zero2pyld
Par yield curve given zero curve
Syntax
Description
[
returns a par yield curve given a zero curve and its maturity dates. If either input
for ParRates
,CurveDates
] = zero2pyld(ZeroRates
,CurveDates
,Settle
)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 datetime
to convert serial date
numbers to formatted datetime arrays. ParRates
is the same for
any of these input data types.
[
adds optional name-value pair argumentsParRates
,CurveDates
] = zero2pyld(___,Name,Value
)
Examples
Compute Par Yield Curve Given a Zero Curve and Maturity Dates Using datetime Inputs
Given a zero curve over a set of maturity dates, a settlement date, and annual compounding for the input zero curve and monthly compounding for the output par rates, use datetime
inputs to compute a par yield curve.
ZeroRates = [0.0457 0.0487 0.0506 0.0507 0.0505 0.0504 0.0506 0.0516 0.0539 0.0530]; 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 = 12; InputBasis = 2; OutputCompounding = 1; OutputBasis = 2; [ParRates, CurveDates] = zero2pyld(ZeroRates, CurveDates,... Settle, 'InputCompounding',12,'InputBasis',2,'OutputCompounding',1,'OutputBasis',2)
ParRates = 10×1
-0.0436
0.0611
0.0579
0.0567
0.0550
0.0543
0.0541
0.0546
0.0565
0.0561
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
Demonstrate a Roundtrip From zero2pyld
to pyld2zero
Given the following zero curve and its maturity dates, return the ParRates
.
Settle = datetime(2013,2,1); CurveDates = [datetime(2014,2,1) datetime(2015,2,1) datetime(2016,2,1) datetime(2018,2,1) datetime(2020,2,1) datetime(2023,2,1) datetime(2033,2,1) datetime(2043,2,1) ]; OriginalZeroRates = [.11 0.30 0.64 1.44 2.07 2.61 3.29 3.55]'/100; OutputCompounding = 1; OutputBasis = 0; InputCompounding = 1; InputBasis = 0; ParRates = zero2pyld(OriginalZeroRates, CurveDates, Settle, ... 'OutputCompounding', OutputCompounding, 'OutputBasis', OutputBasis, ... 'InputCompounding', InputCompounding, 'InputBasis', InputBasis)
ParRates = 8×1
0.0011
0.0030
0.0064
0.0142
0.0202
0.0251
0.0310
0.0331
For the ParRates
, use the pyld2zero
function to return the ZeroRatesOut
and determine the roundtrip error.
ZeroRatesOut = pyld2zero(ParRates, CurveDates, Settle, ... 'OutputCompounding', OutputCompounding, 'OutputBasis', OutputBasis, ... 'InputCompounding', InputCompounding, 'InputBasis', InputBasis)
ZeroRatesOut = 8×1
0.0011
0.0030
0.0064
0.0144
0.0207
0.0261
0.0329
0.0355
max(abs(OriginalZeroRates - ZeroRatesOut)) % Roundtrip error
ans = 1.4919e-16
Input Arguments
ZeroRates
— Annualized zero rates
decimal fraction
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
.
Data Types: double
CurveDates
— Maturity dates
datetime array | string array | date character vector
Maturity dates which correspond to the input
ZeroRates
, specified as a
NUMBONDS
-by-1
vector using a
datetime array, string array, or date character vectors.
To support existing code, zero2pyld
also
accepts serial date numbers as inputs, but they are not recommended.
Data Types: datetime
| string
| char
Settle
— Common settlement date for ZeroRates
datetime scalar | string scalar | date character vector
Common settlement date for input ZeroRates
,
specified as a scalar datetime, string, or date character vector.
To support existing code, zero2pyld
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: [ParRates,CurveDates] = zero2pyld(ZeroRates,CurveDates,
Settle,'OutputCompounding',3,'OutputBasis',5,'InputCompounding',4,'InputBasis',5)
OutputCompounding
— Compounding frequency of output ParRates
2
(default) | numeric values: 0
,1
,
2
, 3
,
4
, 6
, 12
,
365
, -1
Compounding frequency of output ParRates
,
specified as the comma-separated pair consisting of
'OutputCompounding'
and allowed values:
1
— Annual compounding2
— Semiannual compounding (default)3
— Compounding three times per year4
— Quarterly compounding6
— Bimonthly compounding12
— Monthly compounding
Note
If
InputCompounding
is1
,2
,3
,4
,6
, or12
andOutputCompounding
is not specified, the value ofInputCompounding
is used.If
InputCompounding
is0
(simple),-1
(continuous), or365
(daily), a validOutputCompounding
value must also be specified.If either
InputCompounding
orOutputCompounding
are not specified, the default is2
(semiannual) for both.
Data Types: double
OutputBasis
— Day-count basis of output ParRates
0
(default) | numeric values: 0
,1
,
2
, 3
,
4
, 6
, 7
,
8
, 9
,
10
, 11
,
12
, 13
Day count basis of output ParRates
, 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
For more information, see Basis.
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
InputCompounding
— Compounding frequency of input ZeroRates
2
(default) | numeric values: 0
,1
,
2
, 3
,
4
, 6
, 12
,
365
, -1
Compounding frequency of input ZeroRates
,
specified as the comma-separated pair consisting of
'InputCompounding'
and allowed values:
0
— Simple interest (no compounding)1
— Annual compounding2
— Semiannual compounding (default)3
— Compounding three times per year4
— Quarterly compounding6
— Bimonthly compounding12
— Monthly compounding365
— Daily compounding-1
— Continuous compounding
Note
If
InputCompounding
is set to0
(simple),-1
(continuous), or365
(daily), theOutputCompounding
must also be specified using a valid value.If
InputCompounding
is not specified, thenInputCompounding
is assigned the value specified forOutputCompounding
.If either
InputCompounding
orOutputCompounding
are not specified, the default is2
(semiannual) for both.
Data Types: double
InputBasis
— Day-count basis of input ZeroRates
0
(default) | numeric values: 0
,1
,
2
, 3
,
4
, 6
, 7
,
8
, 9
,
10
, 11
,
12
, 13
Day count basis of the input ZeroRates
,
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
For more information, see Basis.
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
Output Arguments
ParRates
— Par bond coupon rates
numeric
Par bond coupon rates, returned as a
NUMBONDS
-by-1
numeric vector.
ParRates
are ordered by ascending
maturity.
CurveDates
— Maturity dates that correspond to ParRates
datetime | serial date number
Maturity dates that correspond to the ParRates
,
returned as a NUMBONDS
-by-1
vector
of maturity dates that correspond to each par rate contained in
ParRates
.
ParRates
are expressed as serial date numbers
(default) or datetimes (if CurveDates
or
Settle
are datetime arrays).
CurveDates
are ordered by ascending
maturity.
Version History
Introduced before R2006aR2022b: Serial date numbers not recommended
Although zero2pyld
supports serial date numbers,
datetime
values are recommended instead. The
datetime
data type provides flexible date and time
formats, storage out to nanosecond precision, and properties to account for time
zones and daylight saving time.
To convert serial date numbers or text to datetime
values, use the datetime
function. For example:
t = datetime(738427.656845093,"ConvertFrom","datenum"); y = year(t)
y = 2021
There are no plans to remove support for serial date number inputs.
R2017b: Support for optional name-value input arguments
The specification of optional input arguments has changed. While the previous
ordered inputs syntax is still supported, it may no longer be supported in a future
release. Use the new optional name-value pair inputs:
InputCompounding
, InputBasis
,
OutputCompounding
, and
OutputBasis
.
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