Contents

capbyhjm

Price cap instrument from Heath-Jarrow-Morton 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) 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) NINST-by-1 of notional principal amounts or NINST-by-1 cell array where each element is a NumDates-by-2 cell array where the first column is dates and the second column is associated principal amount. The date indicates the last day that the principal value is valid. Default is 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.

    Note:   Use the optional name-value pair argument, Principal, to pass a schedule to compute price for an amortizing cap.

Examples

expand all

Price a 3% Cap Instrument Using an HJM Forward-Rate Tree

Load the file deriv.mat, which provides HJMTree. The HJMTree structure contains the time and forward-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-2000';
Maturity = '01-Jan-2004';

Use capbyhjm to compute the price of the cap instrument.

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

    6.2831

Compute the Price of an Amortizing Cap Using the HJM Model

Load deriv.mat to specify the HJMTree and then define the cap instrument.

load deriv.mat;
Settle = '01-Jan-2000';
Maturity = '01-Jan-2004';
Strike = 0.045;
Reset = 1;
Principal ={{'01-Jan-2001' 100;'01-Jan-2002' 80;'01-Jan-2003' 70;'01-Jan-2004' 30}};

Price the amortizing cap.

Basis = 1;
Price = capbyhjm(HJMTree, Strike, Settle, Maturity, Reset, Basis, Principal)
Price =

    1.4588

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