capbyhjm (Financial Derivatives Toolbox)

Price cap instrument by HJM interest rate tree

Syntax

[Price, PriceTree] = capbyhjm(HJMTree,  Strike, Settle, Maturity,                       
Reset, Basis, Principal, Options)

Arguments

HJMTree
Forward rate tree structure created by hjmtree.

Strike
Number of instruments (NINST)-by-1 vector of rates at which the cap is exercised.

Settle
Settlement dates. NINST-by-1 vector of dates representing the settlement dates of the cap.

Maturity
NINST-by-1 vector of dates representing the maturity dates of the cap.

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`.
`Strike`	Number of instruments (`NINST`)-by-`1` vector of rates at which the cap is exercised.
`Settle`	Settlement dates. `NINST`-by-`1` vector of dates representing the settlement dates of the cap.
`Maturity`	`NINST`-by-`1` vector of dates representing the maturity dates of the cap.
`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] = capbyhjm(HJMTree, Strike, Settle, Maturity, Reset, Basis, Principal, Options) computes the price of a cap instrument from an HJM tree.

Price is the expected price of the cap at time 0.

PriceTree is the tree structure with values of the cap at each node.

The Settle date for every cap is set to the ValuationDate of the HJM tree. The cap argument Settle is ignored.

Examples

Price a 3% cap instrument 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 cap instrument.

```
load deriv 
```

Set the required values. Other arguments will use defaults.

Strike = 0.03;
Settle = '01-Jan-2000';
Maturity = '01-Jan-2004';

Use capbyhjm to compute the price of the cap instrument.

Price = capbyhjm(HJMTree, Strike, Settle, Maturity)

Price =

  6.2831

capbybdt cfbybdt