// ---------------------------------------------------------------------
// Business logic methods.
// ---------------------------------------------------------------------
/// <summary>
/// Computes the BGS convexity correction. The magnitude of the
/// correction, as described in the document "Pricing Analytics for a
/// Balance Guaranteed Swap", prepared by George Scoufis,
/// Reference Number GS-02042007/1 is:
/// F0*{1 - Phi(d1) - (L/B0)^(1 + 2*alpha/sigma^2)*phi(d2)}.
/// Periods in the formula for F0, d1 and d2 are computed with
/// ACT/365 day count.</summary>
/// <param name="lastAmortisationDate">The date of the most recent
/// realised amortisation.</param>
/// <param name="amortisationDate">The date to which the convexity
/// correction is required.</param>
/// <param name="currentBondFactor">The current Bond Factor.</param>
/// <param name="alpha">The parameter alpha in the Bond Factor curve
/// model.</param>
/// <param name="sigma">The parameter sigma in the Bond Factor curve
/// model.</param>
/// <param name="cleanUp">The clean up condition. If the current
/// Bond Factor is less than or equal to the clean up, then the
/// convexity correction is 0.0.</param>
/// <returns>Convexity correction. Logic has been added to cater for
/// the limiting cases: 1) sigma->0; 2) clean up ->0.</returns>
public double ComputeBGSConvexityCorrection(DateTime lastAmortisationDate,
DateTime amortisationDate,
double currentBondFactor,
double alpha,
double sigma,
double cleanUp)
{
IDayCounter dayCountObj = Actual365.Instance;
double tenor = dayCountObj.YearFraction(lastAmortisationDate,
amortisationDate);
var bgs = new BGSConvexityCorrection();
return(bgs.ComputeBGSConvexityCorrection(tenor,
currentBondFactor,
alpha,
sigma,
cleanUp));
}
public void TestComputeBGSConvexityCorrection()
{
// Instantiate the object that will provide access to the BGS
// convexity correction functionality.
var convexityObj = new BGSConvexityCorrection();
Assert.AreNotEqual(convexityObj, null);
IDayCounter dayCountObj = Actual365.Instance;
// Test the case: B0 < L.
_amortisationDate = DateTime.Parse("2011-01-18");
_currentBondFactor = 19 / 100;
_alpha = -0.4532;
_sigma = 2.17 / 100;
_cleanUp = 20 / 100;
_expected = 0.0;
double tenor = dayCountObj.YearFraction(_lastAmortisationDate, _amortisationDate);
_actual = convexityObj.ComputeBGSConvexityCorrection(tenor,
_currentBondFactor,
_alpha,
_sigma,
_cleanUp);
Assert.AreEqual(_expected, _actual);
// Test the limiting case: L = 0.
_amortisationDate = DateTime.Parse("2007-04-16");
_currentBondFactor = 68.29 / 100;
_alpha = -0.3051;
_sigma = 3.12 / 100;
_cleanUp = 0.0;
_expected = 0.6334102389;
tenor = dayCountObj.YearFraction(_lastAmortisationDate, _amortisationDate);
_actual = convexityObj.ComputeBGSConvexityCorrection(tenor,
_currentBondFactor,
_alpha,
_sigma,
_cleanUp);
const double tolerance2 = 1.0E-6;
Assert.AreEqual(_expected, _actual, tolerance2);
// Test the linmiting case: sigma = 0.
_amortisationDate = DateTime.Parse("2007-07-16");
_currentBondFactor = 61.82 / 100;
_alpha = -0.3051;
_sigma = 0.0;
_cleanUp = 10.0 / 100;
_expected = 0.5314066262;
tenor = dayCountObj.YearFraction(_lastAmortisationDate, _amortisationDate);
_actual = convexityObj.ComputeBGSConvexityCorrection(tenor,
_currentBondFactor,
_alpha,
_sigma,
_cleanUp);
const double tolerance3 = 1.0E-5;
Assert.AreEqual(_expected, _actual, tolerance3);
// Test the generic case.
// Full convexity correction.
_amortisationDate = DateTime.Parse("2008-10-15");
_currentBondFactor = 91.73 / 100;
_alpha = -0.3000;
_sigma = 45.0 / 100;
_cleanUp = 10.0 / 100;
_expected = 0.5421666386;
tenor = dayCountObj.YearFraction(_lastAmortisationDate, _amortisationDate);
_actual = convexityObj.ComputeBGSConvexityCorrection(tenor,
_currentBondFactor,
_alpha,
_sigma,
_cleanUp);
const double tolerance4 = 1.0E-7;
Assert.AreEqual(_expected, _actual, tolerance4);
// Truncated convexity correction.
_amortisationDate = DateTime.Parse("2010-01-15");
_currentBondFactor = 28.34 / 100;
_alpha = -0.2567;
_sigma = 2.71 / 100;
_cleanUp = 10.0 / 100;
_expected = 0.1312047820;
tenor = dayCountObj.YearFraction(_lastAmortisationDate, _amortisationDate);
_actual = convexityObj.ComputeBGSConvexityCorrection(tenor,
_currentBondFactor,
_alpha,
_sigma,
_cleanUp);
const double tolerance5 = 1.0E-7;
Assert.AreEqual(_expected, _actual, tolerance5);
}
