Price fixed-rate note from set of zero curves
[ prices
a fixed-rate note from a set of zero curves.Price,DirtyPrice,CFlowAmounts,CFlowDates]
= fixedbyzero(RateSpec,CouponRate,Settle,Maturity)
[ adds
additional name-value pair arguments.Price,DirtyPrice,CFlowAmounts,CFlowDates]
= fixedbyzero(___,Name,Value)
This example shows how to price a 4% fixed-rate note using a set of zero curves by loading the file deriv.mat, which provides ZeroRateSpec, the interest-rate term structure needed to price the note.
load deriv.mat CouponRate = 0.04; Settle = '01-Jan-2000'; Maturity = '01-Jan-2003'; Price = fixedbyzero(ZeroRateSpec, CouponRate, Settle, Maturity)
Price = 98.7159
Assume that a financial institution has an existing swap with three years left to maturity where they are receiving 5% per year in yen and paying 8% per year in USD. The reset frequency for the swap is annual, the principals for the two legs are 1200 million yen and $10 million USD, and both term structures are flat.
Settle = datenum('15-Aug-2015'); Maturity = datenum('15-Aug-2018'); Reset = 1; r_d = .09; r_f = .04; FixedRate_d = .08; FixedRate_f = .05; Principal_d = 10000000; Principal_f = 1200000000; S0 = 1/110;
Construct term structures.
RateSpec_d = intenvset('StartDate',Settle,'EndDate',Maturity,'Rates',r_d,'Compounding',-1); RateSpec_f = intenvset('StartDate',Settle,'EndDate',Maturity,'Rates',r_f,'Compounding',-1);
Use fixedbyzero:
B_d = fixedbyzero(RateSpec_d,FixedRate_d,Settle,Maturity,'Principal',Principal_d,'Reset',Reset); B_f = fixedbyzero(RateSpec_f,FixedRate_f,Settle,Maturity,'Principal',Principal_f,'Reset',Reset);
Compute swap price. Based on Hull (see References), a cross currency swap can be valued with the following formula V_swap = S0*B_f − B_d.
V_swap = S0*B_f - B_d
V_swap = 1.5430e+06
RateSpec — Annualized zero rate term structureAnnualized zero rate term structure, specified using intenvset to create a RateSpec.
Data Types: struct
CouponRate — Annual rateAnnual rate, specified as NINST-by-1 decimal
annual rate or a NINST-by-1 cell
array where each element is a NumDates-by-2 cell
array and the first column is dates and the second column is associated
rates. The date indicates the last day that
the coupon rate is valid.
Data Types: double | cell
Settle — Settlement dateSettlement date, specified either as a scalar or NINST-by-1 vector
of serial date numbers or date character vectors.
Settle must be earlier than Maturity.
Data Types: char | double
Maturity — Maturity dateMaturity 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
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.
[Price,DirtyPrice,CFlowAmounts,CFlowDates]
= fixedbyzero(RateSpec,CouponRate,Settle,Maturity,'Principal',Principal)'FixedReset' — Frequency of payments per year1
(default) | vectorFrequency 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 13Day count basis, 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 schedules100 (default) | vector or cell arrayNotional 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
'EndMonthRule' — End-of-month rule flag for generating dates when Maturity is end-of-month date for month having 30 or fewer days1 (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 countfalse (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 daysholidays.m (default) | MATLAB® date numbersHolidays 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 conventionsactual (default) | character vector | cell array of character vectorsBusiness 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
Price — Fixed-rate note pricesFloating-rate note prices, returned as a (NINST)
by number of curves (NUMCURVES) matrix. Each column
arises from one of the zero curves.
DirtyPrice — Dirty bond priceDirty bond price (clean + accrued interest), returned as a NINST-
by-NUMCURVES matrix. Each column arises from one
of the zero curves.
CFlowAmounts — Cash flow amountsCash flow amounts, returned as a NINST- by-NUMCFS matrix
of cash flows for each bond.
CFlowDates — Cash flow datesCash flow dates, returned as a NINST- by-NUMCFS matrix
of payment dates for each bond.
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.
[1] Hull, J. Options, Futures, and Other Derivatives. Prentice-Hall, 2011.
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