public static DiscountCurve LinearRateInterpol(FinancingId financing, DateTime[] pillars, double[] zcs, ITimeMeasure time)
{
if (pillars.Length != zcs.Length)
throw new Exception("LinearRateDiscountProvider : Incompatible size");
var dates = time[pillars];
var zcRates = new double[pillars.Length];
if (DoubleUtils.EqualZero(dates[0]))
{
if (!DoubleUtils.MachineEquality(1.0, zcs[0]))
throw new Exception("LinearRateInterpol : Discount for refDate must equal to 1.0 ");
zcRates[0] = 0.0;
}
else
{
zcRates[0] = -Math.Log(zcs[0]) / dates[0];
}
for (int i = 1; i < zcs.Length; i++)
{
zcRates[i] = -Math.Log(zcs[i]) / dates[i];
}
return new DiscountCurveFromRate(financing, time, RrFunctions.LinearInterpolation(dates, zcRates));
}
public void TestEval()
{
var abs = new[] { 0.0, 0.5, 0.99, 2.5 };
var vals = new[] { 5.0, 5.4, 3.1, 1.0 };
const double leftSlope = 0.0;
const double rightSlope = 0.98181;
var stepFunc = RrFunctions.LinearInterpolation(abs, vals, leftSlope, rightSlope);
foreach (var i in Enumerable.Range(0, abs.Length))
{
Assert.AreEqual(stepFunc.Eval(abs[i]), vals[i]);
if (i < abs.Length - 1)
{
var midPoint = 0.5 * (abs[i] + abs[i + 1]);
Assert.AreEqual(stepFunc.Eval(midPoint), 0.5 * (vals[i] + vals[i + 1]));
}
}
double leftExtrapolPoint = abs[0] - 10.0;
Assert.AreEqual(stepFunc.Eval(leftExtrapolPoint), vals[0] + leftSlope * (leftExtrapolPoint - abs[0]));
double rightExtrapolPoint = abs[abs.Length - 1] + 10.0;
Assert.AreEqual(stepFunc.Eval(rightExtrapolPoint), vals[abs.Length - 1] + rightSlope * (rightExtrapolPoint - abs[abs.Length - 1]));
}
public static RrFunction ZcRateCoeffFunction(double maturity, double meanReversion)
{
var expMat = Math.Exp(-meanReversion * maturity);
if (DoubleUtils.MachineEquality(1.0, expMat))
{
return(RrFunctions.Affine(1.0, -maturity));
}
return((expMat / meanReversion) * RrFunctions.Exp(meanReversion) - (1.0 / meanReversion));
}
public void TestIntegralExp()
{
var exp = RrFunctions.Exp(0.1);
var step = new StepFunction(new[] { 0.0, 5.0 }, new[] { 0.015, 0.010 }, 0.0);
var f = exp * step;
var integral = f.Integral(0.0);
var testVal = integral.Eval(10.0);
var expintegral = exp.Integral(0.0);
var refVal = 0.015 * (expintegral.Eval(5.0) - expintegral.Eval(0.0))
+ 0.01 * (expintegral.Eval(10.0) - expintegral.Eval(5.0));
Assert.IsTrue(DoubleUtils.Equality(testVal, refVal, 1.5 * DoubleUtils.MachineEpsilon));
}
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());
}
private static double[][] VarSwapDeformation(Bergomi2FModel b2F, double[] fwdVolStart, double[] fwdVolEnd)
{
Debug.Assert(fwdVolStart.Length == fwdVolEnd.Length);
var initCurve = b2F.Xi.Integral(0.0);
var factor1 = (b2F.Xi * RrFunctions.Exp(-b2F.K1)).Integral(0.0);
var factor2 = (b2F.Xi * RrFunctions.Exp(-b2F.K2)).Integral(0.0);
var alpha = Alpha(b2F);
return(EnumerableUtils.For(0, fwdVolStart.Length, i =>
{
double volMatStart = fwdVolStart[i];
double volMatEnd = fwdVolEnd[i];
double initFwdVariance = initCurve.Eval(volMatEnd) - initCurve.Eval(volMatStart);
double def1 = factor1.Eval(volMatEnd) - factor1.Eval(volMatStart);
