public double ShortEndTargetFunction(double guess)
{
DateTime baseDate = _baseCurve.GetBaseDate();
DateTime date0 = _assetDates.First();
DateTime date1 = _assetDates.Last();
double d0 = _baseCurve.GetDiscountFactor(date0);
double d1 = _baseCurve.GetDiscountFactor(date1);
double y = _dayCounter.YearFraction(date0, date1);
double y0 = _dayCounter.YearFraction(baseDate, date0);
double y1 = _dayCounter.YearFraction(baseDate, date1);
double z0 = RateAnalytics.DiscountFactorToZeroRate(d0, y0, _compoundingPeriod);
double z1 = RateAnalytics.DiscountFactorToZeroRate(d1, y1, _compoundingPeriod);
double projectedRate = 1 / y * (d0 / d1 - 1);
double basisSpread = (double)_asset.MarketQuote.value;
double term1 = Math.Pow(1 + 0.25 * (z0 + guess), -4 * y0);
double term2 = Math.Pow(1 + 0.25 * (z1 + guess), -4 * y1);
double term3 = y * term2 * (projectedRate + basisSpread);
double result = -term1 + term2 + term3;
return(result);
}
/// <summary>
/// Bootstraps the specified priceable assets.
/// </summary>
/// <param name="priceableAssets">The priceable assets.</param>
/// <param name="baseZeroCurve">The base Zero Curve</param>
/// <param name="algorithmHolder">The algorithmHolder</param>
/// <returns></returns>
public TermPoint[] Bootstrap(List <IPriceableRateAssetController> priceableAssets,
IRateCurve baseZeroCurve, PricingStructureAlgorithmsHolder algorithmHolder)
{
var items = new SortedDictionary <DateTime, Pair <string, decimal> >();
DateTime baseDate = baseZeroCurve.GetBaseDate();
items.Add(baseDate, new Pair <string, decimal>(null, 1m));
bool firstTime = true;
const double compoundingPeriod = 0.25;
IPriceableRateAssetController previousAsset = null;
IEnumerable <TermPoint> basePillars = baseZeroCurve.GetTermCurve().point;
IDayCounter dayCounter = null;
foreach (IPriceableRateAssetController priceableAsset in priceableAssets)
{
List <DateTime> assetDates;
if (priceableAsset is PriceableSwapRateAsset swap)
{
dayCounter = DayCounterHelper.Parse(swap.DayCountFraction.Value);
assetDates = swap.AdjustedPeriodDates;
}
else
{
PriceableDeposit deposit = priceableAsset as PriceableDeposit;
if (deposit == null)
{
throw new ArgumentException(
$"PriceableAsset must be a PriceableSwapRateAsset or PriceableDeposit, '{priceableAsset.GetType()}' is not implemented.");
}
dayCounter = DayCounterHelper.Parse(deposit.Deposit.dayCountFraction.Value);
assetDates = new List <DateTime> {
deposit.AdjustedStartDate, deposit.GetRiskMaturityDate()
};
}
DateTime maturityDate = priceableAsset.GetRiskMaturityDate();
if (items.Keys.Contains(maturityDate))
{
throw new ArgumentException(
$"Duplicate priceable asset on '{maturityDate:yyyy-MM-dd}'", nameof(priceableAssets));
}
//The min and max values to use with the solver.
const int xmin = -1;
const int xmax = 1;
var accuracy = 10 ^ -12;
if (firstTime)
{
firstTime = false;
// Solve to find the quarterly compounded zero rate spread
var solverFunctions
= new NewtonRaphsonSolverFunctions(priceableAsset, null, algorithmHolder, baseZeroCurve,
baseDate, items, compoundingPeriod, ZeroRateSpreads, dayCounter, assetDates);
var solver = new Newton();
var initialGuess = (double)priceableAsset.MarketQuote.value;
//var solution = new CenteredFiniteDifferenceDerivative();
Func <double, double> f = solverFunctions.ShortEndTargetFunction;
var derivativeOfTargetFunction = new NumericalDerivative().CreateDerivativeFunctionHandle(f, 1);
double zeroRateSpread = solver.Solve(f, derivativeOfTargetFunction, accuracy, initialGuess, xmin, xmax);
// add first point
DateTime startDate = assetDates.First();
decimal df = (decimal)GetAdjustedDiscountFactor(baseDate, startDate, dayCounter, zeroRateSpread, baseZeroCurve);
if (startDate != baseDate)
{
items.Add(startDate, new Pair <string, decimal>(null, df));
}
ZeroRateSpreads.Add(maturityDate, zeroRateSpread);
// add extra points
IEnumerable <TermPoint> extraPoints = basePillars.Where(b => (DateTime)b.term.Items[0] > startDate && (DateTime)b.term.Items[0] < maturityDate);
// Extrapolate the preceding extra points
foreach (TermPoint extraPoint in extraPoints)
{
DateTime date = (DateTime)extraPoint.term.Items[0];
df = (decimal)GetAdjustedDiscountFactor(baseDate, date, dayCounter, zeroRateSpread, baseZeroCurve);
items.Add(date, new Pair <string, decimal>(extraPoint.id, df));
}
// add final point
df = (decimal)GetAdjustedDiscountFactor(baseDate, maturityDate, dayCounter, zeroRateSpread, baseZeroCurve);
items.Add(maturityDate, new Pair <string, decimal>(priceableAsset.Id, df));
}
else
{
items.Add(maturityDate, new Pair <string, decimal>(priceableAsset.Id, 0));
ZeroRateSpreads.Add(maturityDate, (double)priceableAsset.MarketQuote.value);
// Solve to find the quarterly compounded zero rate spread
var solverFunctions
= new NewtonRaphsonSolverFunctions(priceableAsset, previousAsset, algorithmHolder, baseZeroCurve,
baseDate, items, compoundingPeriod, ZeroRateSpreads, dayCounter, assetDates);
Func <double, double> f = solverFunctions.LongEndTargetFunction;
var solver = new Newton();
var initialGuess = (double)priceableAsset.MarketQuote.value;
var derivativeOfTargetFunction = new NumericalDerivative().CreateDerivativeFunctionHandle(f, 1);
double zeroRateSpread = solver.Solve(f, derivativeOfTargetFunction, accuracy, initialGuess, xmin, xmax);
// Update discount factor value
decimal df = (decimal)GetAdjustedDiscountFactor(baseDate, maturityDate, dayCounter, zeroRateSpread, baseZeroCurve);
items[maturityDate].Second = df;
ZeroRateSpreads[maturityDate] = zeroRateSpread;
solverFunctions.UpdateDiscountFactors(baseDate);
}
previousAsset = priceableAsset;
}
// Extrapolate the following extra points
IEnumerable <TermPoint> finalPoints = basePillars.Where(b => (DateTime)b.term.Items[0] > items.Last().Key);
KeyValuePair <DateTime, double> zeroRateSpreadFinal = ZeroRateSpreads.Last();
foreach (TermPoint extraPoint in finalPoints)
{
DateTime date = (DateTime)extraPoint.term.Items[0];
decimal df = (decimal)GetAdjustedDiscountFactor(baseDate, date, dayCounter, zeroRateSpreadFinal.Value, baseZeroCurve);
items.Add(date, new Pair <string, decimal>(extraPoint.id, df));
}
return(TermPointsFactory.Create(items));
}