fixedbyhjm (Financial Derivatives Toolbox)

Price fixed rate note from HJM interest rate tree

Syntax

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

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.

Reset
(Optional) NINST-by-1 vector representing the frequency of payments per year. Default = 1.

Basis
(Optional) NINST-by-1 vector representing the basis used when annualizing the input forward rate tree. Default = 0 (actual/actual).

Principal
(Optional) The notional principal amount. Default = 100.

Options
(Optional) Derivatives pricing options structure created with derivset.

`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.
`Reset`	(Optional) `NINST`-by-`1` vector representing the frequency of payments per year. Default = `1`.
`Basis`	(Optional) `NINST`-by-`1` vector representing the basis used when annualizing the input forward rate tree. Default = `0` (actual/actual).
`Principal`	(Optional) The notional principal amount. Default = `100`.
Options	(Optional) Derivatives pricing options structure created with `derivset`.

Description

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

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

Price a 4% fixed rate note using an HJM forward rate tree.

Load the file deriv.mat, which provides HJMTree. HJMTree contains the time and forward rate information needed to price the note.

```
load deriv 
```

Set the required values. Other arguments will use defaults.

CouponRate = 0.04;
Settle = '01-Jan-2000';
Maturity = '01-Jan-2003';

Use fixedbyhjm to compute the price of the note.

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

Price =

  98.7159

See Also

bondbyhjm, capbyhjm, cfbyhjm, floatbyhjm, floorbyhjm, hjmtree, swapbyhjm

fixedbybdt fixedbyzero