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fixedbyhjm

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

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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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 = '01-Jan-2000';
Maturity = '01-Jan-2003';

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 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 HJM 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 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,PriceTree] = fixedbyhjm(HJMTree,CouponRate,Settle,Maturity,'Reset',4)

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

Data Types: double

Day count basis representing the basis used when annualizing the input forward rate tree, 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

For more information, see basis.

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

Derivatives pricing options structure, specified 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 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 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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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.

Introduced before R2006a

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