public void SolveSmileSimple()
{
var valDate = new DateTime(2018, 07, 28);
var expDate = valDate.AddDays(365);
var fwd = 1000;
double[] strikes = { 0.25, 0.5, 0.75 };
var atmConstraint = new ATMStraddleConstraint
{
ATMVolType = AtmVolType.ZeroDeltaStraddle,
MarketVol = 0.32
};
var smile25d = new RRBFConstraint
{
Delta = 0.25,
FlyVol = 0.01,
RisykVol = 0.02,
WingQuoteType = WingQuoteType.Arithmatic
};
var s = new AssetSmileSolver();
if (IsCoverageOnly)
{
s.Tollerance = 1;
}
var smile = s.Solve(atmConstraint, new[] { smile25d }, valDate, expDate, fwd, strikes, Interpolator1DType.Linear);
if (!IsCoverageOnly)
{
Assert.Equal(atmConstraint.MarketVol, smile[1], 8);
Assert.Equal(smile25d.RisykVol, smile[2] - smile[0], 8);
Assert.Equal(smile25d.FlyVol, (smile[2] + smile[0]) / 2 - atmConstraint.MarketVol, 8);
}
}
public void SolveSmileMarket()
{
var valDate = new DateTime(2018, 07, 28);
var expDate = valDate.AddDays(365);
var tExp = (expDate - valDate).TotalDays / 365.0;
var fwd = 1000;
double[] strikes = { 0.25, 0.5, 0.75 };
var atmConstraint = new ATMStraddleConstraint
{
ATMVolType = AtmVolType.ZeroDeltaStraddle,
MarketVol = 0.32
};
var smile25d = new RRBFConstraint
{
Delta = 0.25,
FlyVol = 0.01,
RisykVol = 0.02,
WingQuoteType = WingQuoteType.Market
};
var s = new AssetSmileSolver();
if (IsCoverageOnly)
{
s.Tollerance = 1;
}
var smile = s.Solve(atmConstraint, new[] { smile25d }, valDate, expDate, fwd, strikes, Interpolator1DType.Linear);
if (!IsCoverageOnly)
{
Assert.Equal(atmConstraint.MarketVol, smile[1], 8);
}
var surface = new GridVolSurface(valDate, strikes, new[] { expDate }, new[] { smile }, StrikeType.ForwardDelta, Interpolator1DType.Linear, Interpolator1DType.Linear, DayCountBasis.Act365F);
//reprice market RR structrure off smile, premium must match
var marketVolC = atmConstraint.MarketVol + smile25d.FlyVol + 0.5 * smile25d.RisykVol;
var marketVolP = atmConstraint.MarketVol + smile25d.FlyVol - 0.5 * smile25d.RisykVol;
var marketKC25 = BlackFunctions.AbsoluteStrikefromDeltaKAnalytic(fwd, 0.25, 0, tExp, marketVolC);
var marketKP25 = BlackFunctions.AbsoluteStrikefromDeltaKAnalytic(fwd, -0.25, 0, tExp, marketVolP);
var marketC25FV = BlackFunctions.BlackPV(fwd, marketKC25, 0, tExp, marketVolC, OptionType.C);
var marketP25FV = BlackFunctions.BlackPV(fwd, marketKP25, 0, tExp, marketVolP, OptionType.P);
var marketRR = marketC25FV - marketP25FV;
var volC25d = surface.GetVolForAbsoluteStrike(marketKC25, expDate, fwd);
var volP25d = surface.GetVolForAbsoluteStrike(marketKP25, expDate, fwd);
var call25FV = BlackFunctions.BlackPV(fwd, marketKC25, 0, tExp, volC25d, OptionType.C);
var put25FV = BlackFunctions.BlackPV(fwd, marketKP25, 0, tExp, volP25d, OptionType.P);
var smileRR = call25FV - put25FV;
if (!IsCoverageOnly)
{
Assert.Equal(marketRR, smileRR, 8);
}
//reprice market BF structrure off smile, premium must match
var marketVolBF = atmConstraint.MarketVol + smile25d.FlyVol;
var marketKBFC25 = BlackFunctions.AbsoluteStrikefromDeltaKAnalytic(fwd, 0.25, 0, tExp, marketVolBF);
var marketKBFP25 = BlackFunctions.AbsoluteStrikefromDeltaKAnalytic(fwd, -0.25, 0, tExp, marketVolBF);
var marketBFC25FV = BlackFunctions.BlackPV(fwd, marketKBFC25, 0, tExp, marketVolBF, OptionType.C);
var marketBFP25FV = BlackFunctions.BlackPV(fwd, marketKBFP25, 0, tExp, marketVolBF, OptionType.P);
var marketBF = marketBFC25FV + marketBFP25FV;
var volCBF25d = surface.GetVolForAbsoluteStrike(marketKBFC25, expDate, fwd);
