public static double pricingVol(IVolSurface volSurf, Date exerciseDate, IOption option, double spot)
{
return(option.IsMoneynessOption ?
//moneyness option , strike i.e. 120% of initialSpot
volSurf.GetValue(exerciseDate, option.Strike * option.InitialSpotPrice, spot):
volSurf.GetValue(exerciseDate, option.Strike, spot));
}
public static IInterpolator1D GenerateCDF2(this IVolSurface surface, int numSamples, DateTime expiry, double fwd, bool returnInverse = false, double strikeScale = 1.0, bool logStrikes = false)
{
var premInterp = GeneratePremiumInterpolator(surface, numSamples, expiry, fwd, OptionType.P);
var t = surface.OriginDate.CalculateYearFraction(expiry, DayCountBasis.Act365F);
var x = new double[numSamples];
var y = new double[numSamples];
var deltaKLow = 0.0000000001;
var deltaKHi = 0.9999999999;
var kStepD = (deltaKHi - deltaKLow) / numSamples;
for (var i = 0; i < x.Length; i++)
{
var deltaKNew = -deltaKLow - i * kStepD;
var newStrikeVol = surface.GetVolForDeltaStrike(-deltaKNew, t, fwd);
var k = BlackFunctions.AbsoluteStrikefromDeltaKAnalytic(fwd, deltaKNew, 0, t, newStrikeVol);
var digital = premInterp.FirstDerivative(k);
y[i] = digital;
x[i] = k * strikeScale;
if (logStrikes)
{
x[i] = Log(x[i]);
}
}
return(returnInverse ?
InterpolatorFactory.GetInterpolator(y, x, Interpolator1DType.MonotoneCubicSpline) :
InterpolatorFactory.GetInterpolator(x, y, Interpolator1DType.MonotoneCubicSpline));
}
public static IInterpolator1D GenerateCompositeSmileBasic(this IVolSurface surface, IVolSurface fxSurface, int numSamples, DateTime expiry, double fwdAsset, double fwdFx, double correlation, bool deltaStrikeOutput = false)
{
var deltaKa = fwdAsset * 0.00001;
var deltaKfx = fwdFx * 0.00001;
var t = surface.OriginDate.CalculateYearFraction(expiry, DayCountBasis.Act365F);
var atmFx = fxSurface.GetVolForAbsoluteStrike(fwdFx, t, fwdFx);
var atmA = surface.GetVolForAbsoluteStrike(fwdAsset, t, fwdAsset);
var compoFwd = fwdAsset * fwdFx;
var atmCompo = Sqrt(atmFx * atmFx + atmA * atmA + 2.0 * correlation * atmA * atmFx);
var lowK = BlackFunctions.AbsoluteStrikefromDeltaKAnalytic(compoFwd, -0.0001, 0, t, atmCompo);
var hiK = BlackFunctions.AbsoluteStrikefromDeltaKAnalytic(compoFwd, -0.9999, 0, t, atmCompo);
var lowKA = BlackFunctions.AbsoluteStrikefromDeltaKAnalytic(fwdAsset, -0.0001, 0, t, atmA);
var hiKA = BlackFunctions.AbsoluteStrikefromDeltaKAnalytic(fwdAsset, -0.9999, 0, t, atmA);
var x = new double[numSamples];
var y = new double[numSamples];
var k = lowK;
var kStep = (hiK - lowK) / numSamples;
var kStepA = (hiKA - lowKA) / numSamples;
var kStepFx = (hiK / hiKA - lowK / lowKA) / numSamples;
for (var i = 0; i < x.Length; i++)
{
x[i] = k;
var kA = lowKA;
var totalP = 0.0;
for (var j = 0; j < numSamples; j++)
{
var kFx = k / kA;
var volFx = fxSurface.GetVolForAbsoluteStrike(kFx, t, fwdFx);
var volA = surface.GetVolForAbsoluteStrike(kA, t, fwdAsset);
var volC = Sqrt(volFx * volFx + volA * volA + 2.0 * correlation * volA * volFx);
var fxBucketLow = kFx - deltaKfx / 2.0;
var fxBucketHi = kFx + deltaKfx / 2.0;
var assetBucketLow = kA - deltaKa / 2.0;
var assetBucketHi = kA + deltaKa / 2.0;
var weight = 1.0;
y[i] += weight * volC;
totalP += weight;
kA += kStepA;
}
y[i] /= totalP;
k += kStep;
}
if (deltaStrikeOutput)
{
x = x.Select((q, ix) => - BlackFunctions.BlackDelta(compoFwd, q, 0.0, t, y[ix], OptionType.P)).ToArray();
}
return(InterpolatorFactory.GetInterpolator(x, y, Interpolator1DType.LinearFlatExtrap));
}
public LVSingleAsset(IVolSurface volSurface, DateTime startDate, DateTime expiryDate, int nTimeSteps, Func <double, double> forwardCurve, string name)
{
_surface = volSurface;
_startDate = startDate;
_expiryDate = expiryDate;
_numberOfSteps = nTimeSteps;
