public static double[] SolveYield(Country country, DateTime settleDate, double cleanPrice, DateTime startDate, DateTime firstCpnDate, DateTime maturityDate, double coupon, long freq, int exDivDays = 0, InflationCurve infCurve = null)
{
bool bLongFirstCpn = firstCpnDate > settleDate && firstCpnDate > startDate.AddDays(1).AddMonths((int)freq).AddDays(-1);
DateTime adjSettleDate = (startDate > settleDate ? startDate : settleDate);
List<DateTime> schedule = GenerateSchedule((bLongFirstCpn && adjSettleDate < firstCpnDate ? startDate : adjSettleDate), maturityDate, freq);
List<DateTime> adjSchedule = GenerateAdjustedSchedule(schedule, null, "F");
double[] result = new double[4];
double guess = coupon / cleanPrice * freq / 12.0, firstCpnSize = 1.0;
long nCpns = schedule.Count, ctr;
// Boundary case
if (settleDate.Date >= maturityDate.Date)
return result;
// Specific country conventions:
// Italy: accrual rounding, semi-annual coupons but yield quoted with annual compounding frequency.
// All (US and Eurozone) bar France use US convention - i.e. last coupon period simple yield.
// Spain: final principal payment use adjusted payment date.
// UK and some others have ex-div periods.
bool bExDiv = (settleDate.AddDays(exDivDays) >= schedule[(bLongFirstCpn ? 2 : 1)]);
double dcf = CalcBondAccrualDcf(adjSettleDate, startDate, firstCpnDate, schedule, country);
// In case of stub period at start
if (firstCpnDate > settleDate)
{
if (bLongFirstCpn)
{
firstCpnSize = 1.0 + (schedule[1] - startDate).TotalDays / (schedule[1] - schedule[0]).TotalDays;
}
else
{
firstCpnSize = (firstCpnDate - (schedule[0] < startDate ? startDate : schedule[0])).TotalDays / (schedule[1] - schedule[0]).TotalDays;
}
}
double accrual = 100.0 * coupon * freq / 1200 * (dcf - (bExDiv ? firstCpnSize : 0.0));
// Interpolate inflation curve.
double[] infFactors = InterpolateInflationFactors(adjSchedule, settleDate, infCurve);
accrual *= infFactors[nCpns];
cleanPrice *= infFactors[nCpns];
// Modify DCF for use in discounting loop. If long first coupon then need to reduce i by 1 in the coupon loop. Do this by incrementing adjusted DCF.
dcf += (bLongFirstCpn ? 2.0 : 1.0) - firstCpnSize;
if (country == Country.IT)
{
accrual = Math.Round(accrual, 5);
}
for (ctr = 0; ctr < 100; ctr++)
{
double pv = -cleanPrice - accrual;
double dPvdY = 0.0;
double d2PvdY2 = 0.0;
double delay = 0.0;
double tmp;
// In final coupon period and US convention
if (nCpns == 2 && country != Country.FR && country != Country.UK)
{
if (country == Country.ES)
{
delay = (adjSchedule[1] - schedule[1]).TotalDays / (schedule[1] - schedule[0]).TotalDays;
}
tmp = 100.0 * infFactors[1] * (1.0 + (bExDiv ? 0.0 : 1.0) * coupon * freq / 1200) / (1.0 + guess * (1.0 + delay - dcf));
pv += tmp;
dPvdY -= (1 + delay - dcf) * tmp / (1.0 + guess * (1.0 + delay - dcf));
d2PvdY2 -= 2.0 * (1 + delay - dcf) * dPvdY / (1.0 + guess * (1.0 + delay - dcf));
}
else
{
// First coupon
int i = (bLongFirstCpn ? 2 : 1);
tmp = firstCpnSize * 100.0 * infFactors[1] * (bExDiv ? 0.0 : 1.0) * coupon * freq / 1200 / Math.Pow(1.0 + guess, i - dcf);
pv += tmp;
dPvdY -= (i - dcf) * tmp / (1.0 + guess);
d2PvdY2 += (i - dcf) * (i + 1 - dcf) * tmp / ((1.0 + guess) * (1.0 + guess));
