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 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));
}