fixedbybk

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

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Syntax

[Price,PriceTree] = fixedbybk(BKTree,CouponRate,Settle,Maturity)
[Price,PriceTree] = fixedbybk(___,Name,Value)

Description

example

[Price,PriceTree] = fixedbybk(BKTree,CouponRate,Settle,Maturity) prices a fixed-rate note from a Black-Karasinski interest-rate tree.

example

[Price,PriceTree] = fixedbybk(___,Name,Value) adds additional name-value pair arguments.

Examples

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Open Live Script

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 = '01-Jan-2004';
Maturity = '01-Jan-2006';

Use fixedbybk to compute the price of the note. 

Price = fixedbybk(BKTree, CouponRate, Settle, Maturity)
Price = 103.5126

Input Arguments

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Interest-rate tree structure, created by bktree

Data Types: struct

Coupon annual 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.

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.

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

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 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

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

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

Data Types: struct

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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Expected fixed-rate note prices at time 0, returned as a NINST-by-1 vector.

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

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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.

See Also

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Topics

Introduced before R2006a

Financial Instruments Toolbox Documentation

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