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

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

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

Examples

Price a 4% Fixed-Rate Note Using an HJM Forward-Rate Tree

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

HJMTree — Interest-rate structure

structure

Interest-rate tree structure, created by hjmtree

Data Types: struct

CouponRate — Coupon annual rate

decimal

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

Data Types: double

Settle — Settlement date

serial date number | character vector

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 — Maturity date

serial date number | character vector

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 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] = fixedbyhjm(HJMTree,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^® date numbers

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

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.PBush contains the clean prices.

• PriceTree.AITree contains the accrued interest.

• PriceTree.tObs contains the observation times.

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.