fitNelsonSiegel

Fit Nelson-Siegel model to bond market data

Since R2020a

Syntax

outCurve = fitNelsonSiegel(Settle,Instruments,CleanPrice)

outCurve = fitNelsonSiegel(___,Name=Value)

Description

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.

Examples

Fit Nelson-Siegel Model to Bond Market Data

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);...
      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 = fininstrument("FixedBond",'Maturity',Maturity,'CouponRate',CouponRate);

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: [3.4799e-08 0.0363 0.0900 16.5823]

Input Arguments

Settle — Settlement date

datetime scalar | string scalar | date character vector

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.

Instruments — Bond instrument objects

scalar | array

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

Data Types: object

CleanPrice — Observed market prices

vector

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)

Basis — Day count basis

0 (actual/actual) (default) | integer from 0 to 13

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

x0 — Initial estimate

[4/10 -1/10 -1/10 2] (default) | vector

Since R2024a

Initial estimate, specified as x0 and a vector.

Data Types: double

lb — Lower bound

[0 -Inf -Inf 0] (default) | vector

Since R2024a

Lower bound, specified as lb and a vector.

Data Types: double

ub — Upper bound

[Inf Inf Inf Inf] (default) | vector

Since R2024a

Upper bound, specified as ub and a vector.

Data Types: double

Output Arguments

outCurve — Fitted Nelson-Siegel model

parametercurve object

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

Version History

Introduced in R2020a

R2024a: Added Optional Name-Value Arguments for Basis, x0, lb, and ub

fitNelsonSiegel supports optional name-value arguments for Basis, x0, lb, and ub.

R2022b: Serial date numbers not recommended

Although fitNelsonSiegel supports serial date numbers, datetime values are recommended instead. The datetime data type provides flexible date and time formats, storage out to nanosecond precision, and properties to account for time zones and daylight saving time.

To convert serial date numbers or text to datetime values, use the datetime function. For example:

t = datetime(738427.656845093,"ConvertFrom","datenum");
y = year(t)

y =

        2021

There are no plans to remove support for serial date number inputs.