public void CheckZeroVolForward(AssetMarket assetMkt)
{
var zcCurve = assetMkt.RiskFreeDiscount;
var market = new Market(new[] { zcCurve }, new[] { assetMkt });
var zeroVol = new MapRawDatas <DateOrDuration, double>(new[] { new DateOrDuration(assetMkt.RefDate) }, new[] { 0.0 });
var blackScholesDesc = new BlackScholesModelDescription(assetMkt.Asset.Name, zeroVol, true);
var mcConfig = new MonteCarloConfig(1, RandomGenerators.GaussianSobol(SobolDirection.Kuo3));
var blackScholesModel = ModelFactory.Instance.Build(blackScholesDesc, market);
var fwdDates = new[] { Duration.Month, 6 * Duration.Month, Duration.Year, 2 * Duration.Year, 5 * Duration.Year }
.Map(d => assetMkt.RefDate + d);
IProduct fwdLeg = ForwardLeg(fwdDates);
PriceResult priceResult = (PriceResult)McPricer.WithDetails(mcConfig).Price(fwdLeg, blackScholesModel, market);
double[] fwds = priceResult.Details.Map(kv => kv.Item3.Value);
var assetFwdCurve = assetMkt.Forward();
double[] refFwds = fwdDates.Map(d => assetFwdCurve.Fwd(d) * zcCurve.Zc(d));
foreach (var i in Enumerable.Range(0, fwdDates.Length))
{
var err = Math.Abs(fwds[i] / refFwds[i] - 1.0);
Assert.LessOrEqual(err, 20.0 * DoubleUtils.MachineEpsilon);
}
}
public override IModelDescription Calibrate(BlackScholesModelCalibDesc bsDesc, Market market)
{
AssetMarket assetMkt = market.AssetMarketFromName(bsDesc.Asset);
var volSurface = assetMkt.VolSurface();
var forwardCurve = assetMkt.Forward();
var optionPricer = BlackScholesWithDividendOption.Build(assetMkt.Spot, assetMkt.Dividends, assetMkt.RiskFreeDiscount, assetMkt.Time);
var calibMaturities = bsDesc.CalibrationMaturities.Map(d => d.ToDate(assetMkt.RefDate));
var calibStrikes = bsDesc.CalibrationStrikes;
var calibDates = assetMkt.Time[calibMaturities];
double[] targetPrices = new double[calibDates.Length];
double[] optionTypes = new double[calibDates.Length];
for (int i = 0; i < calibMaturities.Length; i++)
{
var targetVol = volSurface.Volatility(calibDates[i], calibStrikes[i]);
var optionType = (calibStrikes[i] > forwardCurve.Fwd(calibMaturities[i])) ? 1.0 : -1.0;
targetPrices[i] = optionPricer.Price(calibDates[i], calibStrikes[i], targetVol, optionType);
optionTypes[i] = optionType;
}
var calibratedVols = optionPricer.CalibrateVol(calibDates, targetPrices, bsDesc.CalibrationStrikes, optionTypes);
var sigma = new MapRawDatas <DateOrDuration, double>(bsDesc.CalibrationMaturities, calibratedVols);
return(new BlackScholesModelDescription(bsDesc.Asset, sigma, bsDesc.WithDivs));
}
public Bergomi2FModelDescription(string asset, bool withDivs, MapRawDatas <DateOrDuration, double> sigma,
double k1, double k2, double theta, double nu, double rhoXy, double rhoSx, double rhoSy)
{
Asset = asset;
WithDivs = withDivs;
Sigma = sigma;
K1 = k1;
K2 = k2;
Theta = theta;
Nu = nu;
RhoXY = rhoXy;
RhoSX = rhoSx;
RhoSY = rhoSy;
Asset = asset;
}
public ICalibrationDescription Build(object[,] bag)
{
var assetName = bag.ProcessScalarString("Asset");
var withDivs = !bag.Has("WithDivs") || bag.ProcessScalarBoolean("WithDivs");
var calibDatas = bag.ProcessTimeMatrixDatas("CalibDate");
if (calibDatas.HasCol("Sigma"))
{
var sigmaValues = calibDatas.GetColFromLabel("Sigma");
var sigma = new MapRawDatas <DateOrDuration, double>(calibDatas.RowLabels, sigmaValues);
var bsDescription = new BlackScholesModelDescription(assetName, sigma, withDivs);
return(new ExplicitCalibration <BlackScholesModelDescription>(bsDescription));
}
var calibStrikes = calibDatas.GetColFromLabel("Strike");
return(new BlackScholesModelCalibDesc(assetName, withDivs, calibDatas.RowLabels, calibStrikes));
}
private static RrFunction BuildXi(MapRawDatas <DateOrDuration, double> sigma, ITimeMeasure time)
{
var matVars = EnumerableUtils.For(0, sigma.Pillars.Length, i =>
{
var mat = time[sigma.Pillars[i].ToDate(time.RefDate)];
var variance = sigma.Values[i] * sigma.Values[i] * mat;
return(new { Mat = mat, Variance = variance });
}).OrderBy(t => t.Mat).ToArray();
if (!DoubleUtils.EqualZero(matVars.First().Mat))
{
matVars = matVars.Concat(new[] { new { Mat = 0.0, Variance = 0.0 } })
.OrderBy(t => t.Mat).ToArray();
}
var varianceFunc = RrFunctions.LinearInterpolation(matVars.Map(t => t.Mat),
matVars.Map(t => t.Variance),
0.0, double.NaN);
return(varianceFunc.Derivative());
}
public ICalibrationDescription Build(object[,] bag)
{
string assetName = bag.ProcessScalarString("Asset");
bool withDivs = !bag.Has("WithDivs") || bag.ProcessScalarBoolean("WithDivs");
var calibDatas = bag.ProcessTimeMatrixDatas("Date");
var sigmaValues = calibDatas.GetColFromLabel("Sigma");
var sigma = new MapRawDatas <DateOrDuration, double>(calibDatas.RowLabels, sigmaValues);
double k1 = bag.ProcessScalarDouble("K1");
double k2 = bag.ProcessScalarDouble("K2");
double theta = bag.ProcessScalarDouble("Theta");
double nu = bag.ProcessScalarDouble("Nu");
double rhoXY = bag.ProcessScalarDouble("RhoXY");
double rhoSX = bag.ProcessScalarDouble("RhoSX");
double rhoSY = bag.ProcessScalarDouble("RhoSY");
Bergomi2FModelDescription b2FDescription = new Bergomi2FModelDescription(assetName, withDivs, sigma,
k1, k2, theta, nu, rhoXY, rhoSX, rhoSY);
return(new ExplicitCalibration <Bergomi2FModelDescription>(b2FDescription));
}
public static RrFunction ToStepFunction(this MapRawDatas <DateOrDuration, double> rawDatasFunc, ITimeMeasure time)
{
var abscissae = rawDatasFunc.Pillars.Map(d => time[d.ToDate(time.RefDate)]);
return(new StepFunction(abscissae, rawDatasFunc.Values, rawDatasFunc.Values.First()));
}
public Hw1ModelDescription(Currency currency, double meanReversion, MapRawDatas <DateOrDuration, double> sigma)
{
Sigma = sigma;
MeanReversion = meanReversion;
Currency = currency;
}
public BlackScholesModelDescription(string asset, MapRawDatas <DateOrDuration, double> sigma, bool withDivs)
{
Sigma = sigma;
WithDivs = withDivs;
Asset = asset;
}