for (i++; i < nCpns; i++)
{
tmp = 100.0 * infFactors[i] * coupon * freq / 1200 / Math.Pow(1.0 + guess, i - dcf);
pv += tmp;
dPvdY -= (i - dcf) * tmp / (1.0 + guess);
d2PvdY2 += (i - dcf) * (i + 1 - dcf) * tmp / ((1.0 + guess) * (1.0 + guess));
}
// Final Principal
if (country == Country.ES)
{
delay = (adjSchedule[i - 1] - schedule[i - 1]).TotalDays / (schedule[i - 1] - schedule[i - 2]).TotalDays;
}
tmp = 100.0 * infFactors[i - 1] / Math.Pow(1.0 + guess, i - 1 + delay - dcf);
pv += tmp;
dPvdY -= (i - 1 + delay - dcf) * tmp / (1.0 + guess);
d2PvdY2 += (i - 1 + delay - dcf) * (i + delay - dcf) * tmp / ((1.0 + guess) * (1.0 + guess));
}
// Convergence criterion is Pv within 1.0e-8 after allowing for Price ~ 100
if (Math.Abs(pv) < 1.0e-8)
{
if (country == Country.IT && nCpns > 2)
{
tmp = 1.0 + 0.5 * guess * 12 / freq;
result[0] = tmp * tmp - 1.0;
result[1] = dPvdY / tmp * freq / 12;
result[2] = -result[1] / (cleanPrice + accrual);
result[3] = 0.0001 * (d2PvdY2 * freq * freq / 144 - 0.5 * result[1]) / tmp / tmp;
}
else
{
result[0] = guess * 12 / freq;
result[1] = dPvdY * freq / 12;
result[2] = -result[1] / (cleanPrice + accrual);
result[3] = 0.0001 * d2PvdY2 * freq * freq / 144;
}
return result;
}
else
{
// Halley's method
guess = guess - pv / (dPvdY - pv * d2PvdY2 / (2.0 * dPvdY));
}
}
result[0] = -1.0;
result[1] = -1.0;
result[2] = -1.0;
result[3] = -1.0;
return result;
}
public static double[] SolveZSpread2(Country country, DateTime settleDate, double cleanPrice, DateTime startDate, DateTime firstCpnDate, DateTime maturityDate, double coupon, long freq, DateTime[] curveDates, double[] dfs, List<DateTime> holidays, int exDivDays = 0, InflationCurve infCurve = null)
{
double[] result = new double[2];
bool bLongFirstCpn = firstCpnDate > settleDate && firstCpnDate > startDate.AddDays(1).AddMonths((int)freq).AddDays(-1);
DateTime adjSettleDate = startDate > settleDate ? startDate : settleDate;
List<DateTime> schedule = GenerateSchedule((bLongFirstCpn && adjSettleDate < firstCpnDate ? startDate : adjSettleDate), maturityDate, freq);
List<DateTime> adjSchedule = GenerateAdjustedSchedule(schedule, holidays, "F");
double[] interpTimes = new double[adjSchedule.Count];
List<double> flowZcTimes = new List<double>();
List<double> flowZcRates = new List<double>();
double guess = 0.0, firstCpnSize = 1.0;
long nCpns = schedule.Count, ctr;
int i;
// Boundary case
if (settleDate.Date >= maturityDate.Date)
return result;
bool bExDiv = settleDate.AddDays(exDivDays) >= schedule[bLongFirstCpn ? 2 : 1];
double dcf = CalcBondAccrualDcf(adjSettleDate, startDate, firstCpnDate, schedule, country);
// In case of stub period at start
if (firstCpnDate > settleDate)
{
if (bLongFirstCpn)
{
firstCpnSize = 1.0 + (schedule[1] - startDate).TotalDays / (schedule[1] - schedule[0]).TotalDays;
}
else
{
firstCpnSize = (firstCpnDate - (startDate > schedule[0] ? startDate : schedule[0])).TotalDays / (schedule[1] - schedule[0]).TotalDays;
}
}
double accrual = 100.0 * coupon * freq / 1200 * (dcf - (bExDiv ? firstCpnSize : 0.0));
if (country == Country.IT)
{
accrual = Math.Round(accrual, 5);
}
// Use adjusted schedule dates for payments.
