# zero2fwd

Forward curve given zero curve

## Description

example

[ForwardRates,CurveDates] = zero2fwd(ZeroRates,CurveDates,Settle) returns an implied forward rate curve given a zero curve and its maturity dates. If either input for CurveDates or Settle is a datetime array, CurveDates is returned as a datetime array. Otherwise, CurveDates is returned as a serial date number. Use the function datestr to convert serial date numbers to formatted date character vectors. ForwardRates is the same for any of these input data types.

example

[ForwardRates,CurveDates] = zero2fwd(___,Name,Value) adds optional name-value pair arguments

## Examples

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Given a zero curve over a set of maturity dates, a settlement date, and a compounding rate, use datetime compute the forward rate curve.

ZeroRates = [0.0458
0.0502
0.0518
0.0519
0.0524
0.0519
0.0523
0.0525
0.0541
0.0529];

CurveDates = [datetime(2000,11,6)
datetime(2000,12,11)
datetime(2001,1,15)
datetime(2001,2,5)
datetime(2001,3,4)
datetime(2001,4,2)
datetime(2001,4,30)
datetime(2001,6,25)
datetime(2001,9,4)
datetime(2001,11,12)];

Settle = datetime(2000,11,3);
InputCompounding = 1;
InputBasis = 2;
OutputCompounding = 1;
OutputBasis = 2;

[ForwardRates, CurveDates] = zero2fwd(ZeroRates, CurveDates,...
Settle,'InputCompounding',1,'InputBasis',2,'OutputCompounding',1,'OutputBasis',2)
ForwardRates = 10×1

0.0458
0.0506
0.0535
0.0522
0.0541
0.0498
0.0544
0.0531
0.0594
0.0476

CurveDates = 10x1 datetime
06-Nov-2000
11-Dec-2000
15-Jan-2001
05-Feb-2001
04-Mar-2001
02-Apr-2001
30-Apr-2001
25-Jun-2001
04-Sep-2001
12-Nov-2001

## Input Arguments

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Annualized zero rates, specified as a NUMBONDS-by-1 vector using decimal fractions. In aggregate, the rates constitute an implied zero curve for the investment horizon represented by CurveDates. The first element pertains to forward rates from the settlement date to the first curve date.

Data Types: double

Maturity dates, specified as a NUMBONDS-by-1 vector using a datetime array, string array, or date character vectors that correspond to the ZeroRates.

To support existing code, zero2fwd also accepts serial date numbers as inputs, but they are not recommended.

Data Types: datetime | string | char

Common settlement date for input ZeroRates, specified as scalar datetime, string, or date character vector.

To support existing code, zero2fwd also accepts serial date numbers as inputs, but they are not recommended.

Data Types: datetime | string | char

### Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: [ForwardRates,CurveDates] = zero2fwd(ZeroRates,CurveDates,Settle,'InputCompounding',3,'InputBasis',5,'OutputCompounding',4,'OutputBasis',5)

Compounding frequency of input zero rates, specified as the comma-separated pair consisting of 'InputCompounding' and allowed values:

• 0 — Simple interest (no compounding)

• 1 — Annual compounding

• 2 — Semiannual compounding (default)

• 3 — Compounding three times per year

• 4 — Quarterly compounding

• 6 — Bimonthly compounding

• 12 — Monthly compounding

• 365 — Daily compounding

• -1 — Continuous compounding

Note

If InputCompounding is not specified, then InputCompounding is assigned the value specified for OutputCompounding. If either InputCompounding or OutputCompounding are not specified, the default is 2 (semiannual) for both.

Data Types: double

Day count basis of input zero rates, specified as the comma-separated pair consisting of 'InputBasis' and allowed values:

• 0 = actual/actual

• 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 (ICMA)

• 9 = actual/360 (ICMA)

• 10 = actual/365 (ICMA)

• 11 = 30/360E (ICMA)

• 12 = actual/365 (ISDA)

• 13 = BUS/252

Note

If InputBasis is not specified, then InputBasis is assigned the value specified for OutputBasis. If either InputBasis or Outputbasis are not specified, the default is 0 (actual/actual) for both.

Data Types: double

Compounding frequency of output forward rates, specified as the comma-separated pair consisting of 'OutputCompounding' and allowed values:

• 0 — Simple interest (no compounding)

• 1 — Annual compounding

• 2 — Semiannual compounding (default)

• 3 — Compounding three times per year

• 4 — Quarterly compounding

• 6 — Bimonthly compounding

• 12 — Monthly compounding

• 365 — Daily compounding

• -1 — Continuous compounding

Note

If OutputCompounding is not specified, then OutputCompounding is assigned the value specified for InputCompounding. If either InputCompounding or OutputCompounding are not specified, the default is 2 (semiannual) for both.

Data Types: double

Day count basis of output forward rates, specified as the comma-separated pair consisting of 'OutputBasis' and allowed values:

• 0 = actual/actual

• 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 (ICMA)

• 9 = actual/360 (ICMA)

• 10 = actual/365 (ICMA)

• 11 = 30/360E (ICMA)

• 12 = actual/365 (ISDA)

• 13 = BUS/252

Note

If OutputBasis is not specified, then OutputBasis is assigned the value specified for InputBasis. If either InputBasis or OutputBasis are not specified, the default is 0 (actual/actual) for both.

Data Types: double

## Output Arguments

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Forward curve for the investment horizon represented by CurveDates, returned as a NUMBONDS-by-1 vector of decimal fractions. In aggregate, the rates in ForwardRates constitute a forward curve over the dates in CurveDates. ForwardRates are ordered by ascending maturity.

Maturity dates that correspond to the ForwardRates, returned as a NUMBONDS-by-1 vector of maturity dates that correspond to the ForwardRates.

ForwardRates are expressed as serial date numbers (default) or datetimes (if CurveDates or Settle are datetime arrays), representing the maturity dates for each rate in ForwardRates. These dates are the same dates as those associated with the input ZeroRates, but are ordered by ascending maturity.

## Version History

Introduced before R2006a

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