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floatbyzero

Price floating-rate note from set of zero curves

Syntax

``````[Price,DirtyPrice,CFlowAmounts,CFlowDates] = floatbyzero(RateSpec,Spread,Settle,Maturity)``````
``````[Price,DirtyPrice,CFlowAmounts,CFlowDates] = floatbyzero(___,Name,Value)``````

Description

example

``````[Price,DirtyPrice,CFlowAmounts,CFlowDates] = floatbyzero(RateSpec,Spread,Settle,Maturity)``` prices a floating-rate note from a set of zero curves.`floatbyzero` computes prices of vanilla floating-rate notes and amortizing floating-rate notes.```

example

``````[Price,DirtyPrice,CFlowAmounts,CFlowDates] = floatbyzero(___,Name,Value)``` adds additional name-value pair arguments.```

Examples

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Price a 20-basis point floating-rate note using a set of zero curves.

Load `deriv.mat`, which provides `ZeroRateSpec`, the interest-rate term structure, needed to price the bond.

`load deriv.mat;`

Define the floating-rate note using the required arguments. Other arguments use defaults.

```Spread = 20; Settle = '01-Jan-2000'; Maturity = '01-Jan-2003';```

Use `floatbyzero` to compute the price of the note.

`Price = floatbyzero(ZeroRateSpec, Spread, Settle, Maturity)`
```Price = 100.5529 ```

Price an amortizing floating-rate note using the `Principal` input argument to define the amortization schedule.

Create the `RateSpec`.

```Rates = [0.03583; 0.042147; 0.047345; 0.052707; 0.054302]; ValuationDate = '15-Nov-2011'; StartDates = ValuationDate; EndDates = {'15-Nov-2012';'15-Nov-2013';'15-Nov-2014' ;'15-Nov-2015';'15-Nov-2016'}; Compounding = 1; RateSpec = intenvset('ValuationDate', ValuationDate,'StartDates', StartDates,... 'EndDates', EndDates,'Rates', Rates, 'Compounding', Compounding)```
```RateSpec = struct with fields: FinObj: 'RateSpec' Compounding: 1 Disc: [5x1 double] Rates: [5x1 double] EndTimes: [5x1 double] StartTimes: [5x1 double] EndDates: [5x1 double] StartDates: 734822 ValuationDate: 734822 Basis: 0 EndMonthRule: 1 ```

Create the floating-rate instrument using the following data:

```Settle ='15-Nov-2011'; Maturity = '15-Nov-2015'; Spread = 15;```

Define the floating-rate note amortizing schedule.

`Principal ={{'15-Nov-2012' 100;'15-Nov-2013' 70;'15-Nov-2014' 40;'15-Nov-2015' 10}};`

Compute the price of the amortizing floating-rate note.

`Price = floatbyzero(RateSpec, Spread, Settle, Maturity, 'Principal', Principal)`
```Price = 100.3059 ```

If `Settle` is not on a reset date of a floating-rate note, `floatbyzero` attempts to obtain the latest floating rate before `Settle` from `RateSpec` or the `LatestFloatingRate` parameter. When the reset date for this rate is out of the range of `RateSpec` (and `LatestFloatingRate` is not specified), `floatbyzero` fails to obtain the rate for that date and generates an error. This example shows how to use the `LatestFloatingRate` input parameter to avoid the error.

Create the error condition when a floating-rate instrument’s `StartDate` cannot be determined from the `RateSpec`.

```load deriv.mat; Spread = 20; Settle = '01-Jan-2000'; Maturity = '01-Dec-2003'; Price = floatbyzero(ZeroRateSpec, Spread, Settle, Maturity)```
```Error using floatbyzero (line 256) The rate at the instrument starting date cannot be obtained from RateSpec. Its reset date (01-Dec-1999) is out of the range of dates contained in RateSpec. This rate is required to calculate cash flows at the instrument starting date. Consider specifying this rate with the 'LatestFloatingRate' input parameter.```

Here, the reset date for the rate at `Settle` was 01-Dec-1999, which was earlier than the valuation date of `ZeroRateSpec` (01-Jan-2000). This error can be avoided by specifying the rate at the instrument’s starting date using the `LatestFloatingRate` name-value pair argument.

Define `LatestFloatingRate` and calculate the floating-rate price.

`Price = floatbyzero(ZeroRateSpec, Spread, Settle, Maturity, 'LatestFloatingRate', 0.03)`
```Price = 100.0285```

Define the OIS and Libor rates.