// Convert dates to times for spline interpolator
interpTimes[0] = ((settleDate > startDate ? settleDate : startDate) - curveDates[0]).TotalDays;
for (i = 1; i < adjSchedule.Count; i++)
{
interpTimes[i] = (adjSchedule[i] - curveDates[0]).TotalDays;
}
List<double> flowDfs = InterpDfSpline(interpTimes, curveDates, dfs);
// Calculate base discount factors (before spread) and convert to zero coupon rates. Store rate * freq / 12 for efficiency.
double dt = 12.0 / freq * interpTimes[0] / 365.0;
if (dt > 0.0)
{
flowZcRates.Add((Math.Pow(1.0 / flowDfs[0], 1.0 / dt) - 1.0));
}
else
{
flowZcRates.Add(0.0);
}
flowZcTimes.Add(dt);
for (i = 1; i < nCpns; i++)
{
if (nCpns == 2)
{
dt = 12.0 / freq * interpTimes[i] / 365.0;
flowZcRates.Add((1.0 / flowDfs[i] - 1.0) / dt);
flowZcTimes.Add(dt);
}
else
{
dt = 12.0 / freq * interpTimes[i] / 365.0;
flowZcRates.Add((Math.Pow(1.0 / flowDfs[i], 1.0 / dt) - 1.0));
flowZcTimes.Add(dt);
}
}
// Interpolate inflation curve.
double[] infFactors = InterpolateInflationFactors(adjSchedule, settleDate, infCurve);
accrual *= infFactors[nCpns];
cleanPrice *= infFactors[nCpns];
// Iterative solver: Halley's method as faster convergence than Newton-Raphson.
for (ctr = 0; ctr < 100; ctr++)
{
// Initial payment
double tmp = (cleanPrice + accrual) * Math.Pow(1.0 + (flowZcRates[0] + guess), -flowZcTimes[0]);
double pv = -tmp;
double dPvdZ = flowZcTimes[0] * tmp / (1.0 + flowZcRates[0] + guess);
double d2PvdZ2 = -flowZcTimes[0] * (1.0 + flowZcTimes[0]) * tmp / ((1.0 + flowZcRates[0] + guess) * (1.0 + flowZcRates[0] + guess));
if (nCpns == 2 && country != Country.FR && country != Country.UK)
{
tmp = 100.0 * infFactors[1] * (1.0 + (bExDiv ? 0.0 : coupon) * freq / 1200) / (1.0 + (flowZcRates[1] + guess) * flowZcTimes[1]);
pv += tmp;
dPvdZ -= flowZcTimes[1] * tmp / (1.0 + (flowZcRates[1] + guess) * flowZcTimes[1]);
d2PvdZ2 += 2.0 * flowZcTimes[1] * flowZcTimes[1] * tmp / ((1.0 + (flowZcRates[1] + guess) * flowZcTimes[1]) * (1.0 + (flowZcRates[1] + guess) * flowZcTimes[1]));
}
else
{
// first coupon
i = (bLongFirstCpn ? 2 : 1);
tmp = (bExDiv ? 0.0 : firstCpnSize) * 100.0 * infFactors[i] * coupon * freq / 1200 * Math.Pow(1.0 + flowZcRates[i] + guess, -flowZcTimes[i]);
pv += tmp;
dPvdZ -= flowZcTimes[i] * tmp / (1.0 + flowZcRates[i] + guess);
d2PvdZ2 += flowZcTimes[i] * (1.0 + flowZcTimes[i]) * tmp / ((1.0 + flowZcRates[i] + guess) * (1.0 + flowZcRates[i] + guess));
for (i++; i < nCpns; i++)
{
tmp = 100.0 * infFactors[i] * coupon * freq / 1200 * Math.Pow(1.0 + flowZcRates[i] + guess, -flowZcTimes[i]);
pv += tmp;
dPvdZ -= flowZcTimes[i] * tmp / (1.0 + flowZcRates[i] + guess);
d2PvdZ2 += flowZcTimes[i] * (1.0 + flowZcTimes[i]) * tmp / ((1.0 + flowZcRates[i] + guess) * (1.0 + flowZcRates[i] + guess));
}
// Final principal
tmp = 100.0 * infFactors[i - 1] * Math.Pow(1.0 + flowZcRates[i - 1] + guess, -flowZcTimes[i - 1]);
pv += tmp;
dPvdZ -= flowZcTimes[i - 1] * tmp / (1.0 + flowZcRates[i - 1] + guess);
d2PvdZ2 += flowZcTimes[i - 1] * (1.0 + flowZcTimes[i - 1]) * tmp / ((1.0 + flowZcRates[i - 1] + guess) * (1.0 + flowZcRates[i - 1] + guess));
}
// Convergence criterion is Pv within 1.0e-8 after allowing for Price ~ 100
if (Math.Abs(pv) < 1.0e-7)
{
