floatbyhjm
Price floating-rate note from Heath-Jarrow-Morton interest-rate tree
Syntax
Description
[
prices a floating-rate note from a
Heath-Jarrow-Morton interest-rate tree. Price
,PriceTree
]
= floatbyhjm(HJMTree
,Spread
,Settle
,Maturity
)
floatbyhjm
computes prices of vanilla floating-rate notes, amortizing
floating-rate notes, capped floating-rate notes,
floored floating-rate notes and collared
floating-rate notes.
[
adds
additional name-value pair arguments.Price
,PriceTree
]
= floatbyhjm(___,Name,Value
)
Examples
Price a Floating-Rate Note Using an HJM Tree
Price a 20-basis point floating-rate note using an HJM forward-rate tree.
Load the file deriv.mat
, which provides HJMTree
. The HJMTree
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 floatbyhjm
to compute the price of the note.
Price = floatbyhjm(HJMTree, Spread, Settle, Maturity)
Price = 100.5529
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 HJM tree using the following data:
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)];
HJMTimeSpec = hjmtimespec(RateSpec.ValuationDate, MatDates);
Volatility = [.10; .08; .06; .04];
CurveTerm = [ 1; 2; 3; 4];
HJMVolSpec = hjmvolspec('Proportional', Volatility, CurveTerm, 1e6);
HJMT = hjmtree(HJMVolSpec,RateSpec,HJMTimeSpec);
Compute the price of the amortizing floating-rate note.
Price = floatbyhjm(HJMT, 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.
Price a portfolio of collared floating-rate notes using the following data:
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 HJM tree with the following data:
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)];
HJMTimeSpec = hjmtimespec(RateSpec.ValuationDate, MatDates);
Volatility = [.10; .08; .06; .04];
CurveTerm = [ 1; 2; 3; 4];
HJMVolSpec = hjmvolspec('Proportional', Volatility, CurveTerm, 1e6);
HJMT = hjmtree(HJMVolSpec,RateSpec,HJMTimeSpec);
Create the floating-rate note instrument.
Settle = datetime(2012,4,1); Maturity = datetime(2016,4,1); Spread = 10; Principal = 100;
Compute the price of two capped collared floating-rate notes.
CapStrike = [0.04;0.055]; PriceCapped = floatbyhjm(HJMT, Spread, Settle, Maturity,... 'CapRate', CapStrike)
PriceCapped = 2×1
98.9986
100.2051
Compute the price of two collared floating-rate notes.
FloorStrike = [0.035;0.040]; PriceCollared = floatbyhjm(HJMT, Spread, Settle, Maturity,... 'CapRate', CapStrike, 'FloorRate', FloorStrike)
PriceCollared = 2×1
99.9246
102.2321
Input Arguments
HJMTree
— Interest-rate structure
structure
Interest-rate tree structure, created by hjmtree
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, floatbyhjm
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 HJM 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, floatbyhjm
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] =
floatbyhjm(HJMTree,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.PBush
contains the clean prices.PriceTree.AIBush
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 floatbyhjm
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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