_name = name;
_forwardCurve = forwardCurve;
}
public void AddVolSurface(string name, IVolSurface surface)
{
if (IsFx(name))
{
FundingModel.VolSurfaces[name] = surface;
}
else
{
_assetVols[new VolSurfaceKey(surface.AssetId, surface.Currency)] = surface;
}
}
public BlackScholesProcessWithQuantoForwardAdjustment(IYieldCurve spotRateCurve, IYieldCurve divCurve, IVolSurface volSurf, double rho, IVolSurface fxVolSurf)
: base()
{
_spotRateCurve = spotRateCurve;
_dividendCurve = divCurve;
_volSurf = volSurf;
_correlation = rho;
_fxVolSurf = fxVolSurf;
_isConstantRate = false;
_isConstantVol = false;
}
public CompositeVolSurface(string name, string assetId, Currency ccy, IVolSurface assetSurface, IFundingModel fundingModel, double correlation, CompositeVolType calculationType)
{
AssetSurface = assetSurface;
FundingModel = fundingModel;
Correlation = correlation;
CalculationType = calculationType;
Name = name;
AssetId = assetId;
Currency = ccy;
_Pair = FundingModel.FxMatrix.GetFxPair(AssetSurface.Currency, Currency);
}
public static double InverseCDFex(this IVolSurface surface, double t, double fwd, double p)
{
var deltaK = fwd * 1e-10;
var lowGuess = fwd / 2;
var highGuess = fwd * 2;
var targetFunc = new Func <double, double>(k =>
{
var volM = surface.GetVolForAbsoluteStrike(k - deltaK, t, fwd);
var volP = surface.GetVolForAbsoluteStrike(k + deltaK, t, fwd);
var pvM = BlackFunctions.BlackPV(fwd, k - deltaK, 0.0, t, volM, OptionType.P);
var pvP = BlackFunctions.BlackPV(fwd, k + deltaK, 0.0, t, volP, OptionType.P);
var digi = (pvP - pvM) / (2 * deltaK);
//var digi = BlackFunctions.BlackDigitalPV(fwd, k, 0, t, surface.GetVolForAbsoluteStrike(k, t, fwd), OptionType.P);
return(p - digi);
});
var breakCount = 0;
while (targetFunc(lowGuess) < 0)
{
// highGuess = lowGuess*2.0;
lowGuess /= 2.0;
breakCount++;
if (breakCount == 10)
{
return(lowGuess);
}
}
breakCount = 0;
while (targetFunc(highGuess) > 0)
{
//lowGuess = highGuess/2.0;
highGuess *= 2.0;
breakCount++;
if (breakCount == 10)
{
return(highGuess);
}
}
var b = Math.Solvers.Brent.BrentsMethodSolve(targetFunc, lowGuess, highGuess, 1e-8);
//var b = Math.Solvers.Newton1D.MethodSolve2(targetFunc, fwd, 1e-6, 1000, fwd * 0.00001);
if (double.IsInfinity(b) || double.IsNaN(b))
{
throw new Exception("Invalid strike found");
}
//if (b==lowGuess || b==highGuess)
// throw new Exception("Strike outside of bounds");
return(b);
}
public static IInterpolator1D GenerateCDF(this IVolSurface surface, int numSamples, DateTime expiry, double fwd, bool returnInverse = false)
{
var deltaKLow = 0.0000001;
var deltaKHi = 0.9999999;
var kStepD = (deltaKHi - deltaKLow) / (numSamples + 3);
var deltaKBump = deltaKLow / 10;
var t = surface.OriginDate.CalculateYearFraction(expiry, DayCountBasis.Act365F);
var x = new double[numSamples + 2];
var y = new double[numSamples + 2];
for (var i = 0; i < x.Length; i++)
{
var deltaKNew = deltaKLow + i * kStepD;
var mStrike = deltaKNew - deltaKBump / 2;
var pStrike = deltaKNew + deltaKBump / 2;
var mStrikeVol = surface.GetVolForDeltaStrike(mStrike, t, fwd);
var mk = BlackFunctions.AbsoluteStrikefromDeltaKAnalytic(fwd, -mStrike, 0, t, mStrikeVol);
var pStrikeVol = surface.GetVolForDeltaStrike(pStrike, t, fwd);
var pk = BlackFunctions.AbsoluteStrikefromDeltaKAnalytic(fwd, -pStrike, 0, t, pStrikeVol);
if (i == 0)
{
x[0] = mk / 2.0;
y[0] = 0;
continue;
}
if (i == x.Length - 1)
{
x[i] = pk * 2;
y[i] = 1;
continue;
}
var dkAbs = (pk - mk);
var pPut = BlackFunctions.BlackPV(fwd, pk, 0, t, pStrikeVol, OptionType.P);
var mPut = BlackFunctions.BlackPV(fwd, mk, 0, t, mStrikeVol, OptionType.P);
var digital = (pPut - mPut) / dkAbs;
y[i] = digital;
x[i] = (mk + pk) / 2.0;
}
return(returnInverse ?