```Settle = datenum('15-Mar-2013'); CurveDates = daysadd(Settle,360*[1/12 2/12 3/12 6/12 1 2 3 4 5 7 10],1); OISRates = [.0018 .0019 .0021 .0023 .0031 .006 .011 .017 .021 .026 .03]'; LiborRates = [.0045 .0047 .005 .0055 .0075 .011 .016 .022 .026 .030 .0348]';```

Plot the dual curves.

```figure,plot(CurveDates,OISRates,'r');hold on;plot(CurveDates,LiborRates,'b') datetick legend({'OIS Curve', 'Libor Curve'})```

Create an associated `RateSpec` for the OIS and Libor curves.

```OISCurve = intenvset('Rates',OISRates,'StartDate',Settle,'EndDates',CurveDates); LiborCurve = intenvset('Rates',LiborRates,'StartDate',Settle,'EndDates',CurveDates);```

Define the floating-rate note.

```Maturity = datenum('15-Mar-2018'); % Five year swap FloatSpread = 0; FixedRate = .025; SwapRates = [FixedRate FloatSpread];```

Compute the price for the floating-rate note. The `LiborCurve` term structure will be used to generate the floating cash flows of the floater instrument. The `OISCurve` term structure will be used for discounting the cash flows.

`floatbyzero(OISCurve,0,Settle,Maturity,'ProjectionCurve',LiborCurve)`
```ans = 102.4214 ```

Some instruments require using different interest-rate curves for generating the floating cash flows and discounting. This is when the `ProjectionCurve` parameter is useful. When you provide both `RateSpec` and `ProjectionCurve`, `floatbyzero` uses the `RateSpec` for the purpose of discounting and it uses the `ProjectionCurve` for generating the floating cash flows.

Input Arguments

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Annualized zero rate term structure, specified using `intenvset` to create a `RateSpec`.

Data Types: `struct`

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

Data Types: `double`

Settlement date, specified either as a scalar or `NINST`-by-`1` vector of serial date numbers or date character vectors.

`Settle` must be earlier than `Maturity`.

Data Types: `char` | `double`

Maturity date, specified as a `NINST`-by-`1` vector of serial date numbers or date character vectors representing the maturity date for each swap.

Data Types: `char` | `double`

Name-Value Pair Arguments

Specify optional comma-separated pairs of `Name,Value` arguments. `Name` is the argument name and `Value` is the corresponding value. `Name` must appear inside single quotes (`' '`). You can specify several name and value pair arguments in any order as `Name1,Value1,...,NameN,ValueN`.

Example: ```[Price,DirtyPrice,CFlowAmounts,CFlowDates] = floatbyzero(RateSpec,Spread,Settle,Maturity,'Principal',Principal)```

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Frequency of payments per year, specified as `NINST`-by-`1` vector.

Data Types: `double`

Day count basis, specified as 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

Data Types: `double`

Notional principal amounts, specified as 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`

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 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`

Rate for the next floating payment set at the last reset date, specified as a `NINST`-by-`1`.

Data Types: `double`

The rate curve to be used in generating the future forward rates. This structure must be created using `intenvset`. Use this optional input if the forward curve is different from the discount curve.

Data Types: `struct`

Flag to adjust cash flows based on actual period day count, specified as a `NINST`-by-`1` vector of logicals with values of `0` (false) or `1` (true).

Data Types: `logical`

Holidays used in computing business days, specified as MATLAB date numbers using a `NHolidays`-by-`1` vector.

Data Types: `double`

Business day conventions, specified by 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 non-business days are treated. Non-business days are defined as weekends plus any other date that businesses are not open (e.g. statutory holidays). Values are:

• `actual` — Non-business days are effectively ignored. Cash flows that fall on non-business 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`

Output Arguments

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Floating-rate note prices, returned as a (`NINST`) by number of curves (`NUMCURVES`) matrix. Each column arises from one of the zero curves.

Dirty note price (clean + accrued interest), returned as a `NINST`- by-`NUMCURVES` matrix. Each column arises from one of the zero curves.

Cash flow amounts, returned as a `NINST`- by-`NUMCFS` matrix of cash flows for each note. If there is more than one curve specified in the `RateSpec` input, then the first `NCURVES` rows correspond to the first note, the second `NCURVES` rows correspond to the second note, and so on.

Cash flow dates, returned as a `NINST`- by-`NUMCFS` matrix of payment dates for each note.