# 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 date`RateSched.Dates`

(*n*) is nonzero for rates in the range`RateSched.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 are`NumNodes`

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 R2018a**

### R2022b: 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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