Workflow for Creating and Analyzing a ratecurve and parametercurve

Use ratecurve or irbootstrap to create a ratecurve object.

% Create a ratecurve
Settle = datetime(2019,9,15);
Type = "zero";
ZeroTimes = [calmonths(6) calyears([1 2 3 4 5 7 10 20 30])]';
ZeroRates = [0.0052 0.0055 0.0061 0.0073 0.0094 0.0119 0.0168 0.0222 0.0293 0.0307]';
ZeroDates = Settle + ZeroTimes;
myRC = ratecurve('zero',Settle,ZeroDates,ZeroRates)

myRC = 

  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 0
                Dates: [10×1 datetime]
                Rates: [10×1 double]
               Settle: 15-Sep-2019
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Use zerorates, forwardrates, or discountfactors with the ratecurve object.

CurveSettle = datetime(2019,9,15);

% zerorates
outZeroRates = zerorates(myRC,CurveSettle+30:30:CurveSettle+720)

% forwardrates
outForwardRates = forwardrates(myRC,datetime(2019,12,15),datetime(2021,9,15),6,7)

% discountfactors
outDiscountFactors = discountfactors(myRC,CurveSettle+30:30:CurveSettle+720)

outZeroRates =

  Columns 1 through 14

    0.0052    0.0052    0.0052    0.0052    0.0052    0.0052    0.0052    0.0053    0.0053    0.0054    0.0054    0.0055    0.0055    0.0056

  Columns 15 through 24

    0.0056    0.0057    0.0057    0.0058    0.0058    0.0059    0.0059    0.0060    0.0060    0.0061


outForwardRates =

    0.0062


outDiscountFactors =

  Columns 1 through 14

    0.9996    0.9991    0.9987    0.9983    0.9979    0.9974    0.9970    0.9965    0.9961    0.9956    0.9951    0.9946    0.9941    0.9936

  Columns 15 through 24

    0.9931    0.9926    0.9920    0.9915    0.9910    0.9904    0.9898    0.9893    0.9887    0.9881

Use parametercurve, fitNelsonSiegel, or fitSvensson to create a parametercurve object.

% parametercurve
myPC = parametercurve('zero',datetime(2019,9,15),@(t) polyval([-0.0001 0.003 0.02],t),'Parameters',[-0.0001 0.003 0.02])

myPC = 

  parametercurve with properties:

              Type: "zero"
            Settle: 15-Sep-2019
       Compounding: -1
             Basis: 0
    FunctionHandle: @(t)polyval([-0.0001,0.003,0.02],t)
        Parameters: [-1.0000e-04 0.0030 0.0200]

% fitNelsonSiegel
Settle = datetime(2017,9,15);
  Maturity = [datetime(2019,9,15);datetime(2021,9,15);...
      datetime(2023,9,15);datetime(2026,9,7);...
      datetime(2035,9,15);datetime(2047,9,15)];
  
  CleanPrice = [100.1;100.1;100.8;96.6;103.3;96.3];
  CouponRate = [0.0400;0.0425;0.0450;0.0400;0.0500;0.0425];
  
  nInst = numel(CouponRate);
Bonds(nInst,1) = fininstrument.FinInstrument;
for ii=1:nInst
    Bonds(ii) = fininstrument("FixedBond","Maturity",Maturity(ii),...
        "CouponRate",CouponRate(ii));
end

NSModel = fitNelsonSiegel(Settle,Bonds,CleanPrice)

NSModel = 

  parametercurve with properties:

              Type: "zero"
            Settle: 15-Sep-2017
       Compounding: -1
             Basis: 0
    FunctionHandle: @(t)fitF(Params,t)
        Parameters: [1.2473e-05 0.0362 0.0903 16.4263]

% fitSvensson
Settle = datetime(2017,9,15);
  Maturity = [datetime(2019,9,15);datetime(2021,9,15);...
      datetime(2023,9,15);datetime(2026,9,7);...
      datetime(2035,9,15);datetime(2047,9,15)];
  
