Fixed-Income Toolbox™

fitSmoothingSpline - Fit smoothing spline to bond market data

Class

@IRFunctionCurve

Syntax

CurveObj = IRFunctionCurve.fitSmoothingSpline(Type, Settle, 
Instruments, Lambdafun)
CurveObj = IRFunctionCurve.fitSmoothingSpline(Type, Settle, 
Instruments, Lambdafun, Parameter1', Value1, 'Parameter2', Value2, ...)

Arguments

Note You must have a license for Spline Toolbox software to use the fitSmoothingSpline method.

Type

Type of interest-rate curve for a bond: forward.

Settle

Scalar or column vector of settlement dates.

Instruments

N-by-4 data matrix for Instruments where the first column is Settle date, the second column is Maturity, the third column is dirty price, and the fourth column is a CouponRate for the bond.

Lambdafun

Penalty function that takes as its input time and returns a penalty value. Use a function handle to support the penalty function. The function handle for the penalty function which takes one numeric input (time-to-maturity) and returns one numeric output (penalty to be applied to the curvature of the spline). For more information on defining a function handle, see the MATLAB Programming Fundamentals documentation.

Note The smoothing spline represents the forward curve. The spline is penalized for curvature by specifying a penalty function. This fit may only be done with a FitType of DurationWeightedPrice.

Knots

(Optional) Vector of knot locations (times-to-maturity); by default, knots is set to be a vector comprised of 0 and the time to maturity of all input instruments.

Compounding

(Optional) Compounding value for an IRFunctionCurve object:

-1
1
2 (default)
3
4
6
12

Basis

(Optional) Day-count basis of the interest-rate curve. A vector of integers.

0 = actual/actual (default)
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 (ISMA)
9 = actual/360 (ISMA)
10 = actual/365 (ISMA)
11 = 30/360E (ISMA)
12 = actual/365 (ISDA)

Instrument Parameters

For each bond Instrument, you can specify the following additional instrument parameters as parameter/value pairs by prepending the word Instrument to the parameter field. For example, prepending InstrumentBasis distinguishes a bond instrument's Basis value from the curve's Basis value.

`CouponRate`	(Optional) Decimal number indicating the annual percentage rate used to determine the coupons payable on a bond.
`Period`	(Optional) Coupons per year of the bond. A vector of integers. Allowed values are 0, 1, 2 (default), 3, 4, 6, and 12.
`Basis`	(Optional) Day-count basis of the bond. A vector of integers. 0 = actual/actual (default) 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 (ISMA) 9 = actual/360 (ISMA) 10 = actual/365 (ISMA) 11 = 30/360E (ISMA) 12 = actual/365 (ISDA)
`EndMonthRule`	(Optional) End-of-month rule. A vector. This rule applies only when `Maturity` is an end-of-month date for a month having 30 or fewer days. 0 = ignore rule, meaning that a bond's coupon payment date is always the same numerical day of the month. 1 = set rule on (default), meaning that a bond's coupon payment date is always the last actual day of the month.
`IssueDate`	(Optional) Date when an instrument was issued.
`FirstCouponDate`	(Optional) Date when a bond makes its first coupon payment. When `FirstCouponDate` and `LastCouponDate` are both specified, `FirstCouponDate` takes precedence in determining the coupon payment structure.
`LastCouponDate`	(Optional) Last coupon date of a bond before the maturity date. In the absence of a specified `FirstCouponDate`, a specified `LastCouponDate` determines the coupon structure of the bond. The coupon structure of a bond is truncated at the `LastCouponDate` regardless of where it falls and will be followed only by the bond's maturity cash flow date.
`Face`	(Optional) Face or par value. Default = 100.

Note When using Instrument parameter/value pairs, you can specify simple interest for a bond by specifying the InstrumentPeriod value as 0. If InstrumentBasis and InstrumentPeriod are not specified for a bond, the following default values are used: Basis is 0 (act/act) and Period is 2.

Description

Fcurve = IRFunctionCurve.fitSmoothingSpline(Type, Settle, Instruments, Lambdafun, Parameter1', Value1, 'Parameter2', Value2, ...) fits a smoothing spline to market data for a bond. You must enter the optional arguments for Basis, Compounding, and Knots as parameter/value pairs.

Examples

Settle = repmat(datenum('30-Apr-2008'),[6 1]);
Maturity = [datenum('07-Mar-2009');datenum('07-Mar-2011');...
datenum('07-Mar-2013');datenum('07-Sep-2016');...
datenum('07-Mar-2025');datenum('07-Mar-2036')];

DirtyPrice = [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];
Instruments = [Settle Maturity DirtyPrice CouponRate];
PlottingPoints = datenum('07-Mar-2009'):180:datenum('07-Mar-2036');
Yield = bndyield(DirtyPrice,CouponRate,Settle,Maturity);

SmoothingModel = IRFunctionCurve.fitSmoothingSpline('Forward',datenum('30-Apr-2008'),...
Instruments,@(t) 1000);

To create the plot:

plot(PlottingPoints,SmoothingModel.getParYields(PlottingPoints),'b')
hold on
scatter(Maturity,Yield,'black')