Financial Derivatives Toolbox™

capbybk

Price cap instrument from Black-Karasinski interest-rate tree

Syntax

[Price, PriceTree] = capbybk(BKTree, Strike, Settle, Maturity, Reset, Basis, Principal, Options)

Arguments

`BKTree`	Interest-rate tree structure created by `bktree`.
`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) Day-count basis of the instrument. A vector of integers. 0 = actual/actual (default) 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 (ISMA) 9 = actual/360 (ISMA) 10 = actual/365 (ISMA) 11 = 30/360E (ISMA) 12 = actual/365 (ISDA)
`Principal`	(Optional) The notional principal amount. Default = `100`.
`Options`	(Optional) Derivatives pricing options structure created with `derivset`.

Description

[Price, PriceTree] = capbybk(BKTree, Strike, Settle, Maturity,Reset, Basis, Principal, Options) computes the price of a cap instrument from a Black-Karasinski interest-rate 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 BK tree. The cap argument Settle is ignored.

Examples

Price a 3% cap instrument using a Black-Karasinski interest-rate tree.

Load the file deriv.mat, which provides BKTree. The BKTree structure contains the time and interest-rate information needed to price the cap instrument.

load deriv.mat;

Set the required values. Other arguments will use defaults.

Strike = 0.03;
Settle = '01-Jan-2005';
Maturity = '01-Jan-2009';

Use capbybk to compute the price of the cap instrument.

Price = capbybk(BKTree, Strike, Settle, Maturity)

Price =

  6.8337

capbybk

Syntax

Arguments

Description

Examples

See Also