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 void SampleStrike(AssetMarket assetMkt)
{
DateTime maturity = assetMkt.RefDate + 3 * Duration.Year;
var fwd = assetMkt.Forward().Fwd(maturity);
double t = assetMkt.Time[maturity];
var pricer = BlackScholesWithDividendOption.Build(assetMkt.Spot, assetMkt.Dividends, assetMkt.RiskFreeDiscount, assetMkt.Time);
var vols = GridUtils.RegularGrid(0.05, 1.0, 50);
var moneynesses = GridUtils.RegularGrid(-10.0, 10.0, 51);
foreach (double vol in vols)
{
var stdDev = vol * Math.Sqrt(t);
foreach (double m in moneynesses)
{
var strike = fwd * Math.Exp(stdDev * m);
var price = pricer.Price(t, strike, vol, m > 0 ? 1 : -1);
var impliedVol = pricer.ImpliedVol(t, strike, price, m > 0 ? 1 : -1);
var errRelative = (impliedVol - vol) / vol;
Assert.IsTrue(Math.Abs(errRelative) < 5.0e-13);
}
}
}