result[0] = guess * 12.0 / freq;
result[1] = dPvdZ * freq / 12.0;
return result;
}
else
{
// Halley's method
guess = guess - pv / (dPvdZ - pv * d2PvdZ2 / (2.0 * dPvdZ));
}
}
result[0] = -1.0;
result[1] = 0.0;
return result;
}
public static double[] PriceFromYield(Country country, DateTime settleDate, double yield, DateTime startDate, DateTime firstCpnDate, DateTime maturityDate, double coupon, long freq, int exDivDays = 0, InflationCurve infCurve = null)
{
bool bLongFirstCpn = firstCpnDate > settleDate && firstCpnDate > startDate.AddDays(1).AddMonths((int)freq).AddDays(-1);
DateTime adjSettleDate = (startDate > settleDate ? startDate : settleDate);
List<DateTime> schedule = GenerateSchedule((bLongFirstCpn && adjSettleDate < firstCpnDate ? startDate : adjSettleDate), maturityDate, freq);
List<DateTime> adjSchedule = GenerateAdjustedSchedule(schedule, null, "F");
double[] result = new double[2];
double delay = 0.0, firstCpnSize = 1.0;
long nCpns = schedule.Count;
// Boundary case
if (settleDate.Date >= maturityDate.Date)
{
if (settleDate.Date == maturityDate.Date)
result[0] = 100.0 + coupon * freq / 12;
return result;
}
// Specific country conventions:
// Italy: accrual rounding, semi-annual coupons but yield quoted with annual compounding frequency.
// All (US and Eurozone) bar France use US convention - i.e. last coupon period simple yield.
// Spain: final principal payment use adjusted payment date.
double dcf = CalcBondAccrualDcf(settleDate, startDate, firstCpnDate, schedule, country);
// In case of stub period at start
if (firstCpnDate > settleDate)
{
if (bLongFirstCpn)
{
firstCpnSize = 1.0 + (schedule[1] - startDate).TotalDays / (schedule[1] - schedule[0]).TotalDays;
}
else
{
firstCpnSize = (firstCpnDate - (schedule[0] < startDate ? startDate : schedule[0])).TotalDays / (schedule[1] - schedule[0]).TotalDays;
}
}
double accrual = 100.0 * coupon * freq / 1200 * dcf;
// Interpolate inflation curve.
double[] infFactors = InterpolateInflationFactors(adjSchedule, settleDate, infCurve);
accrual *= infFactors[nCpns];
// Modify DCF for use in discounting loop. If long first coupon then need to reduce i by 1 in the coupon loop. Do this by incrementing adjusted DCF.
dcf += (bLongFirstCpn ? 2.0 : 1.0) - firstCpnSize;
if (country == Country.IT)
{
accrual = Math.Round(accrual, 5);
if (nCpns > 2)
{
yield = 2.0 * (Math.Sqrt(1 + yield) - 1.0);
}
}
double pv = 0.0;
double dPvdY = 0.0;
if (nCpns == 2 && country != Country.FR && country != Country.UK)
{
if (country == Country.ES)
{
delay = (adjSchedule[1] - schedule[1]).TotalDays / (schedule[1] - schedule[0]).TotalDays;
}
pv += 100.0 * infFactors[1] * (1.0 + coupon * freq / 1200) / (1.0 + yield * freq / 12 * (1.0 + delay - dcf));
dPvdY -= 100.0 * infFactors[1] * (1 - dcf) * freq / 12 * (1.0 + coupon * freq / 1200) / Math.Pow(1.0 + yield * freq / 12 * (1.0 + delay - dcf), 2);
}
else
{
int i;
for (i = (bLongFirstCpn ? 2 : 1); i < nCpns; i++)
{
pv += 100.0 * infFactors[i] * coupon * freq / 1200 / Math.Pow(1.0 + yield * freq / 12, i - dcf);
dPvdY -= 100.0 * infFactors[i] * (i - dcf) * freq / 12 * coupon * freq / 1200 / Math.Pow(1.0 + yield * freq / 12, i + 1 - dcf);
// If stub period then first coupon is non-standard size.
