# rangefloatbyhjm

Price range floating note using Heath-Jarrow-Morton tree

## Syntax

``````[Price,PriceTree] = rangefloatbyhjm(HJMTree,Spread,Settle,Maturity,RateSched)``````
``````[Price,PriceTree] = rangefloatbyhjm(___Name,Value)``````

## Description

example

``````[Price,PriceTree] = rangefloatbyhjm(HJMTree,Spread,Settle,Maturity,RateSched)``` prices range floating note using a Heath-Jarrow-Morton tree.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.```

example

``````[Price,PriceTree] = rangefloatbyhjm(___Name,Value)``` adds optional name-value pair arguments.```

## Examples

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

```Rates = [0.035; 0.042147; 0.047345; 0.052707]; ValuationDate = datetime(2011,1,1); StartDates = ValuationDate; EndDates = [datetime(2012,1,1) ; datetime(2013,1,1) ; datetime(2014,1,1) ; datetime(2015,1,1)]; 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 = datetime(2011,1,1); Maturity = datetime(2014,1,1); RateSched(1).Dates = [datetime(2012,1,1) ; datetime(2013,1,1) ; datetime(2014,1,1)]; RateSched(1).Rates = [0.045 0.055 ; 0.0525 0.0675; 0.06 0.08]; % data to build the tree is as follows: Volatility = [.2; .19; .18; .17]; CurveTerm = [ 1; 2; 3; 4]; MaTree = [datetime(2012,1,1) ; datetime(2013,1,1) ; datetime(2014,1,1) ; datetime(2015,1,1)]; HJMTS = hjmtimespec(ValuationDate, MaTree); HJMVS = hjmvolspec('Proportional', Volatility, CurveTerm, 1e6); HJMT = hjmtree(HJMVS, RS, HJMTS); % price the instrument Price = rangefloatbyhjm(HJMT, Spread, Settle, Maturity, RateSched)```
```Price = 90.2348 ```

## Input Arguments

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Interest-rate tree structure, specified by using `hjmtree`.

Data Types: `struct`

Number of basis points over the reference rate, specified as a `NINST`-by-`1` vector.

Data Types: `double`

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 HJM tree. The floating range note argument `Settle` is ignored.

To support existing code, `rangefloatbyhjm` also accepts serial date numbers as inputs, but they are not recommended.

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, `rangefloatbyhjm` also accepts serial date numbers as inputs, but they are not recommended.

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] = rangefloatbyhjm(HJMTree,Spread,Settle,Maturity,RateSched,'Reset',4,'Basis',5,'Principal',10000)`

Frequency of payments per year, specified as the comma-separated pair consisting of `'Reset'` and a `NINST`-by-`1` vector.

Data Types: `double`

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

Data Types: `double`

Notional principal amount, specified as the comma-separated pair consisting of `'Principal'` and a `NINST`-by-`1` vector.

Data Types: `double`

Derivatives pricing options structure, specified as the comma-separated pair consisting of `'Options'` and a structure obtained from using `derivset`.

Data Types: `struct`

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

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Expected prices of the range floating notes at time 0, returned as a `NINST`-by-`1` vector.

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.

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### 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

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