var volPBF25d = surface.GetVolForAbsoluteStrike(marketKBFP25, expDate, fwd);
var callBF25FV = BlackFunctions.BlackPV(fwd, marketKBFC25, 0, tExp, volCBF25d, OptionType.C);
var putBF25FV = BlackFunctions.BlackPV(fwd, marketKBFP25, 0, tExp, volPBF25d, OptionType.P);
var smileBF = callBF25FV + putBF25FV;
if (!IsCoverageOnly)
{
Assert.Equal(marketBF, smileBF, 8);
}
}
public RiskyFlySurface(DateTime originDate, double[] ATMVols, DateTime[] expiries, double[] wingDeltas,
double[][] riskies, double[][] flies, double[] fwds, WingQuoteType wingQuoteType, AtmVolType atmVolType,
Interpolator1DType strikeInterpType, Interpolator1DType timeInterpType, string[] pillarLabels = null)
{
if (pillarLabels == null)
{
PillarLabels = expiries.Select(x => x.ToString("yyyy-MM-dd")).ToArray();
}
else
{
PillarLabels = pillarLabels;
}
if (ATMVols.Length != expiries.Length || expiries.Length != riskies.Length || riskies.Length != flies.Length)
{
throw new Exception("Inputs do not have consistent time dimensions");
}
if (wingDeltas.Length != riskies[0].Length || riskies[0].Length != flies[0].Length)
{
throw new Exception("Inputs do not have consistent strike dimensions");
}
var strikes = new double[2 * wingDeltas.Length + 1];
var vols = new double[expiries.Length][];
if (riskies.SelectMany(x => x).All(x => x == 0) && flies.SelectMany(x => x).All(x => x == 0))
{
for (var s = 0; s < wingDeltas.Length; s++)
{
strikes[s] = wingDeltas[wingDeltas.Length - 1 - s];
strikes[strikes.Length - 1 - s] = 1.0 - wingDeltas[wingDeltas.Length - 1 - s];
}
for (var t = 0; t < expiries.Length; t++)
{
vols[t] = Enumerable.Repeat(ATMVols[t], strikes.Length).ToArray();
}
}
else
{
var atmConstraints = ATMVols.Select(a => new ATMStraddleConstraint
{
ATMVolType = atmVolType,
MarketVol = a
}).ToArray();
var needsFlip = wingDeltas.First() > wingDeltas.Last();
if (needsFlip)
{
for (var s = 0; s < wingDeltas.Length; s++)
{
strikes[s] = wingDeltas[wingDeltas.Length - 1 - s];
strikes[strikes.Length - 1 - s] = 1.0 - wingDeltas[wingDeltas.Length - 1 - s];
}
}
else
{
for (var s = 0; s < wingDeltas.Length; s++)
{
strikes[s] = wingDeltas[s];
strikes[strikes.Length - 1 - s] = 1.0 - wingDeltas[s];
}
}
strikes[wingDeltas.Length] = 0.5;
var wingConstraints = new RRBFConstraint[expiries.Length][];
var f = new AssetSmileSolver();
if (needsFlip)
{
for (var i = 0; i < wingConstraints.Length; i++)
{
var offset = wingDeltas.Length - 1;
wingConstraints[i] = new RRBFConstraint[wingDeltas.Length];
for (var j = 0; j < wingConstraints[i].Length; j++)
{
wingConstraints[i][j] = new RRBFConstraint
{
Delta = wingDeltas[offset - j],
FlyVol = flies[i][offset - j],
RisykVol = riskies[i][offset - j],
WingQuoteType = wingQuoteType,
};
}
vols[i] = f.Solve(atmConstraints[i], wingConstraints[i], originDate, expiries[i], fwds[i], strikes, strikeInterpType);
}
}
else
{
for (var i = 0; i < wingConstraints.Length; i++)
{
wingConstraints[i] = new RRBFConstraint[wingDeltas.Length];
for (var j = 0; j < wingConstraints[i].Length; j++)
{
wingConstraints[i][j] = new RRBFConstraint
{
Delta = wingDeltas[j],
FlyVol = flies[i][j],
RisykVol = riskies[i][j],
WingQuoteType = wingQuoteType,
};
}
vols[i] = f.Solve(atmConstraints[i], wingConstraints[i], originDate, expiries[i], fwds[i], strikes, strikeInterpType);
}
}
}
StrikeInterpolatorType = strikeInterpType;
TimeInterpolatorType = timeInterpType;
Expiries = expiries;
ExpiriesDouble = expiries.Select(x => x.ToOADate()).ToArray();
Strikes = strikes;
StrikeType = StrikeType.ForwardDelta;
ATMs = ATMVols;
