public void LVMC_PathsGenerated()
{
var origin = DateTime.Now.Date;
using var engine = new PathEngine(2.IntPow(IsCoverageOnly ? 6 : 12))
{
Parallelize = false
};
engine.AddPathProcess(new Random.MersenneTwister.MersenneTwister64()
{
UseNormalInverse = true,
UseAnthithetic = true
});
var tenorsStr = new[] { "1m", "2m", "3m", "6m" };
var tenors = tenorsStr.Select(x => new Frequency(x));
var expiries = tenors.Select(t => origin.AddPeriod(RollType.F, new Calendar(), t)).ToArray();
var deltaKs = new[] { 0.1, 0.25, 0.5, 0.75, 0.9 };
var smileVols = new[] { 0.32, 0.3, 0.29, 0.3, 0.32 };
var vols = Enumerable.Repeat(smileVols, expiries.Length).ToArray();
var tExp = (origin.AddMonths(6) - origin).TotalDays / 365.0;
var volSurface = new GridVolSurface(origin, deltaKs, expiries, vols,
StrikeType.ForwardDelta, Interpolator1DType.GaussianKernel,
Interpolator1DType.LinearInVariance, DayCountBasis.Act365F);
var fwdCurve = new Func <double, double>(t => { return(900 + 100 * t / tExp); });
var asset = new LVSingleAsset
(
startDate: origin,
expiryDate: origin.AddMonths(6),
volSurface: volSurface,
forwardCurve: fwdCurve,
nTimeSteps: IsCoverageOnly ? 3 : 100,
name: "TestAsset"
);
engine.AddPathProcess(asset);
var payoff = new EuropeanPut("TestAsset", 900, origin.AddMonths(6));
var payoff2 = new EuropeanCall("TestAsset", 0, origin.AddMonths(6));
engine.AddPathProcess(payoff);
engine.AddPathProcess(payoff2);
engine.SetupFeatures();
engine.RunProcess();
var pv = payoff.AverageResult;
var blackVol = volSurface.GetVolForAbsoluteStrike(900, origin.AddMonths(6), fwdCurve(tExp));
var blackPv = BlackFunctions.BlackPV(fwdCurve(tExp), 900, 0, tExp, blackVol, OptionType.P);
if (!IsCoverageOnly)
{
Assert.True(System.Math.Abs(blackPv / pv - 1.0) < 0.02);
var fwd = payoff2.AverageResult;
Assert.True(System.Math.Abs(fwdCurve(tExp) / fwd - 1.0) < 0.005);
}
}
public void LVMC_PathsGenerated()
{
var origin = DateTime.Now.Date;
var engine = new PathEngine(2.IntPow(17));
//engine.AddPathProcess(new Random.MersenneTwister.MersenneTwister64()
//{
// UseNormalInverse = true,
// UseAnthithetic = false
//});
engine.AddPathProcess(new Random.Sobol.SobolShiftedPathGenerator(new Random.Sobol.SobolDirectionNumbers(s_directionNumbers), 0)
{
UseNormalInverse = true
});
var tenorsStr = new[] { "1m", "2m", "3m", "6m", "9m", "1y" };
var tenors = tenorsStr.Select(x => new Frequency(x));
var expiries = tenors.Select(t => origin.AddPeriod(RollType.F, new Calendar(), t)).ToArray();
var deltaKs = new[] { -0.1, -0.25, -0.5, -0.75, -0.9 };
var smileVols = new[] { 0.32, 0.3, 0.29, 0.3, 0.32 };
var vols = Enumerable.Repeat(smileVols, expiries.Length).ToArray();
var volSurface = new GridVolSurface(origin, deltaKs, expiries, vols,
Core.Basic.StrikeType.ForwardDelta, Interpolator1DType.LinearFlatExtrap,
Interpolator1DType.LinearInVariance, DayCountBasis.Act365F);
var fwdCurve = new Func <double, double>(t => { return(900 + 100 * t); });
var asset = new LVSingleAsset
(
startDate: origin,
expiryDate: origin.AddYears(1),
volSurface: volSurface,
forwardCurve: fwdCurve,
nTimeSteps: 365,
name: "TestAsset"
);
engine.AddPathProcess(asset);
var payoff = new EuropeanPut("TestAsset", 900, origin.AddYears(1));
var payoff2 = new EuropeanCall("TestAsset", 0, origin.AddYears(1));
engine.AddPathProcess(payoff);
engine.AddPathProcess(payoff2);
engine.SetupFeatures();
engine.RunProcess();
var pv = payoff.AverageResult;
var blackVol = volSurface.GetVolForAbsoluteStrike(900, origin.AddYears(1), fwdCurve(1.0));
var blackPv = BlackFunctions.BlackPV(1000, 900, 0, 1, blackVol, OptionType.P);
Assert.Equal(blackPv, pv, 0);
var fwd = payoff2.AverageResult;
Assert.True(System.Math.Abs(fwdCurve(1) / fwd - 1.0) < 0.001);
//var output = new OutputPathsToImage(engine,2000,1000);
}
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);
}
}