# fixedbybk

Price fixed-rate note from Black-Karasinski interest-rate tree

## Syntax

## Description

`[`

prices a fixed-rate note from a Black-Karasinski
interest-rate tree. `Price`

,`PriceTree`

]
= fixedbybk(`BKTree`

,`CouponRate`

,`Settle`

,`Maturity`

)

**Note**

Alternatively, you can use the `FixedBond`

object to price fixed-rate
bond instruments. For more information, see Get Started with Workflows Using Object-Based Framework for Pricing Financial Instruments.

`[`

adds
additional name-value pair arguments.`Price`

,`PriceTree`

]
= fixedbybk(___,`Name,Value`

)

## Examples

### Price a 5% Fixed-Rate Note Using a Black-Karasinski Interest-Rate Tree

Load the file `deriv.mat`

, which provides `BKTree`

. The `BKTree`

structure contains the time and interest-rate information needed to price the note.

`load deriv.mat;`

Set the required values. Other arguments will use defaults.

CouponRate = 0.05; Settle = datetime(2004,1,1); Maturity = datetime(2006,1,1);

Use `fixedbybk`

to compute the price of the note.

Price = fixedbybk(BKTree, CouponRate, Settle, Maturity)

Price = 103.5126

## Input Arguments

`BKTree`

— Interest-rate structure

structure

Interest-rate tree structure, created by `bktree`

**Data Types: **`struct`

`CouponRate`

— Coupon annual rate

decimal

Coupon annual rate, specified as a `NINST`

-by-`1`

vector.

**Data Types: **`double`

`Settle`

— Settlement date

datetime array | string array | date character vector

Settlement date, specified either as a scalar or a
`NINST`

-by-`1`

vector using a datetime array, string array, or date
character vectors.

To support existing code, `fixedbybk`

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

The `Settle`

date for every fixed-rate note
is set to the `ValuationDate`

of the BK Tree. The
fixed-rate note argument `Settle`

is ignored.

`Maturity`

— Maturity date

datetime array | string array | date character vector

Maturity date, specified as a `NINST`

-by-`1`

vector using a
datetime array, string array, or date character
vectors representing the maturity date for each
fixed-rate note.

To support existing code, `fixedbybk`

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

### 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] =
fixedbybk(BKTree,CouponRate,Settle,Maturity,'FixedReset',4)
```

`FixedReset`

— Frequency of payments per year

`1`

(default) | vector

Frequency of payments per year, specified as
the comma-separated pair consisting of
`'FixedReset'`

and a
`NINST`

-by-`1`

vector.

**Data Types: **`double`

`Basis`

— Day count basis

`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.

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 amounts or principal value schedules

`100`

(default) | vector or cell array

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`

`Options`

— Derivatives pricing options structure

structure

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

and a structure using
`derivset`

.

**Data Types: **`struct`

`EndMonthRule`

— End-of-month rule flag for generating dates when `Maturity`

is end-of-month date for month having 30 or fewer days

`1`

(in effect) (default) | nonnegative integer `[0,1]`

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`

`AdjustCashFlowsBasis`

— Flag to adjust cash flows based on actual period day count

`false`

(default) | value of `0`

(false) or `1`

(true)

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`

— Holidays used in computing business days

if not specified, the default
is to use `holidays.m`

(default) | MATLAB^{®} dates

Holidays used in computing business days, specified as the comma-separated pair consisting of
`'Holidays'`

and MATLAB dates using a
`NHolidays`

-by-`1`

vector.

**Data Types: **`datetime`

`BusinessDayConvention`

— Business day conventions

`actual`

(default) | character vector | cell array of character vectors

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

`Price`

— Expected fixed-rate note prices at time 0

vector

Expected fixed-rate note prices 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 MATLAB structure
of trees containing vectors of instrument prices and accrued interest,
and a vector of observation times for each node. Within `PriceTree`

:

`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

### 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.

## Version History

**Introduced before R2006a**

### R2022b: Serial date numbers not recommended

Although `fixedbybk`

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

`bktree`

| `bondbybk`

| `capbybk`

| `cfbybk`

| `floatbybk`

| `floorbybk`

| `swapbybk`

| `FixedBond`

### Topics

- Pricing Using Interest-Rate Tree Models
- Price Portfolio of Bond and Bond Option Instruments
- Bond Portfolio Optimization Using Portfolio Object
- Fixed-Rate Note
- Understanding Interest-Rate Tree Models
- Pricing Options Structure
- Supported Interest-Rate Instrument Functions
- Mapping Financial Instruments Toolbox Functions for Interest-Rate Instrument Objects

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