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fixedbyhjm

Price fixed-rate note from Heath-Jarrow-Morton interest-rate tree

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Syntax

[Price,PriceTree] = fixedbyhjm(HJMTree,CouponRate,Settle,Maturity)
[Price,PriceTree] = fixedbyhjm(___,Name,Value)

Description

example

[Price,PriceTree] = fixedbyhjm(HJMTree,CouponRate,Settle,Maturity) prices a fixed-rate note from a Heath-Jarrow-Morton interest-rate tree.

example

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

Examples

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Open Live Script

This example shows how to price a 4% fixed-rate note using an HJM forward-rate tree by loading the file deriv.mat, which provides HJMTree. The HJMTree structure contains the time and forward-rate information needed to price the note.

load deriv.mat 

CouponRate = 0.04;
Settle = datetime(2000,1,1);
Maturity = datetime(2003,1,1);

Price = fixedbyhjm(HJMTree, CouponRate, Settle, Maturity)
Price = 98.7159

Input Arguments

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Interest-rate tree structure, created by hjmtree

Data Types: struct

Coupon annual rate, specified as a NINST-by-1 vector.

Data Types: double

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, fixedbyhjm 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 HJM tree. The fixed-rate note argument Settle is ignored.

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, fixedbyhjm 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] = fixedbyhjm(HJMTree,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 dates using a NHolidays-by-1 vector.

Data Types: datetime

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.PBush contains the clean prices.

  • PriceTree.AITree contains the accrued interest.

  • PriceTree.tObs contains the observation times.

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.

Version History

Introduced before R2006a

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See Also

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