private void Initialize()
{
var pillarsAsDoubles = _pillarDates.Select(x => x.ToOADate()).ToArray();
switch (_curveType)
{
case PriceCurveType.Linear:
_interp = InterpolatorFactory.GetInterpolator(pillarsAsDoubles, _prices, Interpolator1DType.Linear);
break;
case PriceCurveType.Next:
_interp = InterpolatorFactory.GetInterpolator(pillarsAsDoubles, _prices, Interpolator1DType.NextValue);
break;
case PriceCurveType.NextButOnExpiry:
pillarsAsDoubles = pillarsAsDoubles.Select(x => x - 1).ToArray();
_interp = InterpolatorFactory.GetInterpolator(pillarsAsDoubles, _prices, Interpolator1DType.NextValue);
break;
case PriceCurveType.Constant:
_interp = InterpolatorFactory.GetInterpolator(pillarsAsDoubles, _prices, Interpolator1DType.DummyPoint);
break;
default:
throw new Exception($"Unkown price curve type {_curveType}");
}
}
public HazzardCurve Solve(List <CDS> instruments, double recoveryRate, IIrCurve discountCurve, DateTime buildDate, DayCountBasis basis = DayCountBasis.ACT365F)
{
_curveInstruments = instruments;
_pillars = instruments.OrderBy(x => x.FinalSensitivityDate).Select(c => c.FinalSensitivityDate).ToArray();
_pillarsT = _pillars.Select(p => buildDate.CalculateYearFraction(p, basis)).ToArray();
_numberOfInstruments = _curveInstruments.Count;
_numberOfPillars = _pillars.Length;
_discountCurve = discountCurve;
_buildDate = buildDate;
_basis = basis;
_recoveryRate = recoveryRate;
_currentGuess = instruments.OrderBy(x => x.FinalSensitivityDate).Select((x, ix) => x.Spread / (1.0 - recoveryRate)).ToArray();
_currentCurve = new LinearHazzardInterpolator(_pillarsT, _currentGuess);
_currentPVs = ComputePVs();
ComputeJacobian();
for (var i = 0; i < MaxItterations; i++)
{
ComputeNextGuess();
_currentCurve = new LinearHazzardInterpolator(_pillarsT, _currentGuess);
_currentPVs = ComputePVs();
if (_currentPVs.Max(x => System.Math.Abs(x)) < Tollerance)
{
UsedItterations = i + 1;
break;
}
ComputeJacobian();
}
return(new HazzardCurve(_buildDate, _basis, _currentCurve));
}
public static IInterpolator1D RegressNotContinuous(double[] Xs, double[] Ys, int nSegments)
{
var nSamples = Xs.Length;
//var x = new double[nSegments + 1];
//var y = new double[nSegments + 1];
var samplesPerSegment = nSamples / nSegments;
var interps = new IInterpolator1D[nSegments];
var uBounds = new double[nSegments];
for (var i = 0; i < nSegments; i++)
{
var sampleXs = Xs.Skip(i * samplesPerSegment).Take(samplesPerSegment).ToArray();
var sampleYs = Ys.Skip(i * samplesPerSegment).Take(samplesPerSegment).ToArray();
var lr = LinearRegression.LinearRegressionVector(sampleXs, sampleYs);
var xLo = sampleXs.First();
var xHi = sampleXs.Last();
var yLo = lr.Alpha + lr.Beta * xLo;
var yHi = lr.Alpha + lr.Beta * xHi;
interps[i] = InterpolatorFactory.GetInterpolator(new[] { xLo, xHi }, new[] { yLo, yHi }, Interpolator1DType.Linear);
uBounds[i] = xHi;
}
uBounds[uBounds.Length - 1] = double.MaxValue;
return(new NonContinuousInterpolator(uBounds, interps));
}
private void DumpDataToDisk(KeyValuePair <double, double>[] data, IInterpolator1D fitted, string fileName)
{
var header = new[] { "X,Y,YFited" };
var linesToWrite = header.Concat(data.Select(x => string.Join(",", x.Key, x.Value, fitted.Interpolate(x.Key)))).ToArray();
