCache = new Dictionary<double, double>();
//var assetCDFCache = new Dictionary<double, double>();
//var putFx = fxInv.GeneratePremiumInterpolator(numSamples * 10, expiry, 1.0/fwdFx, OptionType.P);
//var putAsset = surface.GeneratePremiumInterpolator(numSamples * 10, expiry, fwdAsset, OptionType.P);
//var yFx = new Func<double, double>(z =>
//{
// if (fxCDFCache.TryGetValue(z, out var K)) return K;
// K = InverseCDF(putFx, t, 1.0/fwdFx, Statistics.NormSDist(z));
// fxCDFCache.Add(z, K);
// return K;
//});
//var yAsset = new Func<double, double>(z =>
//{
// if (assetCDFCache.TryGetValue(z, out var K)) return K;
// K = InverseCDF(putAsset, t, fwdAsset, Statistics.NormSDist(z));
// var kl = assetCDFCache.Keys.ToList();
// var closerIx = kl.BinarySearch(z);
// var keyIx = ~closerIx;
// if (closerIx < 0 && z < 0 && kl.Count > keyIx)
// {
// if (assetCDFCache[kl[keyIx]] < K)
// K = assetCDFCache[kl[keyIx]];
// }
// assetCDFCache.Add(z, K);
// return K;
//});
var payoff = new Func <double, double, double, double>((z1, z2, kQ) => Max(kQ * yFx(z2) - yAsset(z1), 0));
var integrand = new Func <double, double, double, double>((z1, z2, kQ) => payoff(z1, z2, kQ) * BivariateNormal.PDF(z1, z2, -correlation));
var kStep = (hiK - lowK) / numSamples;
var ks = Enumerable.Range(0, numSamples).Select(kk => lowK + kk * kStep).ToArray();
var premiums = new double[ks.Length];
var vols = new double[ks.Length];
for (var i = 0; i < ks.Length; i++)
{
var ik = new Func <double, double, double>((z1, z2) => integrand(z1, z2, ks[i]));
var pk = Integration.TwoDimensionalGaussLegendre(ik, -5, 5, -5, 5, 16);
//var pk = Integration.TwoDimensionalSimpsons(ik, -5, 5, -5, 5, 100);
pk *= fwdFx;
var volK = BlackFunctions.BlackImpliedVol(compoFwd, ks[i], 0.0, t, pk, OptionType.P);
vols[i] = volK;
premiums[i] = pk;
}
if (strikesInDeltaSpace)
{
ks = ks.Select((ak, ix) => - BlackFunctions.BlackDelta(compoFwd, ak, 0.0, t, vols[ix], OptionType.P)).ToArray();
}
return(InterpolatorFactory.GetInterpolator(ks, vols, Interpolator1DType.CubicSpline));
}
public static IInterpolator1D GenerateCompositeSmile(this IVolSurface surface, IVolSurface fxSurface, int numSamples, DateTime expiry, double fwdAsset, double fwdFx, double rho, bool strikesInDeltaSpace = false)
{
var t = surface.OriginDate.CalculateYearFraction(expiry, DayCountBasis.Act365F);
var atmFx = fxSurface.GetVolForDeltaStrike(0.5, t, fwdFx);
var atmA = surface.GetVolForDeltaStrike(0.5, t, fwdAsset);
var compoFwd = fwdAsset / fwdFx;
var atmCompo = Sqrt(atmFx * atmFx + atmA * atmA + 2.0 * rho * atmA * atmFx);
var lowK = BlackFunctions.AbsoluteStrikefromDeltaKAnalytic(compoFwd, -0.01, 0, t, atmCompo);
var hiK = BlackFunctions.AbsoluteStrikefromDeltaKAnalytic(compoFwd, -0.99, 0, t, atmCompo);
var nuA = Sqrt(t) * atmA;
var nuFx = Sqrt(t) * atmFx;
var cdfFx = new Func <double, double>(k => fxSurface.CDF(expiry, fwdFx, Exp(k)));