InterpolatorFactory.GetInterpolator(y, x, Interpolator1DType.LinearFlatExtrap) :
InterpolatorFactory.GetInterpolator(x, y, Interpolator1DType.LinearFlatExtrap));
}
public LVSingleAsset(IVolSurface volSurface, DateTime startDate, DateTime expiryDate, int nTimeSteps, Func <double, double> forwardCurve, string name, Dictionary <DateTime, double> pastFixings = null, IATMVolSurface fxAdjustSurface = null, double fxAssetCorrelation = 0.0)
{
_surface = volSurface;
_startDate = startDate;
_expiryDate = expiryDate;
_numberOfSteps = nTimeSteps;
_name = name;
_pastFixings = pastFixings ?? (new Dictionary <DateTime, double>());
_forwardCurve = forwardCurve;
_adjSurface = fxAdjustSurface;
_correlation = fxAssetCorrelation;
}
public static IInterpolator1D GeneratePDF(this IVolSurface surface, int numSamples, DateTime expiry, double fwd)
{
var deltaK = fwd * 0.0001;
var t = surface.OriginDate.CalculateYearFraction(expiry, DayCountBasis.Act365F);
var lowStrikeVol = surface.GetVolForDeltaStrike(0.0001, t, fwd);
var lowStrike = BlackFunctions.AbsoluteStrikefromDeltaKAnalytic(fwd, -0.0001, 0, t, lowStrikeVol);
var hiStrikeVol = surface.GetVolForDeltaStrike(0.9999, t, fwd);
var hiStrike = BlackFunctions.AbsoluteStrikefromDeltaKAnalytic(fwd, -0.9999, 0, t, hiStrikeVol);
var x = new double[numSamples + 2];
var y = new double[numSamples + 2];
var k = lowStrike;
var kStep = (hiStrike - lowStrike) / numSamples;
for (var i = 0; i < x.Length; i++)
{
if (i == 0)
{
x[0] = lowStrike / 2.0;
y[0] = 0;
continue;
}
if (i == x.Length - 1)
{
x[i] = k * 2;
y[i] = 0;
continue;
}
var volLow = surface.GetVolForAbsoluteStrike(k - deltaK, t, fwd);
var callLow = BlackFunctions.BlackPV(fwd, k - deltaK, 0, t, volLow, OptionType.C);
var volMid = surface.GetVolForAbsoluteStrike(k, t, fwd);
var callMid = BlackFunctions.BlackPV(fwd, k, 0, t, volMid, OptionType.C);
var volHi = surface.GetVolForAbsoluteStrike(k + deltaK, t, fwd);
var callHi = BlackFunctions.BlackPV(fwd, k + deltaK, 0, t, volHi, OptionType.C);
var digitalLo = (callLow - callMid) / deltaK;
var digitalHi = (callMid - callHi) / deltaK;
y[i] = (digitalLo - digitalHi) / deltaK;
x[i] = k;
k += kStep;
}
var firstPass = InterpolatorFactory.GetInterpolator(x, y, Interpolator1DType.LinearFlatExtrap);
var totalY = ((IIntegrableInterpolator)firstPass).DefiniteIntegral(x.First(), x.Last());
y = y.Select(v => v / totalY).ToArray();
return(InterpolatorFactory.GetInterpolator(x, y, Interpolator1DType.LinearFlatExtrap));
}
public static double[][] ComputeLocalVarianceOnGridFromCalls(this IVolSurface VanillaSurface, double[][] strikes, double[] timeSteps, Func <double, double> forwardFunc)
{
var numberOfTimesteps = timeSteps.Length;
var deltaK = 0.001 * forwardFunc(timeSteps[0]);
var lvGrid = new double[numberOfTimesteps - 1][];
var fwds = timeSteps.Select(t => forwardFunc(t)).ToArray();
//ParallelUtils.Instance.For(1, numberOfTimesteps, 1, it =>
for (var it = 1; it < numberOfTimesteps; it++)
{
var T = timeSteps[it];
var T1 = timeSteps[it - 1];
var fwd = fwds[it];
var fwdtm1 = fwds[it - 1];
var rmq = Log(fwd / fwdtm1) / (T - T1);
