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.
Coupon annual rate, specified as a NINST-by-1 vector.
Data Types: double
Settle — Settlement date serial date number | character vector
Settlement date, specified either as a scalar or NINST-by-1 vector
of serial date numbers or date character vectors.
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.
Data Types: char | double
Maturity — Maturity date serial date number | character vector
Maturity date, specified as a NINST-by-1 vector of
serial date numbers or date character vectors representing the maturity date for each
fixed-rate note.
Data Types: char | double
Name-Value Pair Arguments
Specify optional
comma-separated pairs of Name,Value arguments. Name is
the argument name and Value is the corresponding value.
Name must appear inside quotes. You can specify several name and value
pair arguments in any order as
Name1,Value1,...,NameN,ValueN.
'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.
'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.
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® date numbers
Holidays used in computing business days, specified as the comma-separated pair consisting of
'Holidays' and MATLAB date numbers using a
NHolidays-by-1
vector.
Data Types: double
'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.
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:
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.
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