floatbybdt
Price floating-rate note from Black-Derman-Toy interest-rate tree
Syntax
Description
[
prices a floating-rate note from a Black-Derman-Toy interest-rate tree. Price
,PriceTree
]
= floatbybdt(BDTTree
,Spread
,Settle
,Maturity
)
floatbybdt
computes prices of vanilla floating-rate notes, amortizing
floating-rate notes, capped floating-rate notes, floored floating-rate notes and collared
floating-rate notes.
Note
Alternatively, you can use the FloatBond
object to
price floating-rate bond instruments. For more information, see Get Started with Workflows Using Object-Based Framework for Pricing Financial Instruments.
[
adds
additional name-value pair arguments.Price
,PriceTree
]
= floatbybdt(___,Name,Value
)
Examples
Price a Floating-Rate Note Using a BDT Tree
Price a 20-basis point floating-rate note using a BDT interest-rate tree.
Load the file deriv.mat
, which provides BDTTree
. The BDTTree
structure contains the time and interest-rate information needed to price the note.
load deriv.mat;
Define the floating-rate note using the required arguments. Other arguments use defaults.
Spread = 20; Settle = datetime(2000,1,1); Maturity = datetime(2003,1,1);
Use floatbybdt
to compute the price of the note.
Price = floatbybdt(BDTTree, Spread, Settle, Maturity)
Price = 100.4865
Price an Amortizing Floating-Rate Note
Price an amortizing floating-rate note using the Principal
input argument to define the amortization schedule.
Create the RateSpec
.
Rates = [0.03583; 0.042147; 0.047345; 0.052707; 0.054302]; ValuationDate = datetime(2011,11,15); StartDates = ValuationDate; EndDates = [datetime(2012,11,15) ; datetime(2013,11,15) ; datetime(2014,11,15) ; datetime(2015,11,15) ; datetime(2016,11,15)]; Compounding = 1; RateSpec = intenvset('ValuationDate', ValuationDate,'StartDates', StartDates,... 'EndDates', EndDates,'Rates', Rates, 'Compounding', Compounding)
RateSpec = struct with fields:
FinObj: 'RateSpec'
Compounding: 1
Disc: [5x1 double]
Rates: [5x1 double]
EndTimes: [5x1 double]
StartTimes: [5x1 double]
EndDates: [5x1 double]
StartDates: 734822
ValuationDate: 734822
Basis: 0
EndMonthRule: 1
Create the floating-rate instrument using the following data:
Settle = datetime(2011,11,15); Maturity = datetime(2015,11,15); Spread = 15;
Define the floating-rate note amortizing schedule.
Principal ={{datetime(2012,11,15) 100;datetime(2013,11,15) 70;datetime(2014,11,15) 40;datetime(2015,11,15) 10}};
Build the BDT tree and assume volatility is 10%.
MatDates = [datetime(2012,11,15) ; datetime(2013,11,15) ; datetime(2014,11,15) ; datetime(2015,11,15) ; datetime(2016,11,15) ; datetime(2017,11,15)]; BDTTimeSpec = bdttimespec(ValuationDate, MatDates); Volatility = 0.10; BDTVolSpec = bdtvolspec(ValuationDate, MatDates, Volatility*ones(1,length(MatDates))'); BDTT = bdttree(BDTVolSpec, RateSpec, BDTTimeSpec);
Compute the price of the amortizing floating-rate note.
Price = floatbybdt(BDTT, Spread, Settle, Maturity, 'Principal', Principal)
Price = 100.3059
Price a Collar with a Floating-Rate Note
Price a collar with a floating-rate note using the CapRate
and FloorRate
input argument to define the collar pricing.
Create the RateSpec
.
Rates = [0.0287; 0.03024; 0.03345; 0.03861; 0.04033]; ValuationDate = datetime(2012,4,1); StartDates = ValuationDate; EndDates = [datetime(2013,4,1) ; datetime(2014,4,1) ; datetime(2015,4,1) ; datetime(2016,4,1) ; datetime(2017,4,1)]; Compounding = 1;
Create the RateSpec
.
RateSpec = intenvset('ValuationDate', ValuationDate,'StartDates', StartDates,... 'EndDates', EndDates,'Rates', Rates, 'Compounding', Compounding);
Build the BDT tree and assume volatility is 5%.
MatDates = [datetime(2013,4,1) ; datetime(2014,4,1) ; datetime(2015,4,1) ; datetime(2016,4,1) ; datetime(2017,4,1) ; datetime(2018,4,1)]; BDTTimeSpec = bdttimespec(ValuationDate, MatDates); Volatility = 0.05; BDTVolSpec = bdtvolspec(ValuationDate, MatDates, Volatility*ones(1,length(MatDates))'); BDTT = bdttree(BDTVolSpec, RateSpec, BDTTimeSpec);
Create the floating rate note instrument.
Settle = datetime(2012,4,1); Maturity = datetime(2016,4,1); Spread = 10; Principal = 100;
Compute the price of a collared floating-rate note.
CapStrike = {{datetime(2013,4,1) 0.03;datetime(2015,4,1) 0.055}}; FloorStrike = {{datetime(2013,4,1) 0.025;datetime(2015,4,1) 0.04}}; Price = floatbybdt(BDTT, Spread, Settle, Maturity, 'CapRate',... CapStrike, 'FloorRate', FloorStrike)
Price = 101.2414
Pricing a Floating-Rate Note When the Reset Dates Are Not Tree Level Dates
When using floatbybdt
to
price floating-rate notes, there are cases where the dates specified
in the BDT tree TimeSpec
are not aligned with the
cash flow dates.