var numberOfStrikes = strikes[it - 1].Length;
var cInterp = VanillaSurface.GeneratePremiumInterpolator(numberOfStrikes * 2, T, fwd, OptionType.C);
lvGrid[it - 1] = new double[numberOfStrikes];
if (numberOfStrikes > 1)
{
for (var ik = 0; ik < numberOfStrikes; ik++)
{
var K = strikes[it][ik];
var V = VanillaSurface.GetVolForAbsoluteStrike(K, T, fwd);
var C = BlackFunctions.BlackPV(fwd, K, 0.0, T, V, OptionType.C);
var Vtm1 = VanillaSurface.GetVolForAbsoluteStrike(K, T1, fwdtm1);
//var dcdt = -BlackFunctions.BlackTheta(fwd, K, 0.0, T, V, OptionType.C);
var dcdt = -(BlackFunctions.BlackPV(fwdtm1, K, 0.0, T1, Vtm1, OptionType.C) - C) / (T - T1);
var dcdk = cInterp.FirstDerivative(K);
var d2cdk2 = cInterp.SecondDerivative(K);
var localVariance = d2cdk2 == 0 ? V * V : (dcdt - rmq * (C - K * dcdk)) / (0.5 * K * K * d2cdk2);
lvGrid[it - 1][ik] = localVariance;
}
}
else
{
var K = strikes[it][0];
var V = VanillaSurface.GetVolForAbsoluteStrike(K, T, fwd);
lvGrid[it - 1][0] = V * V;
}
}//, false).Wait();
return(lvGrid);
}
public bool TryGetVolSurface(string name, out IVolSurface volSurface)
{
if (VolSurfaces.TryGetValue(name, out volSurface))
{
return(true);
}
if (TryGetInverseSurface(name, out volSurface))
{
return(true);
}
volSurface = null;
return(false);
}
public bool TryGetVolSurface(string name, out IVolSurface surface, Currency currency = null)
{
surface = null;
if (IsFx(name))
{
return(FundingModel.TryGetVolSurface(name, out surface));
}
if (currency != null)
{
return(_assetVols.TryGetValue(new VolSurfaceKey(name, currency), out surface));
}
surface = _assetVols.Where(x => name.Contains("~") ? x.Key.ToString() == name : x.Key.AssetId == name).FirstOrDefault().Value;
return(surface != default(IVolSurface));
}
public static TO_VolSurface GetTransportObject(this IVolSurface volSurface)
{
switch (volSurface)
{
case RiskyFlySurface rf:
return(new TO_VolSurface {
RiskyFlySurface = rf.GetTransportObject()
});
case GridVolSurface gs:
return(new TO_VolSurface {
GridVolSurface = gs.GetTransportObject()
});
case ConstantVolSurface cs:
return(new TO_VolSurface {
ConstantVolSurface = cs.GetTransportObject()
});
default:
throw new Exception("Unable to serialize volsurface");
}
}
public LVSingleAsset(IVolSurface volSurface, DateTime startDate, DateTime expiryDate, int nTimeSteps, Func <double, double> forwardCurve, string name, Dictionary <DateTime, double> pastFixings = null, IATMVolSurface fxAdjustSurface = null, double fxAssetCorrelation = 0.0)
{
_surface = volSurface;
_startDate = startDate;
_expiryDate = expiryDate;
_numberOfSteps = nTimeSteps;
_name = name;
_pastFixings = pastFixings ?? (new Dictionary <DateTime, double>());
_forwardCurve = forwardCurve;
_adjSurface = fxAdjustSurface;
_correlation = fxAssetCorrelation;
if (volSurface is InverseFxSurface || (_adjSurface != null && _adjSurface?.AssetId == volSurface.AssetId))
{
_siegelInvert = true;
}
if (_adjSurface != null && _adjSurface?.AssetId == volSurface.AssetId)
{
_adjSurface = null;
}
}
public static IInterpolator1D GeneratePremiumInterpolator(this IVolSurface surface, int numSamples, double t, double fwd, OptionType cp)
{
