Documentation

# fixedbyzero

Price fixed-rate note from set of zero curves

## Syntax

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

## Description

example

``````[Price,DirtyPrice,CFlowAmounts,CFlowDates] = fixedbyzero(RateSpec,CouponRate,Settle,Maturity)``` prices a fixed-rate note from a set of zero curves.```

example

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

## Examples

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This example shows how to price a 4% fixed-rate note using a set of zero curves by loading the file `deriv.mat`, which provides `ZeroRateSpec`, the interest-rate term structure needed to price the note.

```load deriv.mat CouponRate = 0.04; Settle = '01-Jan-2000'; Maturity = '01-Jan-2003'; Price = fixedbyzero(ZeroRateSpec, CouponRate, Settle, Maturity)```
```Price = 98.7159 ```

Assume that a financial institution has an existing swap with three years left to maturity where they are receiving 5% per year in yen and paying 8% per year in USD. The reset frequency for the swap is annual, the principals for the two legs are 1200 million yen and \$10 million USD, and both term structures are flat.

```Settle = datenum('15-Aug-2015'); Maturity = datenum('15-Aug-2018'); Reset = 1; r_d = .09; r_f = .04; FixedRate_d = .08; FixedRate_f = .05; Principal_d = 10000000; Principal_f = 1200000000; S0 = 1/110;```

Construct term structures.

```RateSpec_d = intenvset('StartDate',Settle,'EndDate',Maturity,'Rates',r_d,'Compounding',-1); RateSpec_f = intenvset('StartDate',Settle,'EndDate',Maturity,'Rates',r_f,'Compounding',-1);```

Use fixedbyzero:

```B_d = fixedbyzero(RateSpec_d,FixedRate_d,Settle,Maturity,'Principal',Principal_d,'Reset',Reset); B_f = fixedbyzero(RateSpec_f,FixedRate_f,Settle,Maturity,'Principal',Principal_f,'Reset',Reset);```

Compute swap price. Based on Hull (see References), a cross currency swap can be valued with the following formula `V_swap` = `S0*B_f``B_d`.

`V_swap = S0*B_f - B_d`
```V_swap = 1.5430e+06 ```

## Input Arguments

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

Data Types: `struct`

Annual rate, specified as `NINST`-by-`1` decimal annual rate or a `NINST`-by-`1` cell array where each element is a `NumDates`-by-`2` cell array and the first column is dates and the second column is associated rates. The date indicates the last day that the coupon rate is valid.

Data Types: `double` | `cell`

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 fixed-rate note.

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 quotes. You can specify several name and value pair arguments in any order as `Name1,Value1,...,NameN,ValueN`.

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

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

Data Types: `double`

Day count basis, specified as the comma-separated pair consisting of `'Basis'` and 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 the comma-separated pair consisting of `'Principal'` and 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 the comma-separated pair consisting of `'EndMonthRule'` and a 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`

Flag to adjust cash flows based on actual period day count, specified as the comma-separated pair consisting of `'AdjustCashFlowsBasis'` and 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 the comma-separated pair consisting of `'Holidays'` and MATLAB date numbers using a `NHolidays`-by-`1` vector.

Data Types: `double`

Business day conventions, specified as the comma-separated pair consisting of `'BusinessDayConvention'` and 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 bond 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 bond.

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

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### Fixed-Rate Note

A fixed-rate note is a long-term debt security with a preset interest rate and maturity, by which the interest must be paid.

The principal may or may not be paid at maturity. In Financial Instruments Toolbox™, the principal is always paid at maturity. For more information, see Fixed-Rate Note.

 Hull, J. Options, Futures, and Other Derivatives. Prentice-Hall, 2011.