fixedbyhjm
Price fixed-rate note from Heath-Jarrow-Morton interest-rate tree
Syntax
Description
Examples
Price a 4% Fixed-Rate Note Using an HJM Forward-Rate Tree
This example shows how to price a 4% fixed-rate note using an HJM forward-rate tree by loading the file deriv.mat
, which provides HJMTree
. The HJMTree
structure contains the time and forward-rate information needed to price the note.
load deriv.mat
CouponRate = 0.04;
Settle = datetime(2000,1,1);
Maturity = datetime(2003,1,1);
Price = fixedbyhjm(HJMTree, CouponRate, Settle, Maturity)
Price = 98.7159
Input Arguments
HJMTree
— Interest-rate structure
structure
Interest-rate tree structure, created by hjmtree
Data Types: struct
CouponRate
— Coupon annual rate
decimal
Coupon annual rate, specified as a NINST
-by-1
vector.
Data Types: double
Settle
— Settlement date
datetime array | string array | date character vector
Settlement date, specified either as a scalar or a
NINST
-by-1
vector using a datetime array, string array, or date
character vectors.
To support existing code, fixedbyhjm
also
accepts serial date numbers as inputs, but they are not recommended.
The Settle
date for every fixed-rate note is set to the
ValuationDate
of the HJM tree. The fixed-rate note argument
Settle
is ignored.
Maturity
— Maturity date
datetime array | string array | date character vector
Maturity date, specified as a NINST
-by-1
vector using a
datetime array, string array, or date character
vectors representing the maturity date for each
fixed-rate note.
To support existing code, fixedbyhjm
also
accepts serial date numbers as inputs, but they are not recommended.
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: [Price,PriceTree] =
fixedbyhjm(HJMTree,CouponRate,Settle,Maturity,'FixedReset',4)
FixedReset
— Frequency of payments per year
1
(default) | vector
Frequency of payments per year, specified as
the comma-separated pair consisting of
'FixedReset'
and a
NINST
-by-1
vector.
Data Types: double
Basis
— Day count basis
0
(actual/actual) (default) | integer from 0
to 13
Day count basis representing the basis used when annualizing the input forward rate tree,
specified as the comma-separated pair consisting
of 'Basis'
and a
NINST
-by-1
vector.
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
Principal
— Notional principal amounts or principal value schedules
100
(default) | vector or cell array
Notional principal amounts, specified as the comma-separated pair consisting of
'Principal'
and a vector or
cell array.
Principal
accepts a NINST
-by-1
vector
or NINST
-by-1
cell array, where
each element of the cell array is a NumDates
-by-2
cell
array and the first column is dates and the second column is its associated
notional principal value. The date indicates the last day that the
principal value is valid.
Data Types: cell
| double
Options
— Derivatives pricing options structure
structure
Derivatives pricing options structure, specified as the comma-separated pair consisting of
'Options'
and a structure using
derivset
.
Data Types: struct
EndMonthRule
— End-of-month rule flag for generating dates when Maturity
is end-of-month date for month having 30 or fewer days
1
(in effect) (default) | nonnegative integer [0,1]
End-of-month rule flag for generating dates when Maturity
is an
end-of-month date for a month having 30 or fewer
days, specified as the comma-separated pair
consisting of 'EndMonthRule'
and a nonnegative integer [0
,
1
] using a
NINST
-by-1
vector.
0
= Ignore rule, meaning that a payment date is always the same numerical day of the month.1
= Set rule on, meaning that a payment date is always the last actual day of the month.
Data Types: logical
AdjustCashFlowsBasis
— Flag to adjust cash flows based on actual period day count
false
(default) | value of 0
(false) or 1
(true)
Flag to adjust cash flows based on actual period day count, specified as the comma-separated
pair consisting of
'AdjustCashFlowsBasis'
and a
NINST
-by-1
vector of logicals with values of
0
(false) or
1
(true).
Data Types: logical
Holidays
— Holidays used in computing business days
if not specified, the default
is to use holidays.m
(default) | MATLAB® dates
Holidays used in computing business days, specified as the comma-separated pair consisting of
'Holidays'
and MATLAB dates using a
NHolidays
-by-1
vector.
Data Types: datetime
BusinessDayConvention
— Business day conventions
actual
(default) | character vector | cell array of character vectors
Business day conventions, specified as the comma-separated pair consisting of
'BusinessDayConvention'
and a
character vector or a
N
-by-1
cell
array of character vectors of business day
conventions. The selection for business day
convention determines how non-business days are
treated. Non-business days are defined as weekends
plus any other date that businesses are not open
(e.g. statutory holidays). Values are:
actual
— Non-business days are effectively ignored. Cash flows that fall on non-business days are assumed to be distributed on the actual date.follow
— Cash flows that fall on a non-business day are assumed to be distributed on the following business day.modifiedfollow
— Cash flows that fall on a non-business day are assumed to be distributed on the following business day. However if the following business day is in a different month, the previous business day is adopted instead.previous
— Cash flows that fall on a non-business day are assumed to be distributed on the previous business day.modifiedprevious
— Cash flows that fall on a non-business day are assumed to be distributed on the previous business day. However if the previous business day is in a different month, the following business day is adopted instead.
Data Types: char
| cell
Output Arguments
Price
— Expected fixed-rate note prices at time 0
vector
Expected fixed-rate note prices at time 0, returned as a NINST
-by-1
vector.
PriceTree
— Tree structure of instrument prices
structure
Tree structure of instrument prices, returned as a MATLAB structure
of trees containing vectors of instrument prices and accrued interest,
and a vector of observation times for each node. Within PriceTree
:
PriceTree.PBush
contains the clean prices.PriceTree.AITree
contains the accrued interest.PriceTree.tObs
contains the observation times.
More About
Fixed-Rate Note
A fixed-rate note is a long-term debt security with a preset interest rate and maturity, by which the interest must be paid.
The principal may or may not be paid at maturity. In Financial Instruments Toolbox™, the principal is always paid at maturity. For more information, see Fixed-Rate Note.
Version History
Introduced before R2006aR2022b: Serial date numbers not recommended
Although fixedbyhjm
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.
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