System.IO.File.WriteAllLines(fileName, linesToWrite);
}
public void Build(DateTime originDate, double[][] strikes, DateTime[] expiries, double[][] vols, Func <double, double> forwardCurve)
{
OriginDate = originDate;
Expiries = expiries;
ExpiriesDouble = Expiries.Select(t => TimeBasis.CalculateYearFraction(originDate, t)).ToArray();
if (Expiries.Length != strikes.Length)
{
throw new InvalidOperationException("Expiries and first dimension of Strikes must of same length");
}
if (Expiries.Length != vols.Length)
{
throw new InvalidOperationException("Expiries and first dimension of Vols must of same length");
}
Alphas = new double[Expiries.Length];
Betas = new double[Expiries.Length];
Nus = new double[Expiries.Length];
Rhos = new double[Expiries.Length];
for (var i = 0; i < expiries.Length; i++)
{
var vs = vols[i];
var ks = strikes[i];
var t = ExpiriesDouble[i];
var fwd = forwardCurve(t);
Betas[i] = 1.0;
Func <double[], double[]> errorFunc = (x =>
{
var err = ks.Select((k, ix) => vs[ix] - SABR.CalcImpVol_Beta1(fwd, k, t, x[0], x[1], x[2]));
return(err.ToArray());
});
var n2Sol = new Math.Solvers.GaussNewton
{
ObjectiveFunction = errorFunc,
InitialGuess = new double[] { vs.Average(), 0.1, 0.1 },
Tollerance = 1e-8,
JacobianBump = 0.0000001
};
var paramArr = n2Sol.Solve();
Alphas[i] = paramArr[0];
Rhos[i] = paramArr[1];
Nus[i] = paramArr[2];
}
var fwds = ExpiriesDouble.Select(x => forwardCurve(x)).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);
}
public IInterpolator1D[] Regress(IAssetFxModel model)
{
if (_regressors != null)
{
return(_regressors);
}
var o = new IInterpolator1D[_dateIndexes.Length];
var nPaths = _pathwiseValues.First().Length;
var finalSchedules = _portfolio.Select(x => x.ExpectedFlowsByPath(model)).ToArray();
ParallelUtils.Instance.For(0, _dateIndexes.Length, 1, d =>
{
var exposureDate = _regressionDates[d];
var sortedFinalValues = new KeyValuePair <double, double> [nPaths];
for (var p = 0; p < nPaths; p++)
{
var finalValue = 0.0;
foreach (var schedule in finalSchedules)
{
foreach (var flow in schedule[p].Flows)
{
if (flow.SettleDate > exposureDate)
{
finalValue += flow.Pv;
}
}
}
sortedFinalValues[p] = new KeyValuePair <double, double>(_pathwiseValues[d][p], finalValue);
}
sortedFinalValues = sortedFinalValues.OrderBy(q => q.Key).ToArray();
if (_requireContinuity)
{
o[d] = SegmentedLinearRegression.Regress(sortedFinalValues.Select(x => x.Key).ToArray(), sortedFinalValues.Select(y => y.Value).ToArray(), 5);
}
else
{
o[d] = SegmentedLinearRegression.RegressNotContinuous(sortedFinalValues.Select(x => x.Key).ToArray(), sortedFinalValues.Select(y => y.Value).ToArray(), 5);
}
if (DebugMode)
{
DumpDataToDisk(sortedFinalValues, o[d], $@"C:\temp\regData{d}.csv");
}
}).Wait();
_regressors = o;
return(o);
}
private double GetVolForAbsoluteStrike(double strike, IInterpolator1D interp)
{
var cp = strike < 0 ? OptionType.Put : OptionType.Call;
Func <double, double> testFunc = (deltaK =>
{
var vol = interp.Interpolate(-deltaK);
var absK = AbsoluteStrikefromDeltaKAnalytic(_fwd, deltaK, 0, _tExp, vol);
return(absK - strike);
});
var solvedStrike = -Brent.BrentsMethodSolve(testFunc, -0.999999999, -0.000000001, 1e-8);