var cdfA = new Func <double, double>(k => surface.CDF(expiry, fwdAsset, Exp(k)));
var fxCDFCache = new Dictionary <double, double>();
var assetCDFCache = new Dictionary <double, double>();
var yFx = new Func <double, double>(z =>
{
if (fxCDFCache.TryGetValue(z, out var K))
{
return(K);
}
K = Log(fxSurface.InverseCDF(expiry, fwdFx, Statistics.NormSDist(z)));
fxCDFCache.Add(z, K);
return(K);
});
var yA = new Func <double, double>(z =>
{
if (assetCDFCache.TryGetValue(z, out var K))
{
return(K);
}
K = Log(surface.InverseCDF(expiry, fwdAsset, Statistics.NormSDist(z)));
assetCDFCache.Add(z, K);
return(K);
});
//var zfxS = new Func<double, double, double>((zA, K) => Statistics.NormInv(Max(1e-18, Min(1.0 - 1e-18, cdfFx(yA(zA) - Log(K))))));
//var zAs = new Func<double, double, double>((zFx, K) => Statistics.NormInv(Max(1e-18, Min(1.0 - 1e-18, cdfA(yFx(zFx) + Log(K))))));
var zfxS = new Func <double, double, double>((zA, K) => Statistics.NormInv(cdfFx(yA(zA) - Log(K))));
var zAs = new Func <double, double, double>((zFx, K) => Statistics.NormInv(cdfA(yFx(zFx) + Log(K))));
var d = -1.0;
var p2 = 1.0 / Sqrt(2.0 * PI);
//var I1 = new Func<double, double, double>((zA, K) =>
//p2*Exp(yA(zA) - (nuA * zA - nuA * nuA / 2)) * Statistics.NormSDist(d * (zfxS(zA, K) - rho * zA) / Sqrt(1 - rho * rho)) * Exp(-(zA - nuA) * (zA - nuA) / 2.0)
// );
//var I2 = new Func<double, double, double>((zFx, K) =>
//p2*Exp(yFx(zFx) - (nuFx * zFx - nuFx * nuFx / 2)) * Statistics.NormSDist(-d * (zAs(zFx, K) - rho * zFx) / Sqrt(1 - rho * rho)) * Exp(-(zFx - nuFx) * (zFx - nuFx) / 2.0)
// );
var I1 = new Func <double, double, double>((zA, K) =>
p2 * Exp(yA(zA)) * Statistics.NormSDist(d * (zfxS(zA, K) - rho * zA) / Sqrt(1 - rho * rho)) * Exp(-(zA * zA) / 2.0)
);
var I2 = new Func <double, double, double>((zFx, K) =>
p2 * Exp(yFx(zFx)) * Statistics.NormSDist(-d * (zAs(zFx, K) - rho * zFx) / Sqrt(1 - rho * rho)) * Exp(-(zFx * zFx) / 2.0)
);
var kStep = (hiK - lowK) / numSamples;
var ks = Enumerable.Range(0, numSamples).Select(kk => lowK + kk * kStep).ToArray();
var premiums = new double[ks.Length];
var vols = new double[ks.Length];
for (var i = 0; i < ks.Length; i++)
{
var I1k = new Func <double, double>(z => I1(z, ks[i]));
var I2k = new Func <double, double>(z => I2(z, ks[i]));
//var i1 = Integration.GaussLegendre(I1k, -5, 5, 16);
//var i2 = Integration.GaussLegendre(I2k, -5, 5, 16);
var i1 = Integration.SimpsonsRule(I1k, -5, 5, numSamples);
var i2 = Integration.SimpsonsRule(I2k, -5, 5, numSamples);
var pk = d * (i1 - ks[i] * i2);
pk /= fwdFx;
var volK = BlackFunctions.BlackImpliedVol(compoFwd, ks[i], 0.0, t, pk, OptionType.P);
vols[i] = volK;
premiums[i] = pk;
}
if (strikesInDeltaSpace)
{
ks = ks.Select((ak, ix) => - BlackFunctions.BlackDelta(compoFwd, ak, 0.0, t, vols[ix], OptionType.P)).ToArray();
}
return(InterpolatorFactory.GetInterpolator(ks, vols, Interpolator1DType.CubicSpline));
}