if (i == (bLongFirstCpn ? 2 : 1))
{
pv *= firstCpnSize;
dPvdY *= firstCpnSize;
}
}
if (country == Country.ES)
{
delay = (adjSchedule[i - 1] - schedule[i - 1]).TotalDays / (schedule[i - 1] - schedule[i - 2]).TotalDays;
}
pv += 100.0 * infFactors[i - 1] / Math.Pow(1.0 + yield * freq / 12, i - 1 + delay - dcf);
dPvdY -= 100.0 * infFactors[i - 1] * freq / 12 * (i - dcf) / Math.Pow(1.0 + yield * freq / 12, i - 1 + delay - dcf);
}
result[0] = (pv - accrual) / infFactors[nCpns];
result[1] = dPvdY;
// Handle exdiv period. First coupon payment comes out of pv calculation and out of accrual.
if (settleDate.AddDays(exDivDays) >= schedule[1])
{
if (nCpns == 2 && country != Country.FR && country != Country.UK)
{
if (country == Country.ES)
{
delay = (adjSchedule[1] - schedule[1]).TotalDays/(schedule[1] - schedule[0]).TotalDays;
}
result[0] += coupon * infFactors[1] * freq / 12 * (1.0 - 1.0 / (1.0 + yield * freq / 12 * (1.0 + delay - dcf)));
result[1] += (1.0 + delay - dcf) * coupon * infFactors[1] * freq / 12 * freq / 12 / Math.Pow(1.0 + yield * freq / 12 * (1.0 + delay - dcf), 2);
}
else
{
result[0] += (bLongFirstCpn ? firstCpnSize : 1.0) * coupon * infFactors[1] * freq / 12 * (1.0 - Math.Pow(1.0 + yield * freq / 12, dcf - (bLongFirstCpn ? 2.0 : 1.0)));
result[1] += (bLongFirstCpn ? firstCpnSize * (2.0 - dcf) : 1.0 - dcf) * coupon * infFactors[1] * freq / 12 * freq / 12 * Math.Pow(1.0 + yield * freq / 12, dcf - (bLongFirstCpn ? 2.0 : 1.0));
}
}
return result;
}
public static double[] InterpolateInflationFactors(List<DateTime> schedule, DateTime settleDate, InflationCurve infCurve)
{
double[] infFactors;
int k = 0, i = 0;
if (schedule != null)
{
infFactors = new double[schedule.Count + 1];
for (i = 0; i < schedule.Count; i++)
{
if (infCurve == null || infCurve.InterpMethod != 1 || schedule[i].AddMonths(-infCurve.InfGap) < infCurve.FcstDates[0])
infFactors[i] = 1.0;
else
{
while (k < infCurve.FcstDates.Length - 1 && schedule[i].AddMonths(-infCurve.InfGap).Date > infCurve.FcstDates[k].Date)
k++;
// linear interpolation
infFactors[i] = ((schedule[i].AddMonths(-infCurve.InfGap) - infCurve.FcstDates[k - 1]).TotalDays * infCurve.FcstIndex[k] + (infCurve.FcstDates[k] - schedule[i].AddMonths(-infCurve.InfGap)).TotalDays * infCurve.FcstIndex[k - 1]) / (infCurve.FcstDates[k] - infCurve.FcstDates[k - 1]).TotalDays;
infFactors[i] /= infCurve.InitialFixing;
}
}
}
else
infFactors = new double[1];
// Factor for settleDate goes at end
if (infCurve == null || infCurve.InterpMethod != 1 || settleDate.AddMonths(-infCurve.InfGap) < infCurve.FcstDates[0])
infFactors[i] = 1.0;
else
{
k = 0;
while (k < infCurve.FcstDates.Length - 1 && settleDate.AddMonths(-infCurve.InfGap).Date > infCurve.FcstDates[k].Date)
k++;
// linear interpolation
infFactors[i] = ((settleDate.AddMonths(-infCurve.InfGap) - infCurve.FcstDates[k - 1]).TotalDays * infCurve.FcstIndex[k] + (infCurve.FcstDates[k] - settleDate.AddMonths(-infCurve.InfGap)).TotalDays * infCurve.FcstIndex[k - 1]) / (infCurve.FcstDates[k] - infCurve.FcstDates[k - 1]).TotalDays;
infFactors[i] /= infCurve.InitialFixing;
}
return infFactors;
}
// Par-Par Asset Swap pricer
