Discount margin for floating-rate bond
Margin = floatdiscmargin(Price,SpreadSettle,Maturity,RateInfo,LatestFloatingRate)
The input RateInfo determines whether the discount margin
or the zero discount margin is calculated. Principal schedules are supported
using Principal.
Margin = floatdiscmargin(___,Name,Value)
Use floatdiscmargin to compute the discount margin and zero discount margin for a floating-rate note.
Define data for the floating-rate note.
Price = 99.99; Spread = 50; Settle = '20-Jan-2011'; Maturity = '15-Jan-2012'; LatestFloatingRate = 0.05; StubRate = 0.049; SpotRate = 0.05; Reset = 4; Basis = 2;
Compute the discount margin.
dMargin = floatdiscmargin(Price, Spread, Settle, Maturity, ... [StubRate, SpotRate], LatestFloatingRate,'Reset', Reset, 'Basis', Basis, ... 'AdjustCashFlowsBasis', true)
dMargin = 48.4810
Usually you want to set AdjustCashFlowsBasis to true, so cash flows are calculated with adjustments on accrual amounts.
Create an annualized zero-rate term structure to calculate the zero discount margin.
Rates = [0.0500;
0.0505;
0.0510;
0.0520];
StartDates = ['20-Jan-2011';
'15-Apr-2011';
'15-Jul-2011';
'15-Oct-2011'];
EndDates = ['15-Apr-2011';
'15-Jul-2011';
'15-Oct-2011';
'15-Jan-2012'];
ValuationDate = '20-Jan-2011';
RateSpec = intenvset('Compounding', Reset, 'Rates', Rates,...
'StartDates', StartDates, 'EndDates', EndDates,...
'ValuationDate', ValuationDate, 'Basis', Basis);Calculate the zero discount margin using the previous yield curve.
dMargin = floatdiscmargin(Price, Spread, Settle, Maturity, ... RateSpec, LatestFloatingRate,'Reset', Reset, 'Basis', Basis, ... 'AdjustCashFlowsBasis', true)
dMargin = 46.0688
Use floatdiscmargin to compute the discount margin and zero discount margin for a floating-rate note using datetime inputs.
Price = 99.99; Spread = 50; Settle = '20-Jan-2011'; Maturity = '15-Jan-2012'; LatestFloatingRate = 0.05; StubRate = 0.049; SpotRate = 0.05; Reset = 4; Basis = 2; Settle = datetime(Settle,'Locale','en_US'); Maturity = datetime(Maturity,'Locale','en_US'); dMargin = floatdiscmargin(Price, Spread, Settle, Maturity, ... [StubRate, SpotRate], LatestFloatingRate,'Reset', Reset, 'Basis', Basis, ... 'AdjustCashFlowsBasis', true)
dMargin = 48.4810
Price — Bond prices where discount margin is to be computedBond prices where discount margin is to be computed, specified as a
NINST-by-1 matrix.
Note
The spread is calculated against the clean price (the function
internally does not add the accrued interest to the price specified by
the Price input). If the spread is required against
the dirty price, the price of a bond that includes the accrued interest,
you must supply the dirty price for the Price
input.
Data Types: double
Spread — Number of basis points over the reference rateNumber of basis points over the reference rate, specified as a
NINST-by-1 matrix.
Data Types: double
Settle — Settlement date of the floating-rate bondsSettlement date of the floating-rate bonds, specified as serial date
number, date character vector, or datetime array. If supplied as a
NINST-by-1 vector of dates,
all settlement dates must be the same (only a single settlement date is
supported)
Data Types: double | char | datetime
Maturity — Maturity date of the floating-rate bondMaturity date of the floating-rate bond, specified as serial date number, date character vector, or datetime array.
Data Types: double | char | datetime
RateInfo — Interest-rate informationinterest-rate information, specified as
NINST-by-2 vector where the:
First column is the stub rate between the settlement date and the first coupon rate.
Second column is the reference rate for the term of the
floating coupons (for example, the 3-month LIBOR from
settlement date for a bond with a Reset
of 4).