return(interp.Interpolate(solvedStrike));
}
public static IInterpolator1D GeneratePDF(this IInterpolator1D smile, int numSamples, double t, double fwd)
{
var deltaK = fwd * 0.0001;
var atmVol = smile.Interpolate(fwd);
var lowStrike = BlackFunctions.AbsoluteStrikefromDeltaKAnalytic(fwd, -0.0001, 0, t, atmVol);
var hiStrike = BlackFunctions.AbsoluteStrikefromDeltaKAnalytic(fwd, -0.9999, 0, t, atmVol);
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 = smile.Interpolate(k - deltaK);
var callLow = BlackFunctions.BlackPV(fwd, k - deltaK, 0, t, volLow, OptionType.C);
var volMid = smile.Interpolate(k);
var callMid = BlackFunctions.BlackPV(fwd, k, 0, t, volMid, OptionType.C);
var volHi = smile.Interpolate(k + deltaK);
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));
}
private void Initialize()
{
var pillarsAsDoubles = _pillarDates.Select(x => x.ToOADate()).ToArray();
switch (_curveType)
{
case SparsePriceCurveType.Coal:
_interpA = InterpolatorFactory.GetInterpolator(pillarsAsDoubles, _prices, Interpolator1DType.LinearFlatExtrap);
var allDates = _pillarDates.First().CalendarDaysInPeriod(_pillarDates.Last());
var monthlyDates = allDates.Select(x => x.NthLastSpecificWeekDay(DayOfWeek.Friday, 1)).Distinct();
var monthlyPillars = monthlyDates.Select(x => x.ToOADate()).ToArray();
var monthlyPrices = _interpA.Many(monthlyPillars).ToArray();
_interpB = InterpolatorFactory.GetInterpolator(monthlyPillars, monthlyPrices, Interpolator1DType.NextValue);
break;
}
}
private void ComputeJacobian()
{
_jacobian = Math.Matrix.DoubleArrayFunctions.MatrixCreate(_numberOfPillars, _numberOfPillars);
for (var i = 0; i < _numberOfPillars; i++)
{
_currentCurve = new LinearHazzardInterpolator(_pillarsT, _currentGuess.Select((g, ix) => ix == i ? g + JacobianBump : g).ToArray());
var bumpedPVs = ComputePVs();
for (var j = 0; j < bumpedPVs.Length; j++)
{
_jacobian[i][j] = (bumpedPVs[j] - _currentPVs[j]) / JacobianBump;
}
}
_currentCurve = new LinearHazzardInterpolator(_pillarsT, _currentGuess);
}
public IrCurve(DateTime[] pillars, double[] rates, DateTime buildDate, string name, Interpolator1DType interpKind)
{
_interpKind = interpKind;
_pillars = new DateTime[pillars.Length];
pillars.CopyTo(_pillars, 0);
_rates = new double[_pillars.Length];
var pillarsD = new double[_pillars.Length];
_buildDate = buildDate;
for (var i = 0; i < pillars.Length; i++)
{
pillarsD[i] = buildDate.CalculateYearFraction(pillars[i], _basis);
_rates[i] = rates[i];
}
_interpolator = InterpolatorFactory.GetInterpolator(pillarsD.ToArray(), _rates.ToArray(), interpKind, isSorted: true, noCopy: true);
_name = name;
}
public static double InverseCDF(IInterpolator1D putPremiumInterp, double t, double fwd, double p)
{
var deltaK = fwd * 1e-8;
var targetFunc = new Func <double, double>(k =>
{
var digi = putPremiumInterp.FirstDerivative(k);
return(p - digi);
});
var targetFunc2 = new Func <double, double>(k => - putPremiumInterp.SecondDerivative(k));
//var b = Math.Solvers.Brent.BrentsMethodSolve(targetFunc, lowGuess, highGuess, 1e-6);
var b = Math.Solvers.Newton1D.MethodSolve(targetFunc, targetFunc2, fwd, 1e-6, 1000);
if (double.IsInfinity(b) || double.IsNaN(b))
{
throw new Exception("Invalid strike found");
