/// <summary>
///
/// </summary>
/// <param name="bond"></param>
/// <param name="settleDate"></param>
/// <param name="ytm"></param>
/// <returns>the unrounded all-in price</returns>
public static double UnroundedAIP(this BesaJseBond bond, Date settleDate, double ytm)
{
var N = 100.0;
var typicalCoupon = N * bond.annualCouponRate / 2;
var t0 = bond.GetLastCouponDateOnOrBefore(settleDate);
var t1 = bond.GetNextCouponDate(t0);
var tradingWithNextCoupon = t1 - settleDate > bond.booksCloseDateDays;
var d = tradingWithNextCoupon ? settleDate - t0 : settleDate - t1;
var couponAtT1 = tradingWithNextCoupon ? typicalCoupon : 0.0;
var v = 1 / (1 + ytm / 2);
var n = (int)Math.Round((bond.maturityDate - t1) / 182.625);
double brokenPeriod, brokenPeriodDf;
if (n > 0)
{
brokenPeriod = ((double)t1 - settleDate) / (t1 - t0);
brokenPeriodDf = Math.Pow(v, brokenPeriod);
}
else
{
brokenPeriod = ((double)t1 - settleDate) / 182.25;
brokenPeriodDf = 1 / (1 + ytm * brokenPeriod / 2);
}
var A1 = (couponAtT1 + typicalCoupon * v * (1 - Math.Pow(v, n)) / (1 - v) + N * Math.Pow(v, n));
var unroundedAip = brokenPeriodDf * A1;
return(unroundedAip);
}
/// <summary>
///
/// </summary>
/// <param name="bond"></param>
/// <param name="settleDate"></param>
/// <param name="ytm"></param>
/// <returns>the unrounded accrued accrued interest</returns>
public static double UnroundedAccruedInterest(this BesaJseBond bond, Date settleDate)
{
var N = 100.0;
var t0 = bond.GetLastCouponDateOnOrBefore(settleDate);
var t1 = bond.GetNextCouponDate(t0);
var tradingWithNextCoupon = t1 - settleDate > bond.booksCloseDateDays;
var d = tradingWithNextCoupon ? settleDate - t0 : settleDate - t1;
var unroundedAccrued = N * bond.annualCouponRate * d / 365.0;
return(unroundedAccrued);
}
/// <summary>
///
/// </summary>
/// <param name="bond"></param>
/// <param name="settleDate"></param>
/// <param name="ytm"></param>
/// <returns></returns>
public static ResultStore GetSpotMeasures(this BesaJseBond bond, Date settleDate, double ytm)
{
var N = 100.0;
var typicalCoupon = N * bond.annualCouponRate / 2;
var t0 = bond.GetLastCouponDateOnOrBefore(settleDate);
var t1 = bond.GetNextCouponDate(t0);
var n = (int)Math.Round((bond.maturityDate - t1) / 182.625);
var tradingWithNextCoupon = t1 - settleDate > bond.booksCloseDateDays;
var d = tradingWithNextCoupon ? settleDate - t0 : settleDate - t1;
var unroundedAccrued = N * bond.annualCouponRate * d / 365.0;
var roundedAccrued = Math.Round(unroundedAccrued, 5);
var couponAtT1 = tradingWithNextCoupon ? typicalCoupon : 0.0;
var v = 1 / (1 + ytm / 2);
double brokenPeriodDf;
if (n > 0)
{
brokenPeriodDf = Math.Pow(v, ((double)t1 - settleDate) / (t1 - t0));
}
else
{
brokenPeriodDf = 1 / (1 + ytm * ((double)t1 - settleDate) / 365.0);
}
var unroundedAip = brokenPeriodDf *
(couponAtT1 + typicalCoupon * v * (1 - Math.Pow(v, n)) / (1 - v) + N * Math.Pow(v, n));
var unroundedClean = unroundedAip - unroundedAccrued;
var roundedClean = Math.Round(unroundedClean, 5);
var roundedAip = roundedClean + roundedAccrued;
var results = new ResultStore();
results.Add(Keys.RoundedAip, roundedAip);
results.Add(Keys.RoundedClean, roundedClean);
results.Add(Keys.UnroundedAip, unroundedAip);
results.Add(Keys.UnroundedClean, unroundedClean);
results.Add(Keys.UnroundedAccrued, unroundedAccrued);
results.Add(Keys.TradingWithNextCoupon, tradingWithNextCoupon ? 1.0 : 0.0);
return(results);
}
private static double[] DeltaAndConvexity(this BesaJseBond bond, Date settleDate, double ytm)
{
var N = 100.0;
var typicalCoupon = N * bond.annualCouponRate / 2;
var t0 = bond.GetLastCouponDateOnOrBefore(settleDate);
var t1 = bond.GetNextCouponDate(t0);
var v = 1 / (1 + ytm / 2);
var n = (int)Math.Round((bond.maturityDate - t1) / 182.625);
double brokenPeriod, brokenPeriodDf, dB_dZ;
double d2B_dZ2 = 0;
if (n > 0)
{
brokenPeriod = ((double)t1 - settleDate) / (t1 - t0);
brokenPeriodDf = Math.Pow(v, brokenPeriod);
dB_dZ = brokenPeriod * Math.Pow(v, brokenPeriod - 1);
d2B_dZ2 = brokenPeriod * (brokenPeriod - 1) * Math.Pow(v, brokenPeriod - 2);
}
else
{
brokenPeriod = ((double)t1 - settleDate) / 182.25;
brokenPeriodDf = 1 / (1 + ytm * brokenPeriod / 2);
dB_dZ = brokenPeriod / Math.Pow(v + brokenPeriod * (1 - v), 2);
}
var A1 = bond.UnroundedAIP(settleDate, ytm) / brokenPeriodDf;
var dA1_dZ = typicalCoupon * ((1 - (n + 1) * Math.Pow(v, n) + n * Math.Pow(v, n + 1)) / Math.Pow(1 - v, 2)) + n * N * Math.Pow(v, n - 1);
var dA_dZ = dB_dZ * A1 + dA1_dZ * brokenPeriodDf;
var d2A1_dZ2 = typicalCoupon * ((2 - n * (n + 1) * Math.Pow(v, n - 1) + 2 * (Math.Pow(n, 2) - 1) * Math.Pow(v, n) - n * (n - 1) * Math.Pow(v, n + 1)) / Math.Pow(1 - v, 3)) + n * (n - 1) * N * Math.Pow(v, n - 2);
var d2A_dZ2 = d2B_dZ2 * A1 + 2 * dB_dZ * dA1_dZ + d2A1_dZ2 * brokenPeriodDf;
var dA_dy = -(Math.Pow(v, 2) / 2) * dA_dZ;
var d2A_dy2 = (Math.Pow(v, 4) / 4) * d2A_dZ2 + (Math.Pow(v, 3) / 2) * dA_dZ;
var delta = dA_dy / 100;
var convexity = d2A_dy2 / bond.UnroundedAIP(settleDate, ytm);
double[] measures = new double[2];
measures[0] = delta;
measures[1] = convexity;
return(measures);
}