public static double GetModifiedDuration(Cashflow[] cashflows,
IDayCount dayCount,
Frequency frequency,
Date startDate,
Date valueDate,
double yield,
TradingMarket tradeingMarket,
bool irregularPayment = false,
IBondYieldPricer bondYieldPricer = null)
{
const double dy = 1e-4;
if (bondYieldPricer == null)
{
bondYieldPricer = new BondYieldPricer();
}
var priceUp = bondYieldPricer.FullPriceFromYield(cashflows, dayCount, frequency, startDate, valueDate, yield - dy, tradeingMarket, irregularPayment);
var priceDown = bondYieldPricer.FullPriceFromYield(cashflows, dayCount, frequency, startDate, valueDate, yield + dy, tradeingMarket, irregularPayment);
return((priceUp - priceDown) / dy / (priceDown + priceUp));
}
public static Tuple <Date, double>[] Calibrate(
string name,
Date referenceDate,
IMarketInstrument[] marketInstruments,
BusinessDayConvention bda,
IDayCount daycount,
ICalendar calendar,
Compound compound,
Interpolation interpolation,
YieldCurveTrait trait,
CurrencyCode currency,
Date[] knotPoints,
out double fittingError,
IMarketCondition baseMarket = null,
Expression <Func <IMarketCondition, object> >[] expression = null,
double initialValue = double.NaN,
double initialGuess = 0.05,
double xmin = -3,
double xmax = 3.0
)
{
var accuracy = 1.0e-13;
if (marketInstruments.Any(x => !(x.Instrument is Bond)))
{
throw new PricingLibraryException("All instruments must be bond to build a bond curve!");
}
var keyTs = knotPoints.Select(x => daycount.CalcDayCountFraction(referenceDate, x)).ToArray();
var len = keyTs.Length;
baseMarket =
baseMarket
??
new MarketCondition(
x => x.ValuationDate.Value = referenceDate,
x => x.DiscountCurve.Value = null,
x => x.FixingCurve.Value = null,
x => x.HistoricalIndexRates.Value = new Dictionary <IndexType, SortedDictionary <Date, double> >()
);
var bondYieldPricer = new BondYieldPricer();
var bonds = marketInstruments.Select(x => x.Instrument as Bond);
var bondCf = bonds.Select(x => x.GetCashflows(baseMarket, true)).ToList();
var bondPrices =
bonds.Select(
(x, i) =>
bondYieldPricer.FullPriceFromYield(bondCf[i], x.PaymentDayCount, x.PaymentFreq, x.StartDate, referenceDate,
marketInstruments[i].TargetValue, x.BondTradeingMarket, x.IrregularPayment)).ToArray();
var rand = new Random();
// variables : alpha, b1, b2, b3, b4, b5 ...
var numVars = 1 + 2 + len;
var lowerBounds = new double[numVars];
var upperBounds = new double[numVars];
var initials = new double[numVars];
double?finalScore = double.NaN;
for (var i = 0; i < numVars; ++i)
{
lowerBounds[i] = i == 0 ? 0.0 : xmin;
upperBounds[i] = i == 0 ? 1.0 : xmax;
initials[i] = rand.NextDouble() > 0 ? rand.NextDouble() : -rand.NextDouble();
}
var globalSolver = new NLoptSolver(NLoptAlgorithm.GN_DIRECT, (ushort)numVars, accuracy, 100000, NLoptAlgorithm.LN_COBYLA);
globalSolver.SetLowerBounds(lowerBounds);
globalSolver.SetUpperBounds(upperBounds);
globalSolver.SetMinObjective((variables, gradients) =>
{
var error =
bondCf.Select((cfs, i) => GetModelPrice(referenceDate, cfs, daycount, variables, keyTs) - bondPrices[i]).ToArray();
return(error.Sum(x => x * x));
});
double?globalFinalScore;
var globalResult = globalSolver.Optimize(initials, out globalFinalScore);
var localSolvers = new[] { NLoptAlgorithm.LN_BOBYQA, NLoptAlgorithm.LD_AUGLAG, NLoptAlgorithm.LN_COBYLA };
for (var k = 0; k < 3; ++k)
{
var localSolver = new NLoptSolver(localSolvers[k], (ushort)numVars, accuracy, 100000, NLoptAlgorithm.LN_COBYLA);
localSolver.SetLowerBounds(lowerBounds);
localSolver.SetUpperBounds(upperBounds);
localSolver.SetMinObjective((variables, gradients) =>
{
var error = bondCf.Select((cfs, i) => GetModelPrice(referenceDate, cfs, daycount, variables, keyTs) - bondPrices[i]).ToArray();
return(error.Sum(x => x * x));
});
var result = localSolver.Optimize(initials, out finalScore);
}
fittingError = finalScore.Value;
var coeffes = new[]
{
Tuple.Create(referenceDate, initials[0]),
Tuple.Create(referenceDate, -1.0 - initials[1] - initials[2] - initials.Skip(3).Sum() * 1 / 3.0),
Tuple.Create(referenceDate, initials[1]),
Tuple.Create(referenceDate, initials[2]),
}
.Union(knotPoints.Select((x, i) => Tuple.Create(x, initials[i + 3])))
.ToArray();
//var errors = bondCf.Select((cfs, i) => GetModelPrice(referenceDate, cfs, daycount, initials, keyTs)).ToArray();
//for (var i = 0; i < errors.Length; ++i)
//{
// Console.WriteLine("{0},{1},{2}", errors[i], bondPrices[i], errors[i] - bondPrices[i]);
//}
return(coeffes); // Insert 0D point to avoid interpolation jump at the beginning
}