floatbyhjm (Financial Derivatives Toolbox)

Price floating rate note from HJM interest rate tree

Syntax

[Price, PriceTree] = floatbyhjm(HJMTree, Spread, Settle, Maturity, 
Reset, Basis, Principal, Options)

Arguments

HJMTree
Forward rate tree structure created by hjmtree.

Spread
Number of instruments (NINST)-by-1 vector of number of basis points over the reference rate.

Settle
Settlement dates. NINST-by-1 vector of dates representing the settlement dates of the floating rate note.

Maturity
NINST-by-1 vector of dates representing the maturity dates of the floating 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) NINST-by-1 vector of the notional principal amount. Default = 100.

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

`HJMTree`	Forward rate tree structure created by `hjmtree`.
`Spread`	Number of instruments (`NINST`)-by-`1` vector of number of basis points over the reference rate.
`Settle`	Settlement dates. `NINST`-by-`1` vector of dates representing the settlement dates of the floating rate note.
`Maturity`	`NINST`-by-`1` vector of dates representing the maturity dates of the floating 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) `NINST`-by-`1` vector of the notional principal amount. Default = `100`.
Options	(Optional) Derivatives pricing options structure created with `derivset`.

Description

[Price, PriceTree] = floatbyhjm(HJMTree, Spread, Settle, Maturity, Reset, Basis, Principal, Options) computes the price of a floating rate note from an HJM tree.

Price is an NINST-by-1 vector of expected prices of the floating 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 floating rate note is set to the ValuationDate of the HJM tree. The floating rate note argument Settle is ignored.

Examples

Price a 20 basis point floating 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.

Spread = 20;
Settle = '01-Jan-2000';
Maturity = '01-Jan-2003';

Use floatbyhjm to compute the price of the note.

Price = floatbyhjm(HJMTree, Spread, Settle, Maturity)

Price =

  100.5529

See Also

bondbyhjm, capbyhjm, cfbyhjm, fixedbyhjm, floorbyhjm, hjmtree, swapbyhjm

floatbybdt floatbyzero