public static double ParParAssetSwapSpread(DateTime settleDate, DateTime bondEffectiveDate, DateTime bondFirstCpnDate, DateTime bondMaturityDate, double bondCoupon, Country country, DayCountType bondDctType, long bondFreq, double bondCleanPrice, DayCountType floatDctType, long floatFreq, DateTime[] discCurveDates, double[] discDfs, DateTime[] fcstCurveDates, double[] fcstDfs, List<DateTime> holidays, double lastFixing = 0.0, int blendIndex = 0, InflationCurve infCurve = null)
{
bool bLongFirstCpn = bondFirstCpnDate > settleDate && bondFirstCpnDate > bondEffectiveDate.AddDays(1).AddMonths((int)bondFreq).AddDays(-1);
DateTime adjSettleDate = (bondEffectiveDate > settleDate ? bondEffectiveDate : settleDate);
List<DateTime> schedule = GenerateSchedule(bLongFirstCpn && adjSettleDate > bondFirstCpnDate ? bondEffectiveDate : adjSettleDate, bondMaturityDate, bondFreq);
double dcf = CalcBondAccrualDcf(settleDate, bondEffectiveDate, bondFirstCpnDate, schedule, country);
double accrual = 100.0 * bondCoupon * bondFreq / 1200 * dcf;
// Interpolate inflation curve.
double[] infFactors = InterpolateInflationFactors(null, settleDate, infCurve);
double fixedPv = SwapAnalytics.PriceFixedLeg(bondEffectiveDate, bondMaturityDate, bondCoupon, bondDctType, bondFreq, discCurveDates, discDfs, holidays, blendIndex, false, bLongFirstCpn, infCurve, infFactors[0])[0];
return SwapAnalytics.CalcSwapMargin(bondEffectiveDate, bondMaturityDate, -1.0 + (bondCleanPrice + accrual) / 100.0 - fixedPv / infFactors[0], floatDctType, floatFreq, discCurveDates, discDfs, fcstCurveDates, fcstDfs, holidays, lastFixing, blendIndex);
}
public static double PriceFromZSpread(Country country, DateTime settleDate, double spread, DateTime startDate, DateTime firstCpnDate, DateTime maturityDate, double coupon, long freq, DateTime[] curveDates, double[] dfs, List<DateTime> holidays, int exDivDays = 0, InflationCurve infCurve = null)
{
bool bLongFirstCpn = firstCpnDate > settleDate && firstCpnDate > startDate.AddDays(1).AddMonths((int)freq).AddDays(-1);
DateTime adjSettleDate = (startDate > settleDate ? startDate : settleDate);
List<DateTime> schedule = GenerateSchedule((bLongFirstCpn && adjSettleDate < firstCpnDate ? startDate : adjSettleDate), maturityDate, freq);
List<DateTime> adjSchedule = GenerateAdjustedSchedule(schedule, holidays, "F");
double[] interpTimes = new double[adjSchedule.Count];
List<double> flowZcTimes = new List<double>();
List<double> flowZcRates = new List<double>();
double firstCpnSize = 1.0;
long nCpns = schedule.Count;
int i;
bool bExDiv = settleDate.AddDays(exDivDays) >= schedule[(bLongFirstCpn ? 2 : 1)];
spread *= freq / 12.0;
double dcf = CalcBondAccrualDcf(settleDate, startDate, firstCpnDate, schedule, country);
// In case of stub period at start
if (firstCpnDate > settleDate)
{
if (bLongFirstCpn)
{
firstCpnSize = 1.0 + (schedule[1] - startDate).TotalDays / (schedule[1] - schedule[0]).TotalDays;
}
else
{
firstCpnSize = (firstCpnDate - (startDate > schedule[0] ? startDate : schedule[0])).TotalDays / (schedule[1] - schedule[0]).TotalDays;
}
}
double accrual = 100.0 * coupon * freq / 1200 * (dcf - (bExDiv ? firstCpnSize : 0.0));
if (country == Country.IT)
{
accrual = Math.Round(accrual, 5);
}
// Use adjusted schedule dates for payments.