Price floating-rate notes using the following data:
ValuationDate = datetime(2013,9,1); Rates = [0.0235; 0.0239; 0.0311; 0.0323]; EndDates = [datetime(2014,9,1);datetime(2015,9,1);datetime(2016,9,1);datetime(2017,9,1)];
Create the RateSpec
.
RateSpec = intenvset('ValuationDate',ValuationDate,'StartDates',... ValuationDate,'EndDates',EndDates,'Rates',Rates,'Compounding', 1);
Build the BDT tree.
VolCurve = [.10; .11; .11; .12]; BDTVolatilitySpec = bdtvolspec(RateSpec.ValuationDate, EndDates,... VolCurve); BDTTimeSpec = bdttimespec(RateSpec.ValuationDate, EndDates, 1); BDTT = bdttree(BDTVolatilitySpec, RateSpec, BDTTimeSpec);
Compute the price of the floating-rate note using the following data:
Spread = 5;
Settle = datetime(2013,9,1);
Maturity = datetime(2013,12,1);
Reset = 2;
Price = floatbybdt(BDTT, Spread, Settle, Maturity, 'FloatReset', Reset)
Warning: Not all cash flows are aligned with the tree. Result will be approximated. > In floatengbybdt at 204 In floatbybdt at 123 Error using floatengbybdt (line 299) Instrument '1 ' has cash flow dates that span across tree nodes. Error in floatbybdt (line 123) [Price, PriceTree, CFTree, TLPpal] = floatengbybdt(BDTTree, Spread, Settle, Maturity, OArgs{:});
This error indicates that it is not possible to determine the
applicable rate used to calculate the payoff at the reset dates, given
that the applicable rate needed cannot be calculated (the information
was lost due to the recombination of the tree nodes). Note, if the
reset period for an FRN spans more than one tree level, calculating
the payment becomes impossible due to the recombining nature of the
tree. That is, the tree path connecting the two consecutive reset
dates cannot be uniquely determined because there is more than one
possible path for connecting the two payment dates. The simplest solution
is to place the tree levels at the cash flow dates of the instrument,
which is done by specifying BDTTimeSpec
. It is
also acceptable to have reset dates between tree levels, as long as
there are reset dates on the tree levels.
To recover from this error, build a tree that lines up with the instrument.
Basis = intenvget(RateSpec, 'Basis'); EOM = intenvget(RateSpec, 'EndMonthRule'); resetDates = cfdates(ValuationDate, Maturity, Reset ,Basis, EOM); BDTTimeSpec = bdttimespec(RateSpec.ValuationDate,resetDates,Reset); BDTT = bdttree(BDTVolatilitySpec, RateSpec, BDTTimeSpec); Price = floatbybdt(BDTT, Spread, RateSpec.ValuationDate, ... Maturity, 'FloatReset', Reset)
Price = 100.1087
Input Arguments
BDTTree
— Interest-rate structure
structure
Interest-rate tree structure, created by bdttree
Data Types: struct
Spread
— Number of basis points over the reference rate
vector
Number of basis points over the reference 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, floatbybdt
also
accepts serial date numbers as inputs, but they are not recommended.
The Settle
date for every floating-rate note is set to the
ValuationDate
of the BDT tree. The floating-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 floating-rate note.
To support existing code, floatbybdt
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] =
floatbybdt(BDTTree,Spread,Settle,Maturity,'Basis',3)
FloatReset
— Frequency of payments per year
1
(default) | vector
Frequency of payments per year, specified as the comma-separated pair consisting
of 'FloatReset'
and a
NINST
-by-1
vector.
Note
Payments on floating-rate notes (FRNs) are determined by the effective interest-rate between reset dates. If the reset period for an FRN spans more than one tree level, calculating the payment becomes impossible due to the recombining nature of the tree. That is, the tree path connecting the two consecutive reset dates cannot be uniquely determined because there is more than one possible path for connecting the two payment dates.
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
CapRate
— Annual cap rate
decimal
Annual cap rate, specified as the comma-separated pair consisting of
'CapRate'
and a NINST
-by-1
decimal annual rate or NINST
-by-1
cell array,
where each element is a NumDates
-by-2
cell
array, and the cell array first column is dates, and the second column is associated
cap rates. The date indicates the last day that the cap rate is valid.
Data Types: double
| cell
FloorRate
— Annual floor rate
decimal
Annual floor rate, specified as the comma-separated pair consisting of
'FloorRate'
and a
NINST
-by-1
decimal annual rate or
NINST
-by-1
cell array, where each element is a
NumDates
-by-2
cell array, and the cell array
first column is dates, and the second column is associated floor rates. The date
indicates the last day that the floor rate is valid.
Data Types: double
| cell
Output Arguments
Price
— Expected floating-rate note prices at time 0
vector
Expected floating-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.PTree
contains the clean prices.PriceTree.AITree
contains the accrued interest.PriceTree.tObs
contains the observation times.
More About
Floating-Rate Note
A floating-rate note is a security like a bond, but the interest rate of the note is reset periodically, relative to a reference index rate, to reflect fluctuations in market interest rates.
Version History
Introduced before R2006aR2022b: Serial date numbers not recommended
Although floatbybdt
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.
See Also
bdttree
| bondbybdt
| capbybdt
| cfbybdt
| fixedbybdt
| floorbybdt
| swapbybdt
| FloatBond
Topics
- Computing Instrument Prices
- Pricing a Portfolio Using the Black-Derman-Toy Model
- Price Portfolio of Bond and Bond Option Instruments
- Compute LIBOR Fallback
- Floating-Rate Note
- Understanding Interest-Rate Tree Models
- Pricing Options Structure
- Supported Interest-Rate Instrument Functions
- Mapping Financial Instruments Toolbox Functions for Interest-Rate Instrument Objects
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