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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

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 the clean 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) Scalar that sets the compounding frequency per year for the IRFunctionCurve object:

  • -1 =  Continuous compounding

  • 1 = Annual compounding

  • 2 = Semiannual compounding (default)

  • 3 = Compounding three times per year

  • 4 = Quarterly compounding

  • 6 = Bimonthly compounding

  • 12 = Monthly compounding

Basis

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

  • 0 = actual/actual (default)

  • 1 = 30/360 (SIA)

  • 2 = actual/360

  • 3 = actual/365

  • 4 = 30/360 (BMA)

  • 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/actual (ISDA)

  • 13 = BUS/252

For more information, see basis.

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.

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 (BMA)

  • 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/actual (ISDA)

  • 13 = BUS/252

For more information, see basis.

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; used when bond has an irregular first coupon period. When FirstCouponDate and LastCouponDate are both specified, FirstCouponDate takes precedence in determining the coupon payment structure. If you do not specify a FirstCouponDate, the cash flow payment dates are determined from other inputs.

LastCouponDate

(Optional) Last coupon date of a bond before the maturity date; used when bond has an irregular last coupon period. 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 is followed only by the bond's maturity cash flow date. If you do not specify a LastCouponDate, the cash flow payment dates are determined from other inputs.

Face

(Optional) Face or par value. Default = 100.

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')];

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

How To

  

 

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