Financial Derivatives Toolbox™

fixedbyhjm - Price fixed-rate note from HJM interest-rate tree

Syntax

[Price, PriceTree] = fixedbyhjm(HJMTree, CouponRate, Settle, Maturity, Reset, Basis, Principal, Options)

Arguments

`HJMTree`	Forward-rate tree structure created by `hjmtree`.
`CouponRate`	Decimal annual rate.
`Settle`	Settlement dates. Number of instruments (`NINST`)-by-`1` vector of dates representing the settlement dates of the fixed-rate note.
`Maturity`	`NINST`-by-`1` vector of dates representing the maturity dates of the fixed-rate note.
`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] = fixedbyhjm(HJMTree, CouponRate, Settle,Maturity, Reset, Basis, Principal, Options) computes the price of a fixed-rate note from a HJM forward-rate tree.

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

Examples

Price a 4% fixed-rate note 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 note.

load deriv.mat

Set the required values. Other arguments will use defaults.

CouponRate = 0.04;
Settle = '01-Jan-2000';
Maturity = '01-Jan-2003';

Use fixedbyhjm to compute the price of the note.

Price = fixedbyhjm(HJMTree, CouponRate, Settle, Maturity)

Price =

  98.7159

fixedbyhjm - Price fixed-rate note from HJM interest-rate tree

Syntax

Arguments

Description

Examples

See Also