}
return(b);
}
public static IInterpolator1D GenerateCDF(this IInterpolator1D smile, int numSamples, double t, double fwd)
{
var deltaK = fwd * 0.0001;
var atmVol = smile.Interpolate(fwd);
var lowStrike = BlackFunctions.AbsoluteStrikefromDeltaKAnalytic(fwd, -0.0001, 0, t, atmVol);
var hiStrike = BlackFunctions.AbsoluteStrikefromDeltaKAnalytic(fwd, -0.9999, 0, t, atmVol);
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] = k / 2.0;
y[0] = 0;
continue;
}
if (i == x.Length - 1)
{
x[i] = k * 2;
y[i] = 1;
continue;
}
var volLow = smile.Interpolate(k - deltaK / 2.0);
var putLow = BlackFunctions.BlackPV(fwd, k - deltaK / 2.0, 0, t, volLow, OptionType.P);
var volHi = smile.Interpolate(k + deltaK / 2.0);
var putHi = BlackFunctions.BlackPV(fwd, k + deltaK / 2.0, 0, t, volHi, OptionType.P);
var digital = (putHi - putLow) / deltaK;
y[i] = digital;
x[i] = k;
k += kStep;
}
return(InterpolatorFactory.GetInterpolator(x, y, Interpolator1DType.Linear));
}
public IrCurve(DateTime[] pillars, double[] rates, DateTime buildDate, string name, Interpolator1DType interpKind, Currency ccy, string collateralSpec = null, RateType rateStorageType = RateType.Exponential)
{
_interpKind = interpKind;
_rateStorageType = rateStorageType;
_pillars = new DateTime[pillars.Length];
pillars.CopyTo(_pillars, 0);
_rates = new double[_pillars.Length];
var pillarsD = new double[_pillars.Length];
_buildDate = buildDate;
for (var i = 0; i < pillars.Length; i++)
{
pillarsD[i] = buildDate.CalculateYearFraction(pillars[i], _basis);
_rates[i] = rates[i];
}
_interpolator = InterpolatorFactory.GetInterpolator(pillarsD.ToArray(), _rates.ToArray(), interpKind, isSorted: true, noCopy: true);
_name = name;
Currency = ccy;
CollateralSpec = collateralSpec ?? (string.IsNullOrWhiteSpace(_name) ? null :
(_name.Contains("[")) ? _name.Split('[').Last().Trim("[]".ToCharArray()) : _name.Split('.').Last());
}
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);
}
private void Initialize()
{
var pillarsAsDoubles = PillarDates.Select(x => x.ToOADate()).ToArray();
_interp = InterpolatorFactory.GetInterpolator(pillarsAsDoubles, Contangos, 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);
}
public static double Average(this IInterpolator1D interp, IEnumerable <double> Xs) => Xs.Average(x => interp.Interpolate(x));
public HazzardCurve(DateTime originDate, DayCountBasis basis, IInterpolator1D hazzardRateInterpolator)
{
OriginDate = originDate;
Basis = basis;
_hazzardCurve = hazzardRateInterpolator;
}
public static double MinY(this IInterpolator1D interp, IEnumerable <double> Xs) => Xs.Min(x => interp.Interpolate(x));
public static double Sum(this IInterpolator1D interp, IEnumerable <double> Xs) => Xs.Sum(x => interp.Interpolate(x));
private void UpdateInterpolator() => _interp = InterpolatorFactory.GetInterpolator(_strikes, _currentGuess, _interpType);
public static double VanillaPV(double T, double S, double K, IInterpolator1D r_interp, double sigma, OptionType CP, IInterpolator1D fwd_interp, int n, bool isAmerican)
{
var deltaT = T / (double)n;
var u = System.Math.Exp(sigma * System.Math.Sqrt(2.0 * deltaT));
var d = System.Math.Exp(-sigma * System.Math.Sqrt(2.0 * deltaT));
var Z = sigma * System.Math.Sqrt(deltaT / 2.0);
