floatbycir
Price floating-rate note from Cox-Ingersoll-Ross interest-rate tree
Syntax
Description
[
prices a floating-rate note from a Cox-Ingersoll-Ross (CIR) interest-rate tree. Price
,PriceTree
]
= floatbycir(CIRTree
,Spread
,Settle
,Maturity
)
floatbycir
computes prices of vanilla floating-rate notes,
amortizing floating-rate notes, capped floating-rate notes, floored floating-rate notes,
and collared floating-rate notes using a CIR++ model with the Nawalka-Beliaeva (NB) approach.
Note
Alternatively, you can use the FloatBond
object to
price floating-rate note 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
]
= floatbycir(___,Name,Value
)
Examples
Price a Floating-Rate Note Using a CIR Interest-Rate Tree
Define a Spread
of 20-basis points for a floating-rate note.
Spread = 20;
Create a RateSpec
using the intenvset
function.
Rates = [0.035; 0.042147; 0.047345; 0.052707]; Dates = [datetime(2017,1,1) ; datetime(2018,1,1) ; datetime(2019,1,1) ; datetime(2020,1,1) ; datetime(2021,1,1)]; ValuationDate = datetime(2017,1,1); EndDates = Dates(2:end)'; Compounding = 1; RateSpec = intenvset('ValuationDate', ValuationDate, 'StartDates', ValuationDate, 'EndDates',EndDates,'Rates', Rates, 'Compounding', Compounding);
Create a CIR
tree.
NumPeriods = length(EndDates); Alpha = 0.03; Theta = 0.02; Sigma = 0.1; Settle = datetime(2017,1,1); Maturity = datetime(2021,1,1); CIRTimeSpec = cirtimespec(ValuationDate, Maturity, NumPeriods); CIRVolSpec = cirvolspec(Sigma, Alpha, Theta); CIRT = cirtree(CIRVolSpec, RateSpec, CIRTimeSpec)
CIRT = struct with fields:
FinObj: 'CIRFwdTree'
VolSpec: [1x1 struct]
TimeSpec: [1x1 struct]
RateSpec: [1x1 struct]
tObs: [0 1 2 3]
dObs: [736696 737061 737426 737791]
FwdTree: {[1.0350] [1.0790 1.0500 1.0298] [1.1275 1.0887 1.0594 1.0390 1.0270] [1.1905 1.1406 1.1014 1.0718 1.0512 1.0390 1.0350]}
Connect: {[3x1 double] [3x3 double] [3x5 double]}
Probs: {[3x1 double] [3x3 double] [3x5 double]}
Price the 20-basis point floating-rate note.
[Price,PriceTree] = floatbycir(CIRT,Spread,Settle,Maturity)
Price = 100.7143
PriceTree = struct with fields:
FinObj: 'CIRPriceTree'
PTree: {[100.7143] [100.5113 100.5385 100.5589] [100.3333 100.3508 100.3650 100.3756 100.3821] [100.1680 100.1753 100.1816 100.1866 100.1903 100.1925 100.1932] [100 100 100 100 100 100 100]}
AITree: {[0] [0 0 0] [0 0 0 0 0] [0 0 0 0 0 0 0] [0 0 0 0 0 0 0]}
tObs: [0 1 2 3 4]
Connect: {[3x1 double] [3x3 double] [3x5 double]}
Probs: {[3x1 double] [3x3 double] [3x5 double]}
Input Arguments
CIRTree
— Interest-rate tree structure
structure
Interest-rate tree structure, created by cirtree
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, floatbycir
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 CIR 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, floatbycir
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] =
floatbycir(CIRTree,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
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
nonbusiness days are treated. Nonbusiness days are defined as weekends plus any other
date that businesses are not open (e.g. statutory holidays). Values are:
actual
— Nonbusiness days are effectively ignored. Cash flows that fall on nonbusiness 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.
For the NINST
-by-1
cell array, each element
is a NumDates
-by-2
cell array, where 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.PriceTree.Connect
contains the connectivity vectors. Each element in the cell array describes how nodes in that level connect to the next. For a given tree level, there areNumNodes
elements in the vector, and they contain the index of the node at the next level that the middle branch connects to. Subtracting 1 from that value indicates where the up-branch connects to, and adding 1 indicated where the down branch connects to.PriceTree.Probs
contains the probability arrays. Each element of the cell array contains the up, middle, and down transition probabilities for each node of the level.
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.
References
[1] Cox, J., Ingersoll, J.,and S. Ross. "A Theory of the Term Structure of Interest Rates." Econometrica. Vol. 53, 1985.
[2] Brigo, D. and F. Mercurio. Interest Rate Models - Theory and Practice. Springer Finance, 2006.
[3] Hirsa, A. Computational Methods in Finance. CRC Press, 2012.
[4] Nawalka, S., Soto, G., and N. Beliaeva. Dynamic Term Structure Modeling. Wiley, 2007.
[5] Nelson, D. and K. Ramaswamy. "Simple Binomial Processes as Diffusion Approximations in Financial Models." The Review of Financial Studies. Vol 3. 1990, pp. 393–430.
Version History
Introduced in R2018aR2022b: Serial date numbers not recommended
Although floatbycir
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
bondbycir
| capbycir
| cfbycir
| fixedbycir
| floorbycir
| oasbycir
| optbndbycir
| optfloatbycir
| optembndbycir
| optemfloatbycir
| rangefloatbycir
| swapbycir
| swaptionbycir
| instfloat
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