var lowStrikeVol = surface.GetVolForDeltaStrike(0.001, t, fwd);
var lowStrike = BlackFunctions.AbsoluteStrikefromDeltaKAnalytic(fwd, -0.001, 0, t, lowStrikeVol);
var hiStrikeVol = surface.GetVolForDeltaStrike(0.999, t, fwd);
var hiStrike = BlackFunctions.AbsoluteStrikefromDeltaKAnalytic(fwd, -0.999, 0, t, hiStrikeVol);
var x = new double[numSamples + 2];
var y = new double[numSamples + 2];
var k = lowStrike;
var kStep = (hiStrike - lowStrike) / (numSamples + 1.0);
var vol = surface.GetVolForAbsoluteStrike(k / 10, t, fwd);
var call = BlackFunctions.BlackPV(fwd, k / 10, 0, t, vol, cp);
y[0] = call;
x[0] = k / 10;
for (var i = 0; i < x.Length - 1; i++)
{
vol = surface.GetVolForAbsoluteStrike(k, t, fwd);
call = BlackFunctions.BlackPV(fwd, k, 0, t, vol, cp);
y[i + 1] = call;
x[i + 1] = k;
k += kStep;
}
vol = surface.GetVolForAbsoluteStrike(k * 10, t, fwd);
call = BlackFunctions.BlackPV(fwd, k * 10, 0, t, vol, cp);
y[x.Length - 1] = call;
x[x.Length - 1] = k * 10;
return(InterpolatorFactory.GetInterpolator(x, y, Interpolator1DType.MonotoneCubicSpline));
}
public BlackScholesProcess(IYieldCurve spotRateCurve, IYieldCurve divCurve, IVolSurface volSurf, double[] times = null)
{
_spotRateCurve = spotRateCurve;
_dividendCurve = divCurve;
_volSurf = volSurf;
_isConst = false;
if (times == null)
{
return;
}
//cache forward rate
_spotRateCurveForwardrateDict = new Dictionary <double, double>();
_dividendCurveForwardrateDict = new Dictionary <double, double>();
for (var i = 0; i < times.Length - 1; ++i)
{
var t0 = times[i];
var dt = times[i + 1] - times[i];
_spotRateCurveForwardrateDict[Math.Round(t0, Precision)] = _spotRateCurve.GetForwardRate(t0, dt, _spotRateCurve.Compound);
_dividendCurveForwardrateDict[Math.Round(t0, Precision)] = _dividendCurve.GetForwardRate(t0, dt, _dividendCurve.Compound);
}
_isCached = true;
}
public void AddVolSurface(VolSurfaceKey key, IVolSurface surface) => _assetVols[key] = surface;
public static IInterpolator1D GeneratePremiumInterpolator(this IVolSurface surface, int numSamples, DateTime expiry, double fwd, OptionType cp) => GeneratePremiumInterpolator(surface, numSamples, surface.OriginDate.CalculateYearFraction(expiry, DayCountBasis.Act365F), fwd, cp);
public void AddVolSurface(string name, IVolSurface surface) => _assetVols[new VolSurfaceKey(surface.AssetId, surface.Currency)] = surface;
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));
}
public static double[][] ComputeLocalVarianceOnGrid(this IVolSurface VanillaSurface, double[][] strikes, double[] timeSteps, Func <double, double> forwardFunc)
{
var numberOfTimesteps = timeSteps.Length;
var deltaK = 0.001 * forwardFunc(timeSteps[0]);
var lvGrid = new double[numberOfTimesteps - 1][];
var Ss = new double[numberOfTimesteps];
for (var i = 0; i < Ss.Length; i++)
{
Ss[i] = forwardFunc(timeSteps[i]);
}
for (var it = 1; it < numberOfTimesteps; it++)
{
var numberOfStrikes = strikes[it - 1].Length;
lvGrid[it - 1] = new double[numberOfStrikes];
double K, V, S, Td, dwdT, localVariance, TdSq, T, T1;
double V_t1, V_Kp2, V_Km2, K_tm1, St;