var p = new double[n * 2 + 1];
double exercise, spot;
double cp = CP == OptionType.Call ? 1 : -1;
//initial values at time T
for (var i = 0; i <= 2 * n; i++)
{
spot = S * System.Math.Pow(d, n - i);
p[i] = System.Math.Max(0, cp * (S * System.Math.Pow(u, System.Math.Max(i - n, 0)) * System.Math.Pow(d, System.Math.Max(n - i, 0)) - K));
}
//move back to earlier times
for (var j = n - 1; j >= 0; j--)
{
var t_step = T * (double)j / (double)n;
var t_stepPrev = T * (double)(j + 1) / (double)n;
var r = System.Math.Log(System.Math.Exp(r_interp.Interpolate(t_stepPrev) * t_stepPrev) / System.Math.Exp(r_interp.Interpolate(t_step) * t_step)) / deltaT;
var q = r - System.Math.Log(fwd_interp.Interpolate(t_stepPrev) / fwd_interp.Interpolate(t_step)) / deltaT;
var df1p = System.Math.Exp(-r * deltaT);
var pu = (System.Math.Exp((r - q) * deltaT / 2.0) - System.Math.Exp(-Z)) / (System.Math.Exp(Z) - System.Math.Exp(-Z));
var pd = (System.Math.Exp(Z) - System.Math.Exp((r - q) * deltaT / 2.0)) / (System.Math.Exp(Z) - System.Math.Exp(-Z));
pu *= pu;
pd *= pd;
var pm = 1 - (pu + pd);
for (var i = 0; i <= j * 2; i++)
{
spot = S * System.Math.Pow(u, i - j);
p[i] = df1p * (pd * p[i] + pm * p[i + 1] + pu * p[i + 2]);
if (isAmerican)
{
if (CP == OptionType.Put)
{
exercise = K - spot; //exercise value
}
else
{
exercise = spot - K; //exercise value
}
if (p[i] < exercise)
{
p[i] = exercise;
}
}
}
}
return(p[0]);
}
public static double[] Many(this IInterpolator1D interp, IEnumerable <double> Xs) => Xs.Select(x => interp.Interpolate(x)).ToArray();
public LinearHazzardInterpolator(double[] xs, double[] hs)
{
_xs = xs;
_hs = hs;
_linearInterp = InterpolatorFactory.GetInterpolator(xs, hs, Interpolator1DType.LinearFlatExtrap);
}
public static TO_Interpolator1d ToTransportObject(this IInterpolator1D interp)
{
switch (interp)
{
case LinearInterpolatorFlatExtrap i1:
return(new TO_Interpolator1d
{
Xs = i1.Xs,
Ys = i1.Ys,
Type = Interpolator1DType.LinearFlatExtrap
});
case LinearInterpolator i2:
return(new TO_Interpolator1d
{
Xs = i2.Xs,
Ys = i2.Ys,
Type = Interpolator1DType.Linear
});
case LinearInVarianceInterpolator i3:
return(new TO_Interpolator1d
{
Xs = i3.Xs,
Ys = i3.Ys,
Type = Interpolator1DType.LinearInVariance
});
case GaussianKernelInterpolator i4:
return(new TO_Interpolator1d
{
Xs = i4.Xs,
Ys = i4.Ys,
Type = Interpolator1DType.GaussianKernel
});
case NextInterpolator i5:
return(new TO_Interpolator1d
{
Xs = i5.Xs,
Ys = i5.Ys,
Type = Interpolator1DType.NextValue
});
case PreviousInterpolator i6:
return(new TO_Interpolator1d
{
Xs = i6.Xs,
Ys = i6.Ys,
Type = Interpolator1DType.PreviousValue
});
case CubicHermiteSplineInterpolator i7:
return(new TO_Interpolator1d
{
Xs = i7.Xs,
Ys = i7.Ys,
Type = Interpolator1DType.CubicSpline
});
case DummyPointInterpolator i8:
return(new TO_Interpolator1d
{
Xs = new[] { i8.Point },
Ys = new[] { i8.Point },
Type = Interpolator1DType.DummyPoint
});
case ConstantHazzardInterpolator i9:
return(new TO_Interpolator1d
{
Xs = new[] { i9.H },
Ys = new[] { i9.H },
Type = Interpolator1DType.ConstantHazzard
});
default:
throw new InvalidOperationException($"We don't have a way of serializing a {interp.GetType().Name} interpolator");
}
}