zero2disc
Discount curve given zero curve
Syntax
Description
[
returns a discount curve given a zero curve and its maturity dates. If either inputs
for or areDiscRates
,CurveDates
] = zero2disc(ZeroRates
,CurveDates
,Settle
)CurveDates
Settle
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. The DiscRates
output is the
same for any of these input data types.
[
adds optional name-value pair argumentsDiscRates
,CurveDates
] = zero2disc(___,Name,Value
)
Examples
Compute a Discount Curve Given a Zero Curve and Maturity Dates Using datetime Inputs
Given a zero curve over a set of maturity dates and a settlement date, compute a discount curve using datetime
inputs.
ZeroRates = [0.0464
0.0509
0.0524
0.0525
0.0531
0.0525
0.0530
0.0531
0.0549
0.0536];
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);
Compounding = 365;
Basis = 3;
[DiscRates, CurveDates] = zero2disc(ZeroRates, CurveDates,...
Settle, Compounding, Basis)
DiscRates = 10×1
0.9996
0.9947
0.9896
0.9866
0.9826
0.9787
0.9745
0.9665
0.9552
0.9466
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
ZeroRates
— Annualized zero rates
decimal fraction
Annualized zero rates, specified as a
NUMBONDS
-by-1
vector using
decimal fractions. In aggregate, the zero 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 that correspond to the input
ZeroRates
, specified as
NUMBONDS
-by-1
vector using a
datetime array, string array, or date character vectors.
To support existing code, zero2disc
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 ZeroRates
, specified
as a scalar datetime, string, or date character vector.
Settle
is the settlement date for the bonds from
which the zero curve was bootstrapped.
To support existing code, zero2disc
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: [DiscRates,CurveDates] =
zero2disc(ZeroRates,CurveDates,Settle,'Compounding',4,'Basis',6)
Compounding
— Rate at which input ZeroRates
zero rates are compounded when annualized
2
(default) | numeric values: 0
,1
,
2
, 3
,
4
, 6
, 12
,
365
, -1
Rate at which the input ZeroRates
are
compounded when annualized, specified as the comma-separated pair
consisting of 'Compounding'
and allowed numeric
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
Data Types: double
Basis
— Day-count basis used for annualizing input ZeroRates
0
(default) | numeric values: 0
,1
,
2
, 3
,
4
, 6
, 7
,
8
, 9
,
10
, 11
,
12
, 13
Day-count basis used for annualizing the input
ZeroRates
, specified as the comma-separated
pair consisting of 'Basis'
and allowed numeric
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.
Data Types: double
Output Arguments
DiscRates
— Discount factors
decimal
Discount factors, returned as a
NUMBONDS
-by-1
vector of
decimal fractions. In aggregate, the discount factors constitute a
discount curve for the investment horizon represented by
CurveDates
.
CurveDates
— Maturity dates that correspond to DiscRates
serial date number | datetime
Maturity dates that correspond to the DiscRates
,
returned as a NUMBONDS
-by-1
vector
of maturity dates that correspond to the discount factors. This vector
is the same as the input vector CurveDates
, but is
sorted by ascending maturity.
If either inputs for CurveDates
or
Settle
are 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.
Version History
Introduced before R2006aR2022b: Serial date numbers not recommended
Although zero2disc
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 optional name-value pair inputs: Compounding
and Basis
.
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