double y, yPlus, yPlus2, yMinus, yMinus2, dwdY, dwdY_p, dwdY_m, d2wd2Y, w, w_t1, w_kPlus2, w_kMinus2; //, Y1, Y2;
T = timeSteps[it];
T1 = timeSteps[it - 1];
Td = T - T1;
TdSq = Sqrt(Td);
S = Ss[it];
St = Ss[it - 1];
var fwd = forwardFunc(T);
for (var ik = 0; ik < numberOfStrikes; ik++)
{
K = strikes[it][ik];
K_tm1 = K * St / S;
y = Log(K / S);
yPlus = Log((K + deltaK) / S);
yPlus2 = Log((K + deltaK * 2) / S);
yMinus = Log((K - deltaK) / S);
yMinus2 = Log((K - deltaK * 2) / S);
//Y1 = Log(Sqrt(K * K + 2 * deltaK * K) / S);
//Y2 = Log(Sqrt(K * K - 2 * deltaK * K) / S);
V = VanillaSurface.GetVolForAbsoluteStrike(K, T, fwd);
w = V * V * T;
V_t1 = VanillaSurface.GetVolForAbsoluteStrike(K_tm1, T1, fwd);
w_t1 = V_t1 * V_t1 * T1;
V_Kp2 = VanillaSurface.GetVolForAbsoluteStrike(K + deltaK * 2, T, fwd);
w_kPlus2 = V_Kp2 * V_Kp2 * T;
V_Km2 = VanillaSurface.GetVolForAbsoluteStrike(K - deltaK * 2, T, fwd);
w_kMinus2 = V_Km2 * V_Km2 * T;
dwdT = (w - w_t1) / Td;
dwdY_m = (w - w_kMinus2) / (y - yMinus2);
dwdY_p = (w_kPlus2 - w) / (yPlus2 - y);
dwdY = (dwdY_m + dwdY_p) / 2;
//d2wd2Y = (dwdY_p - dwdY_m) / (Y1 - Y2);
d2wd2Y = (dwdY_p - dwdY_m) / (yPlus - yMinus);
localVariance = dwdT / (1 - y / w * dwdY + 0.25 * (-0.25 - 1 / w + (y * y / (w))) * dwdY * dwdY + 0.5 * d2wd2Y);
lvGrid[it - 1][ik] = localVariance;
}
}
return(lvGrid);
}
public void RemoveVolSurface(IVolSurface surface)
{
var key = new VolSurfaceKey(surface.AssetId, surface.Currency);
_assetVols.Remove(key);
}
public static double StrikeForPV(double targetPV, double forward, double knownAverage, IVolSurface volSurface, DateTime evalDate, DateTime avgStartDate, DateTime avgEndDate, double riskFree, OptionType callPut)
{
var minStrike = forward / 100.0;
var maxStrike = forward * 100.0;
var volDate = avgStartDate.Average(avgEndDate);
Func <double, double> testFunc = (absK =>
{
var vol = volSurface.GetVolForAbsoluteStrike(absK, volDate, forward);
var pv = PV(forward, knownAverage, vol, absK, evalDate, avgStartDate, avgEndDate, riskFree, callPut);
return(targetPV - pv);
});
var solvedStrike = Math.Solvers.Brent.BrentsMethodSolve(testFunc, minStrike, maxStrike, 1e-8);
return(solvedStrike);
}
private bool TryGetInverseSurface(string name, out IVolSurface volSurface)
{
var inverseName = name.Substring(name.Length - 3, 3) + "/" + name.Substring(0, 3);
return(VolSurfaces.TryGetValue(inverseName, out volSurface));
}
public static double StrikeForPV(double targetPV, double[] forwards, DateTime[] fixingDates, IVolSurface volSurface, DateTime evalDate, DateTime payDate, double riskFree, OptionType callPut)
{
var minStrike = forwards.Min() / 100.0;
var maxStrike = forwards.Max() * 100.0;
var ixMin = Array.BinarySearch(fixingDates, evalDate);
if (ixMin < 0)
{
ixMin = ~ixMin;
}
Func <double, double> testFunc = (absK =>
{
var vols = fixingDates.Select((d, ix) => ix >= ixMin ? volSurface.GetVolForAbsoluteStrike(absK, d, forwards[ix]) : 0.0).ToArray();
var pv = PV(forwards, fixingDates, evalDate, payDate, vols, absK, riskFree, callPut);
return(targetPV - pv);
});
var solvedStrike = Math.Solvers.Brent.BrentsMethodSolve(testFunc, minStrike, maxStrike, 1e-8);
return(solvedStrike);
}