Note
If the RateInfo argument is an annualized
zero-rate term structure created by intenvset (Financial Instruments Toolbox),
the zero discount margin is calculated.
Data Types: double
LatestFloatingRate — Rate for next floating payment set at last reset dateRate for the next floating payment set at the last reset date,
specified as NINST-by-1 vector.
Data Types: 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.
Margin =
floatdiscmargin(Price,Spread,Settle,Maturity,RateInfo,LatestFloatingRate,'Reset',2,'Basis',5)'Reset' — Frequency of payments per year1 (default) | numericFrequency of payments per year, specified as
NINST-by-1 vector.
Data Types: double
'Basis' — Day-count basis used for time factor calculations0 (actual/actual) (default) | integers of the set [0...13] | vector of integers of the set [0...13]Day-count basis used for time factor calculations, specified as a
NINST-by-1 vector. Values
are:
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 amounts100 (default) | numericNotional principal amounts, specified as a
NINST-by-1 vector or a
NINST-by-1 cell array
where each element is a
NUMDATES-by-2 cell array
where the first column is dates and the second column is the
associated principal amount. The date indicates the last day that
the principal value is valid.
Data Types: double | cell
'EndMonthRule' — End-of-month rule flag1 (in effect) (default) | nonnegative integer 0 or
1End-of-month rule flag, specified as a
NINST-by-1 vector. This
rule applies only when Maturity is an
end-of-month date for a month having 30 or fewer days.
0 = Ignore rule, meaning that a
bond coupon payment date is always the same numerical
day of the month.
1 = Set rule on, meaning that a
bond coupon payment date is always the last actual day
of the month.
Data Types: logical
'AdjustCashFlowsBasis' — Adjust cash flows according to accrual amount0 (not in effect) (default) | nonnegative integer 0 or
1Adjusts cash flows according to the accrual amount, specified as a
NINST-by-1 vector of logicals.
Note
Usually you want to set
AdjustCashFlowsBasis to
1, so cash flows are calculated with
adjustments on accrual amounts. The default is set to
0 to be consistent with floatbyzero (Financial Instruments Toolbox).
Data Types: logical
'Holidays' — Dates for holidaysholidays.m used (default)Dates for holidays, specified as
NHOLIDAYS-by-1 vector of
MATLAB® dates using serial date numbers, date character
vectors, or datetime arrays. Holidays are used in computing business
days.
Data Types: double | char | datetime
'BusinessDayConvention' — Business day conventions'actual'
(default) | character vector with values'actual',
'follow',
'modifiedfollow', 'previous'or
'modifiedprevious'Business day conventions, specified as a
NINST-by-1 cell array of
character vectors of business day conventions to be used in
computing payment dates. The selection for business day convention
determines how nonbusiness days are treated. Nonbusiness days are
defined as weekends plus any other date that businesses are not open
(for example, statutory holidays). Values are:
'actual' — Nonbusiness 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 nonbusiness 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 nonbusiness day are assumed to be distributed
on the previous business day.
'modifiedprevious' — Cash
flows that fall on a nonbusiness 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
Margin — Discount marginDiscount margin, returned as a
NINST-by-1 vector of the
discount margin if RateInfo is specified as a
NINST-by-2 vector of stub and
spot rates.
If RateInfo is specified as an annualized zero
rate term structure created by intenvset (Financial Instruments Toolbox),
Margin is returned as a
NINST-by-NCURVES matrix of the
zero discount margin.
[1] Fabozzi, Frank J., Mann, Steven V. Floating-Rate Securities. John Wiley and Sons, New York, 2000.
[2] Fabozzi, Frank J., Mann, Steven V. Introduction to Fixed Income Analytics: Relative Value Analysis, Risk Measures and Valuation. John Wiley and Sons, New York, 2010.
[3] O'Kane, Dominic, Sen, Saurav. “Credit Spreads Explained.” Lehman Brothers Fixed Income Quantitative Research, March 2004.
bndspread | datetime | floatmargin | floatbyzero (Financial Instruments Toolbox) | intenvset (Financial Instruments Toolbox)
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