Table of Contents

Curves

A yield curve gives discount factors, zero rates and forward rates from its reference date. FlatForward is the simplest; a bootstrapped curve fits the market's quotes.

Bootstrapping

Each quote becomes a rate helper: a deposit, a FRA, a futures contract, a swap or an overnight swap. The piecewise curve finds, pillar by pillar, the values that reprice every helper. This one bootstraps a Euribor 6M curve from two deposits and eight swaps, on illustrative quotes:

(int Years, double Rate)[] swapQuotes =
    [(2, 0.0225), (3, 0.0232), (5, 0.0245), (7, 0.0256), (10, 0.0270), (15, 0.0283), (20, 0.0288), (30, 0.0285)];
RateHelper[] helpers =
[
    new DepositRateHelper(0.0205 + shift, new Euribor(new Period(3, TimeUnit.Months)), context),
    new DepositRateHelper(0.0210 + shift, new Euribor6M(), context),
    .. swapQuotes.Select(q =>
        new SwapRateHelper(q.Rate + shift, new EuriborSwapIsdaFixA(new Period(q.Years, TimeUnit.Years)), context)),
];
var curve = new PiecewiseLogLinearDiscount(today, helpers, new Actual365Fixed(), context);

A helper takes its quote as a number and the context it is dated in. The curve runs its bootstrap when it is built, and is immutable from then on: a new quote means a new curve.

The curve's name gives what it interpolates and how. PiecewiseLogLinearDiscount interpolates the log of the discount factors linearly; PiecewiseLinearZero, PiecewiseCubicZero, PiecewiseFlatForward and the rest are QuantLib's other choices, and PiecewiseYieldCurve<TTraits, TInterpolator, TBootstrap> takes them as type arguments. The GlobalPiecewise curves fit every pillar at once, with QuantLib's global bootstrap.

Reading it

DayCounter dc = new Actual365Fixed();
foreach (int years in new[] { 1, 2, 5, 10, 20, 25 })
{
    Date d = Today + new Period(years, TimeUnit.Years);
    double discount = curve.Discount(d);
    double zero = curve.ZeroRate(d, dc, Compounding.Continuous).Rate;
    double forward = curve.ForwardRate(d, d + new Period(6, TimeUnit.Months), new Actual360(), Compounding.Simple).Rate;
    table.Add($"{years}Y", Table.D(d), Table.N(discount, 6), Table.Percent(zero), Table.Percent(forward));
}
Tenor Date Discount Zero rate 6M forward
1Y 2027-10-15 0.978380 2.1857% 2.2388%
2Y 2028-10-15 0.956486 2.2214% 2.4126%
5Y 2031-10-15 0.885807 2.4238% 2.7943%
10Y 2036-10-15 0.764483 2.6833% 3.0842%
20Y 2046-10-15 0.562262 2.8770% 2.7046%
25Y 2051-10-15 0.490797 2.8450% 2.6977%

ZeroRate and ForwardRate return an InterestRate, the rate with its day counter, compounding and frequency.

Other curves

  • Multi-curve: an €STR curve for discounting and a Euribor curve bootstrapped on it, each swap helper given the discounting curve (multi-curve bootstrapping).
  • Interpolated curves from given nodes: InterpolatedDiscountCurve<TInterpolator>, InterpolatedZeroCurve<TInterpolator>, InterpolatedForwardCurve<TInterpolator>.
  • Spreaded curves over another curve: ZeroSpreadedTermStructure, ForwardSpreadedTermStructure, and the piecewise spreads.
  • Fitted bond curves, the Nelson-Siegel family and splines: FittedBondDiscountCurve with its fitting methods.