Riskies = riskies;
Flies = flies;
WingDeltas = wingDeltas;
Forwards = fwds;
WingQuoteType = wingQuoteType;
AtmVolType = atmVolType;
base.Build(originDate, strikes, expiries, vols);
}
public SVIVolSurface(DateTime originDate, double[] ATMVols, DateTime[] expiries, double[] wingDeltas,
double[][] riskies, double[][] flies, double[] fwds, WingQuoteType wingQuoteType, AtmVolType atmVolType,
Interpolator1DType timeInterpType, SviType sviType = SviType.Raw, string[] pillarLabels = null) : base()
{
if (pillarLabels == null)
{
PillarLabels = expiries.Select(x => x.ToString("yyyy-MM-dd")).ToArray();
}
else
{
PillarLabels = pillarLabels;
}
if (ATMVols.Length != expiries.Length || expiries.Length != riskies.Length || riskies.Length != flies.Length)
{
throw new Exception("Inputs do not have consistent time dimensions");
}
if (wingDeltas.Length != riskies[0].Length || riskies[0].Length != flies[0].Length)
{
throw new Exception("Inputs do not have consistent strike dimensions");
}
var atmConstraints = ATMVols.Select(a => new ATMStraddleConstraint
{
ATMVolType = atmVolType,
MarketVol = a
}).ToArray();
var needsFlip = wingDeltas.First() > wingDeltas.Last();
var strikes = new double[2 * wingDeltas.Length + 1];
if (needsFlip)
{
for (var s = 0; s < wingDeltas.Length; s++)
{
strikes[s] = wingDeltas[wingDeltas.Length - 1 - s];
strikes[strikes.Length - 1 - s] = 1.0 - wingDeltas[wingDeltas.Length - 1 - s];
}
}
else
{
for (var s = 0; s < wingDeltas.Length; s++)
{
strikes[s] = wingDeltas[s];
strikes[strikes.Length - 1 - s] = 1.0 - wingDeltas[s];
}
}
strikes[wingDeltas.Length] = 0.5;
var wingConstraints = new RRBFConstraint[expiries.Length][];
RawParams = new SviRawParameters[expiries.Length];
var f = new AssetSmileSolver();
if (needsFlip)
{
for (var i = 0; i < wingConstraints.Length; i++)
{
var offset = wingDeltas.Length - 1;
wingConstraints[i] = new RRBFConstraint[wingDeltas.Length];
for (var j = 0; j < wingConstraints[i].Length; j++)
{
wingConstraints[i][j] = new RRBFConstraint
{
Delta = wingDeltas[offset - j],
FlyVol = flies[i][offset - j],
RisykVol = riskies[i][offset - j],
WingQuoteType = wingQuoteType,
};
}
RawParams[i] = f.SolveSviRaw(atmConstraints[i], wingConstraints[i], originDate, expiries[i], fwds[i], true);
}
}
else
{
for (var i = 0; i < wingConstraints.Length; i++)
{
wingConstraints[i] = new RRBFConstraint[wingDeltas.Length];
for (var j = 0; j < wingConstraints[i].Length; j++)
{
wingConstraints[i][j] = new RRBFConstraint
{
Delta = wingDeltas[j],
FlyVol = flies[i][j],
RisykVol = riskies[i][j],
WingQuoteType = wingQuoteType,
};
}
RawParams[i] = f.SolveSviRaw(atmConstraints[i], wingConstraints[i], originDate, expiries[i], fwds[i], true);
}
}
OriginDate = originDate;
TimeInterpolatorType = timeInterpType;
Expiries = expiries;
ExpiriesDouble = expiries.Select(x => originDate.CalculateYearFraction(x, TimeBasis)).ToArray();
_interps = new IInterpolator1D[5];
_interps[0] = InterpolatorFactory.GetInterpolator(ExpiriesDouble, RawParams.Select(x => x.A).ToArray(), TimeInterpolatorType);
_interps[1] = InterpolatorFactory.GetInterpolator(ExpiriesDouble, RawParams.Select(x => x.B).ToArray(), TimeInterpolatorType);
_interps[2] = InterpolatorFactory.GetInterpolator(ExpiriesDouble, RawParams.Select(x => x.M).ToArray(), TimeInterpolatorType);
_interps[3] = InterpolatorFactory.GetInterpolator(ExpiriesDouble, RawParams.Select(x => x.Rho).ToArray(), TimeInterpolatorType);
_interps[4] = InterpolatorFactory.GetInterpolator(ExpiriesDouble, RawParams.Select(x => x.Sigma).ToArray(), TimeInterpolatorType);