  CleanPrice = [100.1;100.1;100.8;96.6;103.3;96.3];
  CouponRate = [0.0400;0.0425;0.0450;0.0400;0.0500;0.0425];
  
  nInst = numel(CouponRate);
Bonds(nInst,1) = fininstrument.FinInstrument;
for ii=1:nInst
    Bonds(ii) = fininstrument("FixedBond","Maturity",Maturity(ii),...
        "CouponRate",CouponRate(ii));
end

SvenModel = fitSvensson(Settle,Bonds,CleanPrice)

SvenModel = 

  parametercurve with properties:

              Type: "zero"
            Settle: 15-Sep-2017
       Compounding: -1
             Basis: 0
    FunctionHandle: @(t)fitF(Params,t)
        Parameters: [2.2821 -41.8873 41.4090 -5.9589 0.3255 3.2356]

Use zerorates, discountfactors, forwardrates with the myPC parametercurve object.

% zerorates
CurveSettle = datetime('15-Sep-2019');
outZeroRates = zerorates(myPC,CurveSettle+30:30:CurveSettle+720)

% discountfactors
CurveSettle = datetime('15-Sep-2019');
outDiscountFactors = discountfactors(myPC,CurveSettle+30:30:CurveSettle+720)

% forwardrates
outForwardRates = forwardrates(myPC,datetime(2019,9,15),datetime(2020,9,15),6,7)

outZeroRates =

  Columns 1 through 14

    0.0202    0.0205    0.0207    0.0210    0.0212    0.0215    0.0217    0.0219    0.0222    0.0224    0.0226    0.0229    0.0231    0.0233

  Columns 15 through 24

    0.0235    0.0238    0.0240    0.0242    0.0244    0.0246    0.0249    0.0251    0.0253    0.0255


outDiscountFactors =

  Columns 1 through 14

    0.9983    0.9966    0.9949    0.9931    0.9913    0.9895    0.9876    0.9857    0.9838    0.9818    0.9798    0.9778    0.9757    0.9736

  Columns 15 through 24

    0.9715    0.9693    0.9671    0.9649    0.9627    0.9604    0.9581    0.9558    0.9534    0.9510


outForwardRates =

    0.0229

Convert RateSpec to a ratecurve Object

You can create a RateSpec using intenvset or toRateSpec from an IRDataCurve object. Then, you can convert this previously created RateSpec to a ratecurve object.

% Assume there is a RateSpec
Settle = datetime('01-Oct-2019');
ZeroTimes = [calmonths(6) calyears([1 2 3 4 5 7 10 20 30])]';
ZeroRates = [0.0052 0.0055 0.0061 0.0073 0.0094 0.0119 0.0168 0.0222 0.0293 0.0307]';
ZeroDates = Settle + ZeroTimes;
Basis = 1;
RateSpec = intenvset('StartDates', Settle, 'EndDates', ZeroDates, ...
    'Rates', ZeroRates, 'Basis', Basis)

RateSpec = 

  struct with fields:

           FinObj: 'RateSpec'
      Compounding: 2
             Disc: [10×1 double]
            Rates: [10×1 double]
         EndTimes: [10×1 double]
       StartTimes: [10×1 double]
         EndDates: [10×1 double]
       StartDates: 737699
    ValuationDate: 737699
            Basis: 1
     EndMonthRule: 1

% Convert the RateSpec to a ratecurve
myRC = ratecurve("zero",RateSpec.ValuationDate,RateSpec.EndDates,RateSpec.Rates,...
"Compounding",RateSpec.Compounding,"Basis",RateSpec.Basis)

myRC = 

  ratecurve with properties:

                 Type: "zero"
          Compounding: 2
                Basis: 1
                Dates: [10×1 datetime]
                Rates: [10×1 double]
               Settle: 01-Oct-2019
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

% Check the discount factors
OldDF = intenvget(intenvset(RateSpec,'EndDates',datetime('01-Oct-2024')),'Disc')
NewDF = discountfactors(myRC,datetime('01-Oct-2024'))

OldDF =

    0.9424

NewDF =

    0.9424

In this case, the RateSpec and ratecurve are identical. This may not always be the case because yearfrac is used to compute times in ratecurve while date2time is used in computing a RateSpec. For more information, see Difference Between yearfrac and date2time.