// Convert dates to times for spline interpolator
interpTimes[0] = (settleDate - curveDates[0]).TotalDays;
for (i = 1; i < adjSchedule.Count; i++)
{
interpTimes[i] = (adjSchedule[i] - curveDates[0]).TotalDays;
}
List<double> flowDfs = InterpDfSpline(interpTimes, curveDates, dfs);
// Calculate base discount factors (before spread) and convert to zero coupon rates. Store rate * freq / 12 for efficiency.
double dt = 12.0 / freq * interpTimes[0] / 365.0;
if (dt > 0.0)
{
flowZcRates.Add((Math.Pow(1.0 / flowDfs[0], 1.0 / dt) - 1.0));
}
else
{
flowZcRates.Add(0.0);
}
flowZcTimes.Add(dt);
for (i = 1; i < nCpns; i++)
{
if (nCpns == 2)
{
dt = 12.0 / freq * interpTimes[i] / 365.0;
flowZcRates.Add((1.0 / flowDfs[i] - 1.0) / dt);
flowZcTimes.Add(dt);
}
else
{
dt = 12.0 / freq * interpTimes[i] / 365.0;
flowZcRates.Add((Math.Pow(1.0 / flowDfs[i], 1.0 / dt) - 1.0));
flowZcTimes.Add(dt);
}
}
// Interpolate inflation curve.
double[] infFactors = InterpolateInflationFactors(adjSchedule, settleDate, infCurve);
accrual *= infFactors[nCpns];
// Initial payment
double pv = -accrual * Math.Pow(1.0 + (flowZcRates[0] + spread), -flowZcTimes[0]);
if (nCpns == 2 && country != Country.FR && country != Country.UK)
{
pv += 100.0 * infFactors[1] * (1.0 + (bExDiv ? 0.0 : coupon) * freq / 1200) / (1.0 + (flowZcRates[1] + spread) * flowZcTimes[1]);
}
else
{
// first coupon
i = (bLongFirstCpn ? 2 : 1);
pv += firstCpnSize * 100.0 * infFactors[i] * (bExDiv ? 0.0 : coupon) * freq / 1200 * Math.Pow(1.0 + flowZcRates[i] + spread, -flowZcTimes[i]);
for (i++; i < nCpns; i++)
{
pv += 100.0 * infFactors[i] * coupon * freq / 1200 * Math.Pow(1.0 + flowZcRates[i] + spread, -flowZcTimes[i]);
}
// Final principal
pv += 100.0 * infFactors[i - 1] * Math.Pow(1.0 + flowZcRates[i - 1] + spread, -flowZcTimes[i - 1]);
}
return pv * Math.Pow(1.0 + (flowZcRates[0] + spread), flowZcTimes[0]) / infFactors[nCpns];
}
public static double SolveZSpread(Country country, DateTime settleDate, double cleanPrice, DateTime startDate, DateTime firstCpnDate, DateTime maturityDate, double coupon, long freq, DateTime[] curveDates, double[] dfs, List<DateTime> holidays, int exDivDays = 0, InflationCurve infCurve = null)
{
return SolveZSpread2(country, settleDate, cleanPrice, startDate, firstCpnDate, maturityDate, coupon, freq, curveDates, dfs, holidays, exDivDays, infCurve)[0];
}
