Quantcast

Documentation Center

  • Trial Software
  • Product Updates

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 (BMA)

  • 5 = 30/360 (ISDA)

  • 6 = 30/360 (European)

  • 7 = actual/365 (Japanese)

  • 8 = actual/actual (ICMA)

  • 9 = actual/360 (ICMA)

  • 10 = actual/365 (ICMA)

  • 11 = 30/360E (ICMA)

  • 12 = actual/actual (ISDA)

  • 13 = BUS/252

For more information, see basis.

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

expand all

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)
Warning: Caps are valued at Tree ValuationDate rather than Settle 
Warning: Not all cash flows are aligned with the tree. Result will be
approximated. 
Warning: Not all cash flows are aligned with the tree. Result will be
approximated. 

Price =

    6.8337

See Also

| | |

Was this topic helpful?