rangefloatbycir
Price range floating note using Cox-Ingersoll-Ross tree
Syntax
Description
[
adds additional name-value pair arguments.Price
,PriceTree
]
= rangefloatbycir(___,Name,Value
)
Examples
Price a Range Floating-Rate Note Using a CIR Interest-Rate Tree
Create a RateSpec
using the intenvset
function.
Rates = [0.035; 0.042147; 0.047345; 0.052707]; Dates = {'Jan-1-2017'; 'Jan-1-2018'; 'Jan-1-2019'; 'Jan-1-2020'; 'Jan-1-2021'}; ValuationDate = 'Jan-1-2017'; 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 = '01-Jan-2017'; Maturity = '01-Jan-2020'; CIRTimeSpec = cirtimespec(Settle, Maturity, 3); 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]
dObs: [736696 737061 737426]
FwdTree: {[1.0350] [1.0790 1.0500 1.0298] [1.1275 1.0887 1.0594 1.0390 1.0270]}
Connect: {[3x1 double] [3x3 double]}
Probs: {[3x1 double] [3x3 double]}
Define the range note instrument that matures in Jan-1-2014 and has the following RateSchedule:
Spread = 100; Settle = 'Jan-1-2017'; Maturity = 'Jan-1-2020'; RateSched(1).Dates = {'Jan-1-2018'; 'Jan-1-2019' ; 'Jan-1-2020'}; RateSched(1).Rates = [0.045 0.055 ; 0.0525 0.0675; 0.06 0.08];
Compute the price of the range floating note.
[Price,PriceTree] = rangefloatbycir(CIRT,Spread,Settle,Maturity,RateSched)
Price = 91.6849
PriceTree = struct with fields:
FinObj: 'CIRPriceTree'
PTree: {[91.6849] [88.9878 92.6039 95.1352] [88.6954 91.8547 94.3896 96.2429 97.3723] [100 100 100 100 100]}
AITree: {[0] [0 0 0] [0 0 0 0 0] [0 0 0 0 0]}
tObs: [0 1 2 3]
Connect: {[3x1 double] [3x3 double]}
Probs: {[3x1 double] [3x3 double]}
Input Arguments
CIRTree
— Interest-rate tree structure
structure
Interest-rate tree structure, specified by using cirtree
.
Data Types: struct
Spread
— Number of basis points over reference rate
numeric
Number of basis points over the reference rate, specified as a
NINST
-by-1
vector.
Data Types: double
Settle
— Settlement date for floating range note
datetime array | string array | date character vector
Settlement date for the floating range note, specified as a
NINST
-by-1
vector using a datetime array, string
array, or date character vectors. The Settle
date for every range
floating instrument is set to the ValuationDate
of the CIR tree. The
floating range note argument Settle
is ignored.
To support existing code, rangefloatbycir
also
accepts serial date numbers as inputs, but they are not recommended.
Maturity
— Maturity date for floating range note
datetime array | string array | date character vector
Maturity date for the floating-rate note, specified as a
NINST
-by-1
vector using a datetime array, string
array, or date character vectors.
To support existing code, rangefloatbycir
also
accepts serial date numbers as inputs, but they are not recommended.
RateSched
— Range of rates within which cash flows are nonzero
structure
Range of rates within which cash flows are nonzero, specified as a
NINST
-by-1
vector of structures. Each element
of the structure array contains two fields:
RateSched.Dates
—NDates
-by-1
cell array of dates corresponding to the range schedule.RateSched.Rates
—NDates
-by-2
array with the first column containing the lower bound of the range and the second column containing the upper bound of the range. Cash flow for dateRateSched.Dates
(n) is nonzero for rates in the rangeRateSched.Rates
(n,1) <Rate
<RateSched.Rate
(n,2).
Data Types: struct
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] =
rangefloatbycir(CIRTree,Spread,Settle,Maturity,RateSched,'Reset',4,'Basis',5,'Principal',10000)
Reset
— Frequency payment per year
1
(default) | numeric
Frequency of payments per year, specified as the comma-separated pair consisting
of 'Reset'
and a NINST
-by-1
vector.
Note
Payments on range floating notes are determined by the effective interest-rate between reset dates. If the reset period for a range 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 of instrument
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 of integers.
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 amount
100
(default) | numeric
Notional principal amount, specified as the comma-separated pair consisting of
'Principal'
and a
NINST
-by-1
vector.
Data Types: double
EndMonthRule
— End-of-month rule flag for generating caplet dates
1
(in effect) (default) | nonnegative integer with value 0
or
1
End-of-month rule flag, specified as the comma-separated pair consisting of
'EndMonthRule'
and a nonnegative integer with a value of
0
or 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
Output Arguments
Price
— Expected prices of range floating notes at time 0
vector
Expected prices of the range floating notes 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 structure containing trees of vectors of instrument prices and accrued interest, and a vector of observation times for each node. Values are:
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
Range Note
A range note is a structured (market-linked) security whose coupon rate is equal to the reference rate as long as the reference rate is within a certain range.
If the reference rate is outside of the range, the coupon rate is 0
for that period. This type of instrument entitles the holder to cash flows that depend on
the level of some reference interest rate and are floored to be positive. The note holder
gets direct exposure to the reference rate. In return for the drawback that no interest is
paid for the time the range is left, they offer higher coupon rates than comparable standard
products, vanilla floating notes. For more information, see Range Note.
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 rangefloatbycir
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
| floatbycir
| floorbycir
| oasbycir
| optbndbycir
| optfloatbycir
| optembndbycir
| optemfloatbycir
| swapbycir
| swaptionbycir
| instrangefloat
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