zero2pyld (Financial Toolbox)

zero2pyld
Par yield curve given a zero curve

Syntax

[ParRates, CurveDates] = zero2pyld(ZeroRates, CurveDates, Settle,
     OutputCompounding, OutputBasis, InputCompounding, InputBasis)

Arguments

ZeroRates
A number of bonds (NUMBONDS) by 1 vector of annualized zero rates, as decimal fractions. In aggregate, the rates constitute an implied zero curve for the investment horizon represented by CurveDates.

CurveDates
A NUMBONDS-by-1 vector of maturity dates (as serial date numbers) that correspond to the zero rates.

Settle
A serial date number that is the common settlement date for the zero rates.

OutputCompounding
(Optional) Output compounding. A scalar that sets the compounding frequency per year for annualizing the output forward rates. Allowed values are:

1
annual compounding

2
semi-annual compounding (default)

3
compounding three times per year

4
quarterly compounding

6
bimonthly compounding

12
monthly compounding

365
daily compounding

-1
continuous compounding

OutputBasis
(Optional) Output day-count basis for annualizing the forward rates. 0 = actual/actual (default), 1 = 30/360, 2 = actual/360, 3 = actual/365.

InputCompounding
(Optional) A scalar that indicates the compounding frequency per year used for annualizing the input zero rates. Allowed values are the same as for OutputCompounding. Default = OutputCompounding.

InputBasis
(Optional) Input day-count basis used for annualizing the input zero rates. Allowed values are the same as for OutputBasis. Default = OutputBasis.

`ZeroRates`	A number of bonds (`NUMBONDS`) by 1 vector of annualized zero rates, as decimal fractions. In aggregate, the rates constitute an implied zero curve for the investment horizon represented by `CurveDates`.
`CurveDates`	A `NUMBONDS`-by-1 vector of maturity dates (as serial date numbers) that correspond to the zero rates.
`Settle`	A serial date number that is the common settlement date for the zero rates.
`OutputCompounding`	(Optional) Output compounding. A scalar that sets the compounding frequency per year for annualizing the output forward rates. Allowed values are:
	`1`	annual compounding
	2	semi-annual compounding (default)
	3	compounding three times per year
	4	quarterly compounding
	6	bimonthly compounding
	12	monthly compounding
	365	daily compounding
	-1	continuous compounding
`OutputBasis`	(Optional) Output day-count basis for annualizing the forward rates. 0 = actual/actual (default), 1 = 30/360, 2 = actual/360, 3 = actual/365.
`InputCompounding`	(Optional) A scalar that indicates the compounding frequency per year used for annualizing the input zero rates. Allowed values are the same as for `OutputCompounding`. Default = `OutputCompounding`.
`InputBasis`	(Optional) Input day-count basis used for annualizing the input zero rates. Allowed values are the same as for `OutputBasis`. Default = `OutputBasis`.

Description
[ParRates, CurveDates] = zero2pyld(ZeroRates, CurveDates, Settle,OutputCompounding, OutputBasis, InputCompounding, InputBasis) returns a par yield curve given a zero curve and its maturity dates.


`ParRates`	A `NUMBONDS`-by-1 vector of annualized par yields, as decimal fractions. (Par yields = coupon rates.) In aggregate, the yield rates in `ParRates` constitute a par yield curve for the investment horizon represented by `CurveDates`.
`CurveDates`	A `NUMBONDS`-by-1 vector of maturity dates (as serial date numbers) that correspond to the par yield rates. This vector is the same as the input vector `CurveDates`.

Examples
Given a zero curve over a set of maturity dates and a settlement date

ZeroRates = [0.0457
             0.0487
             0.0506
             0.0507
             0.0505
             0.0504
             0.0506
             0.0516
             0.0539
             0.0530];
CurveDates = [datenum('06-Nov-2000')
              datenum('11-Dec-2000')
              datenum('15-Jan-2001')
              datenum('05-Feb-2001')
              datenum('04-Mar-2001')
              datenum('02-Apr-2001')
              datenum('30-Apr-2001')
              datenum('25-Jun-2001')
              datenum('04-Sep-2001')
              datenum('12-Nov-2001')];

Settle = datenum('03-Nov-2000');

Set annual compounding for the par yield curve, on an actual/actual basis. The zero curve was compounded monthly, on an actual/365 basis.

OutputCompounding = 1;
OutputBasis = 0;
InputCompounding = 12;
InputBasis = 3;

Execute the function

[ParRates, CurveDates] = zero2pyld(ZeroRates, CurveDates,... 
Settle, OutputCompounding, OutputBasis, InputCompounding,... 
InputBasis)

which returns the par yield curve at the maturity dates.

ParRates =

    0.0479
    0.0511
    0.0530
    0.0531
    0.0526
    0.0524
    0.0525
    0.0534
    0.0555
    0.0543

CurveDates =

      730796
      730831
      730866
      730887
      730914
      730943
      730971
      731027
      731098
      731167

For readability, ZeroRates and ParRates are shown only to the basis point. However, MATLAB computed them at full precision. If you enter ZeroRates as shown, ParRates may differ due to rounding.

See Also
pyld2zero and other functions for Term Structure of Interest Rates

zero2fwd Glossary