# rangefloatbyhw

Price range floating note using Hull-White tree

## Syntax

## Description

`[`

prices
range floating note using a Hull-White tree.`Price`

,`PriceTree`

]
= rangefloatbyhw(`HWTree`

,`Spread`

,`Settle`

,`Maturity`

,`RateSched`

)

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.

`[`

adds optional name-value pair arguments.`Price`

,`PriceTree`

]
= rangefloatbyhw(___,`Name,Value`

)

## Examples

### Compute the Price of a Range Note Using a Hull-White Tree

This example shows how to compute the price of a range note using a Hull-White tree with the following interest-rate term structure data.

Rates = [0.035; 0.042147; 0.047345; 0.052707]; ValuationDate = 'Jan-1-2011'; StartDates = ValuationDate; EndDates = {'Jan-1-2012'; 'Jan-1-2013'; 'Jan-1-2014'; 'Jan-1-2015'}; Compounding = 1; % define RateSpec RS = intenvset('ValuationDate', ValuationDate, 'StartDates', StartDates,... 'EndDates', EndDates, 'Rates', Rates, 'Compounding', Compounding); % range note instrument matures in Jan-1-2014 and has the following RateSchedule: Spread = 100; Settle = 'Jan-1-2011'; Maturity = 'Jan-1-2014'; RateSched(1).Dates = {'Jan-1-2012'; 'Jan-1-2013' ; 'Jan-1-2014'}; RateSched(1).Rates = [0.045 0.055 ; 0.0525 0.0675; 0.06 0.08]; % data to build the tree is as follows: VolDates = ['1-Jan-2012'; '1-Jan-2013'; '1-Jan-2014';'1-Jan-2015']; VolCurve = 0.01; AlphaDates = '01-01-2015'; AlphaCurve = 0.1; HWVS = hwvolspec(RS.ValuationDate, VolDates, VolCurve,... AlphaDates, AlphaCurve); HWTS = hwtimespec(RS.ValuationDate, VolDates, Compounding); HWT = hwtree(HWVS, RS, HWTS); % price the instrument Price = rangefloatbyhw(HWT, Spread, Settle, Maturity, RateSched)

Price = 96.6107

## Input Arguments

`HWTree`

— Interest-rate tree structure

structure

Interest-rate tree structure, specified by using `hwtree`

.

**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

serial date number | date character vector | cell array of date character vectors

Settlement date for the floating range note, specified as a `NINST`

-by-`1`

vector
of serial date numbers or date character vectors. The `Settle`

date
for every range floating instrument is set to the `ValuationDate`

of
the HW tree. The floating range note argument `Settle`

is
ignored.

**Data Types: **`double`

| `char`

| `cell`

`Maturity`

— Maturity date for floating range note

serial date number | date character vector | cell array of date character vectors

Maturity date for the floating-rate note, specified as a `NINST`

-by-`1`

vector
of serial date numbers or date character vectors.

**Data Types: **`double`

| `char`

| `cell`

`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] = rangefloatbyhw(HWTree,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.

**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`

`Options`

— Derivatives pricing options structure

structure

Derivatives pricing options structure, specified as the comma-separated pair consisting of
`'Options'`

and a structure
obtained from using `derivset`

.

**Data Types: **`struct`

`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.

## 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, like vanilla floating notes. For more information, see Range Note.

## References

[1] Jarrow, Robert. “Modelling Fixed Income Securities and
Interest Rate Options.” *Stanford Economics and Finance.* 2nd
Edition. 2002.

## Version History

**Introduced in R2012a**

## See Also

`hwtree`

| `cfbyhw`

| `capbyhw`

| `swapbyhw`

| `floorbyhw`

| `fixedbyhw`

| `bondbyhw`

| `rangefloatbybk`

| `rangefloatbybdt`

| `rangefloatbyhjm`

| `instrangefloat`

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