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); } } }