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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(HJMTree, CouponRate, Settle,
Maturity, Reset, Basis, Principal, Options, EndMonthRule)
[Price, PriceTree] = fixedbyhjm(HJMTree, CouponRate, Settle,
Maturity, Name,Value)

## Input Arguments

 HJMTree Forward-rate tree structure created by hjmtree. CouponRate Decimal annual rate. Settle Settlement dates. Number of instruments (NINST)-by-1 vector of dates representing the settlement dates of the fixed-rate note. Maturity NINST-by-1 vector of dates representing the maturity dates of the fixed-rate note.

### Ordered Input or Name-Value Pair Arguments

Enter the following optional inputs using an ordered syntax or as name-value pair arguments. You cannot mix ordered syntax with name-value pair arguments.

 Reset NINST-by-1 vector representing the frequency of payments per year. Default: 1 Basis Day-count basis of the instrument. A vector of integers. 0 = actual/actual 1 = 30/360 (SIA)2 = actual/3603 = actual/3654 = 30/360 (PSA)5 = 30/360 (ISDA)6 = 30/360 (European)7 = actual/365 (Japanese)8 = actual/actual (ISMA)9 = actual/360 (ISMA)10 = actual/365 (ISMA)11 = 30/360E (ISMA) 12 = actual/365 (ISDA)13 = BUS/252For more information, see basis. Default: 0 (actual/actual) Principal NINST-by-1 of notional principal amounts or NINST-by-1 cell array where each element is a NumDates-by-2 cell array where the first column is dates and the second column is associated principal amount. The date indicates the last day that the principal value is valid. Default: 100 Options Derivatives pricing options structure created with derivset. EndMonthRule End-of-month rule. A NINST-by-1 vector. This rule applies only when Maturity is an end-of-month date for a month having 30 or fewer days.0 = Ignore rule, meaning that a bond coupon payment date is always the same numerical day of the month.1 = Set rule on, meaning that a bond coupon payment date is always the last actual day of the month. Default: 1

### 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.

 AdjustCashFlowsBasis Adjust the cash flows based on the actual period day count. NINST-by-1 of logicals. Default: False BusinessDayConvention Require payment dates to be business dates. NINST-by-1 cell array with possible choices of business day convention:actual followmodifiedfollowpreviousmodifiedprevious Default: actual Holidays Holidays used for business day convention. NHOLIDAYS-by-1 of MATLAB® date numbers. Default: If no dates are specified, holidays.m is used.

## Description

[Price, PriceTree] = fixedbyhjm(HJMTree, CouponRate, Settle,
Maturity)
computes the price of a fixed-rate note from a HJM forward-rate tree.

[Price, PriceTree] = fixedbyhjm(HJMTree, CouponRate, Settle,
Maturity, Reset, Basis, Principal, Options, EndMonthRule)
computes the price of a fixed-rate note from a HJM forward-rate tree using optional input asrguments.

[Price, PriceTree] = fixedbyhjm(HJMTree, CouponRate, Settle,
Maturity, Name,Value)
computes the price of a price of a fixed-rate note from a HJM forward-rate tree with additional options specified by one or more Name,Value pair arguments.

Price is an NINST-by-1 vector of expected prices of the fixed-rate note at time 0.

PriceTree is a structure of trees containing vectors of instrument prices and accrued interest, and a vector of observation times for each node.

PriceTree.PBush contains the clean prices.

PriceTree.AIBush contains the accrued interest.

PriceTree.tObs contains the observation times.

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.

## Examples

expand all

### 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

```