_fwdsInterp = InterpolatorFactory.GetInterpolator(ExpiriesDouble, fwds, Interpolator1DType.Linear);
}
public SabrVolSurface(DateTime originDate, double[] ATMVols, DateTime[] expiries, double[] wingDeltas,
double[][] riskies, double[][] flies, double[] fwds, WingQuoteType wingQuoteType, AtmVolType atmVolType,
Interpolator1DType timeInterpType, string[] pillarLabels = null)
{
if (pillarLabels == null)
{
PillarLabels = expiries.Select(x => x.ToString("yyyy-MM-dd")).ToArray();
}
else
{
PillarLabels = pillarLabels;
}
if (ATMVols.Length != expiries.Length || expiries.Length != riskies.Length || riskies.Length != flies.Length)
{
throw new Exception("Inputs do not have consistent time dimensions");
}
if (wingDeltas.Length != riskies[0].Length || riskies[0].Length != flies[0].Length)
{
throw new Exception("Inputs do not have consistent strike dimensions");
}
var atmConstraints = ATMVols.Select(a => new ATMStraddleConstraint
{
ATMVolType = atmVolType,
MarketVol = a
}).ToArray();
var needsFlip = wingDeltas.First() > wingDeltas.Last();
var strikes = new double[2 * wingDeltas.Length + 1];
if (needsFlip)
{
for (var s = 0; s < wingDeltas.Length; s++)
{
strikes[s] = wingDeltas[wingDeltas.Length - 1 - s];
strikes[strikes.Length - 1 - s] = 1.0 - wingDeltas[wingDeltas.Length - 1 - s];
}
}
else
{
for (var s = 0; s < wingDeltas.Length; s++)
{
strikes[s] = wingDeltas[s];
strikes[strikes.Length - 1 - s] = 1.0 - wingDeltas[s];
}
}
strikes[wingDeltas.Length] = 0.5;
var wingConstraints = new RRBFConstraint[expiries.Length][];
var parameters = new SABRParameters[expiries.Length];
var f = new AssetSmileSolver();
if (needsFlip)
{
for (var i = 0; i < wingConstraints.Length; i++)
{
var offset = wingDeltas.Length - 1;
wingConstraints[i] = new RRBFConstraint[wingDeltas.Length];
for (var j = 0; j < wingConstraints[i].Length; j++)
{
wingConstraints[i][j] = new RRBFConstraint
{
Delta = wingDeltas[offset - j],
FlyVol = flies[i][offset - j],
RisykVol = riskies[i][offset - j],
WingQuoteType = wingQuoteType,
};
}
parameters[i] = f.SolveSABR(atmConstraints[i], wingConstraints[i], originDate, expiries[i], fwds[i], 1.0);
}
}
else
{
for (var i = 0; i < wingConstraints.Length; i++)
{
wingConstraints[i] = new RRBFConstraint[wingDeltas.Length];
for (var j = 0; j < wingConstraints[i].Length; j++)
{
wingConstraints[i][j] = new RRBFConstraint
{
Delta = wingDeltas[j],
FlyVol = flies[i][j],
RisykVol = riskies[i][j],
WingQuoteType = wingQuoteType,
};
}
parameters[i] = f.SolveSABR(atmConstraints[i], wingConstraints[i], originDate, expiries[i], fwds[i], 1.0);
}
}
OriginDate = originDate;
TimeInterpolatorType = timeInterpType;
Expiries = expiries;
ExpiriesDouble = expiries.Select(x => originDate.CalculateYearFraction(x, TimeBasis)).ToArray();
Alphas = parameters.Select(x => x.Alpha).ToArray();
Betas = parameters.Select(x => x.Beta).ToArray();
Nus = parameters.Select(x => x.Nu).ToArray();
Rhos = parameters.Select(x => x.Rho).ToArray();
_alphaInterp = InterpolatorFactory.GetInterpolator(ExpiriesDouble, Alphas, TimeInterpolatorType);
_betaInterp = InterpolatorFactory.GetInterpolator(ExpiriesDouble, Betas, TimeInterpolatorType);
_rhoInterp = InterpolatorFactory.GetInterpolator(ExpiriesDouble, Rhos, TimeInterpolatorType);
_nuInterp = InterpolatorFactory.GetInterpolator(ExpiriesDouble, Nus, TimeInterpolatorType);
_fwdsInterp = InterpolatorFactory.GetInterpolator(ExpiriesDouble, fwds, TimeInterpolatorType);
}
