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fitFunction

Custom fit interest-rate curve object to bond market data

Syntax

CurveObj = IRFunctionCurve.fitFunction(Type, Settle,
FunctionHandle, Instruments, IRFitOptionsObj)
CurveObj = IRFunctionCurve.fitFunction(Type, Settle,
FunctionHandle, Instruments, IRFitOptionsObj, 'Parameter1',
Value1, 'Parameter2', Value2, ...)

Arguments

Type

Type of interest-rate curve for a bond: zero, forward, or discount.

Settle

Scalar for the Settle date of the curve.

FunctionHandle

Function handle that defines the interest-rate curve. The function handle takes two numeric vectors (time-to-maturity and a vector of function coefficients) and returns one numeric output (interest rate or discount factor). For more information on defining a function handle, see the MATLAB® Programming Fundamentals documentation.

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.

IRFitOptionsObj

Object constructed from IRFitOptions.

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 bond. 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. For example, InstrumentBasis distinguishes a bond instrument's Basis value from the curve's Basis value.

InstrumentPeriod

(Optional) Coupons per year of the bond. A vector of integers. Allowed values are 0, 1, 2 (default), 3, 4, 6, and 12.

InstrumentBasis

(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.

InstrumentEndMonthRule

(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.

InstrumentIssueDate

(Optional) Date when an instrument was issued.

InstrumentFirstCouponDate

(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.

InstrumentLastCouponDate

(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.

InstrumentFace

(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

CurveObj = IRFunctionCurve.fitFunction(Type, Settle, FunctionHandle, Instruments, IRFitOptionsObj, 'Parameter1', Value1, 'Parameter2', Value2, ...) fits a bond to a custom fitting function. You must enter the optional arguments for Basis and Compounding 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];
CurveSettle = datenum('30-Apr-2008');
OptOptions = optimoptions('lsqnonlin','display','iter');
functionHandle = @(t,theta) polyval(theta,t);    

CustomModel = IRFunctionCurve.fitFunction('Zero', CurveSettle, ...
functionHandle,Instruments, ...
IRFitOptions([.05 .05 .05],'FitType','price',...
'OptOptions',OptOptions));
                                        Norm of      First-order 
 Iteration  Func-count     f(x)          step          optimality   CG-iterations
     0          4         38036.7                      4.92e+04
     1          8         38036.7             10       4.92e+04            0
     2         12         38036.7            2.5       4.92e+04            0
     3         16         38036.7          0.625       4.92e+04            0
     4         20         38036.7        0.15625       4.92e+04            0
     5         24         30741.5      0.0390625       1.72e+05            0
     6         28         30741.5       0.078125       1.72e+05            0
     7         32         30741.5      0.0195312       1.72e+05            0
     8         36         28713.6     0.00488281       2.33e+05            0
     9         40         20323.3     0.00976562       9.47e+05            0
    10         44         20323.3      0.0195312       9.47e+05            0
    11         48         20323.3     0.00488281       9.47e+05            0
    12         52         20323.3      0.0012207       9.47e+05            0
    13         56         19698.8    0.000305176       1.08e+06            0
    14         60           17493    0.000610352          7e+06            0
    15         64           17493      0.0012207          7e+06            0
    16         68           17493    0.000305176          7e+06            0
    17         72         15455.1    7.62939e-05       2.25e+07            0
    18         76         15455.1    0.000177499       2.25e+07            0
    19         80         13317.1     3.8147e-05       3.18e+07            0
    20         84         12865.3    7.62939e-05       7.83e+07            0
    21         88         11779.8    7.62939e-05       7.58e+06            0
    22         92         11747.6    0.000152588       1.45e+05            0
    23         96         11720.9    0.000305176       2.33e+05            0
    24        100         11667.2    0.000610352       1.48e+05            0
    25        104         11558.6      0.0012207       3.55e+05            0
    26        108         11335.5     0.00244141       1.57e+05            0
    27        112         10863.8     0.00488281       6.36e+05            0
    28        116         9797.14     0.00976562       2.53e+05            0
    29        120         6882.83      0.0195312       9.18e+05            0
    30        124         6882.83      0.0373993       9.18e+05            0
    31        128         3218.45     0.00934981       1.96e+06            0
    32        132         612.703      0.0186996       3.01e+06            0
    33        136         13.0998      0.0253882       3.05e+06            0
    34        140       0.0762922     0.00154002       5.05e+04            0
    35        144       0.0731652    3.61102e-06           29.9            0
    36        148       0.0731652    6.32335e-08          0.063            0

Local minimum possible.

lsqnonlin stopped because the final change in the sum of squares relative to 
its initial value is less than the default value of the function tolerance.
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