double def2 = factor2.Eval(volMatEnd) - factor2.Eval(volMatStart);
return new[] { (1.0 - b2F.Theta) * def1, b2F.Theta * def2 }.Mult(b2F.Nu * alpha / initFwdVariance);
}));
}
public static RrFunction IntegratedCovariance(RrFunction instantCovariance, double meanReversion1, double meanReversion2, double startDate = 0.0)
{
var integratedExpCov = (instantCovariance * RrFunctions.Exp(meanReversion1 + meanReversion2)).Integral(startDate);
return(integratedExpCov * RrFunctions.Exp(-(meanReversion1 + meanReversion2)));
}
public static RrFunction IntegratedDrift(RrFunction instantDrift, double meanReversion, double startDate = 0.0)
{
var integratedExpDrift = (instantDrift * RrFunctions.Exp(meanReversion)).Integral(startDate);
return(integratedExpDrift * RrFunctions.Exp(-meanReversion));
}
public double[] CalibrateVol(double[] maturities, double[] targetPrices, double[] strikes, double[] optionTypes)
{
Contract.Requires(EnumerableUtils.IsSorted(maturities));
Contract.Requires(maturities.Length == strikes.Length &&
strikes.Length == targetPrices.Length &&
targetPrices.Length == optionTypes.Length);
double[] variances = new double[maturities.Length + 1];
double[] varPillars = new[] { 0.0 }.Concat(maturities).ToArray();
double[] calibVols = new double[maturities.Length];
for (int step = 0; step < maturities.Length; step++)
{
var maturity = maturities[step];
var strike = strikes[step];
var targetPrice = targetPrices[step];
var q = optionTypes[step];
//Proxy using Lehman Formula
double proxyFwd, proxyDk;
affineDivUtils.LehmanProxy(maturity, spot, out proxyFwd, out proxyDk);
double lehmanTargetVol = BlackScholesOption.ImpliedVol(targetPrice, proxyFwd, strike + proxyDk, maturity, q);
var pricer = new BsDivPrice(maturities[step], strikes[step], spot, affineDivUtils, quadPoints, quadWeights);
Func <double, double> volToLehmanVolErr = v =>
{
variances[1 + step] = v * v * maturity;
var varFunc = RrFunctions.LinearInterpolation(varPillars, variances);
Func <double, double> volFunc = t => Math.Sqrt(varFunc.Eval(t) / t);
var price = pricer.Price(volFunc, q);
return(BlackScholesOption.ImpliedVol(price, proxyFwd, strike + proxyDk, maturity, q) - lehmanTargetVol);
};//TODO use a cache
//Bracket & Solve
double v1 = lehmanTargetVol;
double v2;
if (step == 0)
{
v2 = lehmanTargetVol - volToLehmanVolErr(lehmanTargetVol);
}
else
{
var volIfZeroVolOnStep = Math.Sqrt(calibVols[step - 1] * calibVols[step - 1] * maturities[step - 1] / maturities[step]);
var minError = volToLehmanVolErr(volIfZeroVolOnStep);
if (minError > 0.0) //saturation case
{
calibVols[step] = volIfZeroVolOnStep;
variances[1 + step] = volIfZeroVolOnStep * volIfZeroVolOnStep * maturity;
continue;
}
v2 = volIfZeroVolOnStep;
}
if (!RootUtils.Bracket(volToLehmanVolErr, v1, v2, out v1, out v2))
{
throw new Exception("Failed to inverse vol");
}
var impliedVol = RootUtils.Brenth(volToLehmanVolErr, v1, v2, 1.0e-10, 2.0 * DoubleUtils.MachineEpsilon, 10);
calibVols[step] = impliedVol;
variances[1 + step] = impliedVol * impliedVol * maturity;
}
return(calibVols);
}
