qlPiecewiseYieldCurve – create a yield curve bootsrapped from market quotes

This function creates a Yield curve which defined by a set of quotes of prices of (potentially heterogeneous) market instruments maturing at different dates. See also Live Running Example and online view-only spreadsheet.

Usage:

=qlPiecewiseYieldCurve(<ObjPrefix>, <NDays>, <Calendar>,
                       <RateHelpers>, <DayCounter>,
                       <Jumps>, <JumpDates>,
                       <Accuracy>, <TraitsID>,
                       <InterpolatorID>)

<ObjPrefix>

Optional prefix for names of objects created with this function

<NDays>

Number of dates from the EvaluationDate at which the discount factor is 1.0, i.e., number of days to the value date of the curve

<Calendar>

The calendar used for determining the business days. For example, “TARGET” (see TARGET Calendar)

<RateHelpers>

Sequence of “Rate Helpers” (see “Rate Helpers” in QuantLib) that encapsulate the market information about the yield curve

<DayCounter>

Day count convention used to calculate the interest earned over a specific period of time (see Day Count(ing) Conventions). For example, “Actual/360”.

<Jumps>

A sequence of values representing discontinuities in the yield curve. The JumpDates parameter specifies the associated dates of these discontinuities

<JumpDates>

Sequence of dates at which the yield curve is discontinuous. The parameter <Jumps> specifies the size of the discontinuity.

<Accuracy>

Optional accuracy for which the iterative bootstrap process should aim for.

<TraitsID>

A string specifying the type of the curve that will be create. Possible values are Discount, ZeroYield, or ForwardRate. The corresponding quantity is interpolated along the curve.

<InterpolatorID>

Type of interpolation to do between the implied rates. Possible values are BackwardFlat, ForwardFlat, Linear, LogLinear, LogParabolic, KrugerLogCubic, MonotonicLogCubicNaturalSpline. See also Interpolation in QuantLib

Excel Example

This is a very simple example that demonstrates building a yield curve based on quotes on two EONIA swaps. The function qlYieldTSDiscount is then used to extract the discount factor at three months implied by the curve.

=qlEonia(“EONIAIndx”)	->	EONIAIndx#0000
=qlOISRateHelper(“OIS1M”, 2, “1M”,0.01,R[-1]C)	->	OIS1M#0003
=qlOISRateHelper(“OIS6M”, 2, “6M”,0.01,R[-2]C)	->	OIS6M#0001
=qlPiecewiseYieldCurve(“YC”, 2, “TARGET”,R[-2]C:R[-1]C, “ACT/360”, ,,,”Discount”, “ForwardFlat”)	->	YC#0001
=qlYieldTSDiscount(R[-1]C,”3M”)	->	0.999112

QLW/Java example

Here is example usage in QLW – QuantLib-Addin like interface from Java and Python

// Copyright (C) 2012 Bojan Nikolic <bojan@bnikolic.co.uk>
//

import co.uk.bnikolic.qlw.property_t;
import co.uk.bnikolic.qlw.qlw;
import co.uk.bnikolic.qlw.StringVector;
import co.uk.bnikolic.qlw.LongVector;
import co.uk.bnikolic.qlw.PropertyVector;
import co.uk.bnikolic.qlw.DoubleVector;

public class qlPiecewiseYieldCurve {
    
    public static void main(String[] args) throws Exception {

        StringVector helpers=new StringVector();
        helpers.add(mkOISHelp("1M", 0.02));
        helpers.add(mkOISHelp("6M", 0.2));

        property_t dcc=new property_t("Actual/365 (Fixed)");
        
        String yc=qlw.qlPiecewiseYieldCurve("yc",
                                            new property_t(2), 
                                            "TARGET", 
                                            helpers, 
                                            dcc,
                                            new PropertyVector(),
                                            new PropertyVector(),
                                            new property_t(0.0001), 
                                            new property_t("Discount"),
                                            new property_t("ForwardFlat"));

        PropertyVector periods=new PropertyVector();
        for(int i=1; i<5; ++i)
            {
                periods.add(new property_t((i)+"M"));
            }
        DoubleVector discounts=qlw.qlYieldTSDiscount(yc,
                                                     periods, 
                                                     qlw.OH_NULL());
        for(int i=0; i<discounts.size(); ++i)
            {
                System.out.println("Discount at " + qlw.OH_GetString(periods.get(i)) +
                                   " is: " + discounts.get(i));
            }

    }

    public static String mkOISHelp(String term, double rate)
    {
        String index=qlw.qlEonia("eonia"+term, 
                                 qlw.OH_NULL());
        
        String oishelp=qlw.qlOISRateHelper("OISHelp"+term, 
                                           2,
                                           term, 
                                           new property_t(rate),
                                           index,
                                           qlw.OH_NULL());
        return oishelp;
    }

}

QLW/Python Example

The following example shows piecewise curve bootstrapped from OIS (see qlOISRateHelper – create a Rate Helper referencing an overnight index swap) data.

# Copyright (C) 2012-2018 Bojan Nikolic <bojan@bnikolic.co.uk>

from qlww import *

def mkOISHelp(term,  rate):
    index=qlEonia("eonia"+term, 
                  N());
        
    oishelp=qlOISRateHelper("OISHelp"+term, 
                            2,
                            term, 
                            property_t(rate),
                            index,
                            N()  );
    return oishelp;


helpers=StringVector()
helpers.push_back(mkOISHelp("1M", 0.2))
helpers.push_back(mkOISHelp("3M", 0.2))
helpers.push_back(mkOISHelp("6M", 0.5))
helpers.push_back(mkOISHelp("12M", 0.5))

dcc=P("Actual/365 (Fixed)");

yc=qlPiecewiseYieldCurve(UU("yc"),
                         P(2), 
                         "TARGET", 
                         helpers, 
                         dcc,
                         PropertyVector(),
                         PropertyVector(),
                         P(0.0001), 
                         P("ZeroYield"),
                         P("ForwardFlat"))

periods=[str(i)+"M" for i in range(1,12)]
discounts=qlYieldTSDiscount(yc,
                            PropV(periods),
                            N())

for i in range(len(discounts)):
    print("Discount at " + periods[i] +
          " is: " + str(discounts[i]))