zero2fwd (Financial Toolbox)

zero2fwd
Forward curve given a zero curve

Syntax

[ForwardRates, CurveDates] = zero2fwd(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
[ForwardRates, CurveDates] = zero2fwd(ZeroRates, CurveDates, Settle, OutputCompounding, OutputBasis, InputCompounding, InputBasis) returns an implied forward rate curve given a zero curve and its maturity dates.


`ForwardRates`	A `NUMBONDS`-by-1 vector of decimal fractions. In aggregate, the rates in `ForwardRates` constitute a forward curve over the dates in `CurveDates`.
`CurveDates`	A `NUMBONDS`-by-1 vector of maturity dates (as serial date numbers) that correspond to the forward rates in. 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 = [0.0458
             0.0502
             0.0518
             0.0519
             0.0524
             0.0519
             0.0523
             0.0525
             0.0541
             0.0529];

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 forward curve, on an actual/actual basis. The zero curve was compounded daily on an actual/365 basis.

OutputCompounding = 1;
OutputBasis = 0;
InputCompounding = 365;
InputBasis = 3;

Execute the function

[ForwardRates, CurveDates] = zero2fwd(ZeroRates, CurveDates,... 
Settle, OutputCompounding, OutputBasis, InputCompounding,... 
InputBasis)

which returns the forward rate curve ForwardRates at the maturity dates CurveDates.

ForwardRates =

      0.0469
      0.0519
      0.0550
      0.0536
      0.0556
      0.0511
      0.0559
      0.0546
      0.0612
      0.0487

CurveDates =

      730796
      730831
      730866
      730887
      730914
      730943
      730971
      731027
      731098
      731167

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

See Also
fwd2zero and other functions for Term Structure of Interest Rates

zero2disc zero2pyld