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Fit Nelson-Siegel model to bond market data

Since R2020a



outCurve = fitNelsonSiegel(Settle,Instruments,CleanPrice) fits a Nelson-Siegel model to bond data.

After creating a parametercurve object for outCurve, you can use the associated object functions discountfactors, zerorates, and forwardrates.


outCurve = fitNelsonSiegel(___,Name=Value) fits a Nelson-Siegel model to bond data using optional name-value arguments for Basis, x0, lb, and ub.


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Define the bond data and use fininstrument to create FixedBond instrument objects.

 Settle = datetime(2017,9,15);
  Maturity = [datetime(2019,9,15);datetime(2021,9,15);...
  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),...

Use fitNelsonSiegel to create a parametercurve object.

NSModel = fitNelsonSiegel(Settle,Bonds,CleanPrice)
Local minimum possible.

lsqnonlin stopped because the final change in the sum of squares relative to 
its initial value is less than the value of the function tolerance.
NSModel = 
  parametercurve with properties:

              Type: "zero"
            Settle: 15-Sep-2017
       Compounding: -1
             Basis: 0
    FunctionHandle: @(t)fitF(Params,t)
        Parameters: [3.5556e-08 0.0363 0.0900 16.5823]

Input Arguments

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Settlement date, specified as a scalar datetime, string, or date character vector.

To support existing code, fitNelsonSiegel also accepts serial date numbers as inputs, but they are not recommended.

Bond instrument objects, specified as a scalar bond object or an array of bond instruments objects using FixedBond.

Data Types: object

Observed market prices, specified as a vector.

Data Types: double

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: NSModel = fitNelsonSiegel(Settle,Bonds,CleanPrice,Basis=4)

Since R2024a

Day count basis, specified as Basis and a scalar or a NINST-by-1 matrix.

  • 0 — actual/actual

  • 1 — 30/360 (SIA)

  • 2 — actual/360

  • 3 — actual/365

  • 4 — 30/360 (PSA)

  • 5 — 30/360 (ISDA)

  • 6 — 30/360 (European)

  • 7 — actual/365 (Japanese)

  • 8 — actual/actual (ICMA)

  • 9 — actual/360 (ICMA)

  • 10 — actual/365 (ICMA)

  • 11 — 30/360E (ICMA)

  • 12 — actual/365 (ISDA)

  • 13 — BUS/252

For more information, see Basis.

Data Types: double

Since R2024a

Initial estimate, specified as x0 and a vector.

Data Types: double

Since R2024a

Lower bound, specified as lb and a vector.

Data Types: double

Since R2024a

Upper bound, specified as ub and a vector.

Data Types: double

Output Arguments

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Fitted Nelson-Siegel model, returned as a parametercurve object.

Version History

Introduced in R2020a

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