bondbyhjm (Financial Derivatives Toolbox)

Price bond by HJM interest rate tree

Syntax

[Price, PriceTree] = bondbyhjm(HJMTree, CouponRate, Settle, 
Maturity, Period, Basis, EndMonthRule, IssueDate, 
FirstCouponDate, LastCouponDate, StartDate, Face, Options)

Arguments

HJMTree
Forward rate tree structure created by hjmtree.

CouponRate
Decimal annual rate.

Settle
Settlement date. A vector of serial date numbers or date strings. Settle must be earlier than or equal to Maturity.

Maturity
Maturity date. A vector of serial date numbers or date strings.

Period
(Optional) Coupons per year of the bond. A vector of integers. Allowed values are 1, 2, 3, 4, 6, and 12. Default = 2.

Basis
(Optional) Day-count basis of the bond. A vector of integers.
0 = actual/actual (default), 1 = 30/360, 2 = actual/360,
3 = actual/365.

EndMonthRule
(Optional) End-of-month rule. A vector. This rule applies only when Maturity is an end-of-month date for a month having 30 or fewer days. 0 = ignore rule, meaning that a bond's coupon payment date is always the same numerical day of the month. 1 = set rule on (default), meaning that a bond's coupon payment date is always the last actual day of the month.

IssueDate
(Optional) Date when a bond was issued.

FirstCouponDate
Date when a bond makes its first coupon payment. When FirstCouponDate and LastCouponDate are both specified, FirstCouponDate takes precedence in determining the coupon payment structure.

LastCouponDate
Last coupon date of a bond prior to the maturity date. In the absence of a specified FirstCouponDate, a specified LastCouponDate determines the coupon structure of the bond. The coupon structure of a bond is truncated at the LastCouponDate regardless of where it falls and will be followed only by the bond's maturity cash flow date.

StartDate
Ignored.

Face
Face value. Default is 100.

Options
(Optional) Derivatives pricing options structure created with derivset.

`HJMTree`	Forward rate tree structure created by `hjmtree`.
`CouponRate`	Decimal annual rate.
`Settle`	Settlement date. A vector of serial date numbers or date strings. `Settle` must be earlier than or equal to `Maturity`.
`Maturity`	Maturity date. A vector of serial date numbers or date strings.
`Period`	(Optional) Coupons per year of the bond. A vector of integers. Allowed values are `1`, `2`, `3`, `4`, `6`, and `12`. Default = `2`.
`Basis`	(Optional) Day-count basis of the bond. A vector of integers. `0` = actual/actual (default), `1` = 30/360, `2` = actual/360, `3` = actual/365.
`EndMonthRule`	(Optional) End-of-month rule. A vector. This rule applies only when `Maturity` is an end-of-month date for a month having 30 or fewer days. `0` = ignore rule, meaning that a bond's coupon payment date is always the same numerical day of the month. `1` = set rule on (default), meaning that a bond's coupon payment date is always the last actual day of the month.
`IssueDate`	(Optional) Date when a bond was issued.
`FirstCouponDate`	Date when a bond makes its first coupon payment. When `FirstCouponDate` and `LastCouponDate` are both specified, `FirstCouponDate` takes precedence in determining the coupon payment structure.
`LastCouponDate`	Last coupon date of a bond prior to the maturity date. In the absence of a specified `FirstCouponDate`, a specified `LastCouponDate` determines the coupon structure of the bond. The coupon structure of a bond is truncated at the `LastCouponDate` regardless of where it falls and will be followed only by the bond's maturity cash flow date.
`StartDate`	Ignored.
`Face`	Face value. Default is `100`.
Options	(Optional) Derivatives pricing options structure created with `derivset`.

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

Description

bondbyhjm is a dynamic programming subroutine for hjmprice.

Price is a number of instruments (NINST)-by-1 matrix of expected prices 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.

Examples

Price a 4% bond 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 bond.

load deriv

Set the required values. Other arguments will use defaults.

CouponRate = 0.04;
Settle = '01-Jan-2000';
Maturity = '01-Jan-2004';

Use bondbyhjm to compute the Price of the bond.

Price = bondbyhjm(HJMTree, CouponRate, Settle, Maturity)
Warning: Not all cash flows are aligned with the tree. Result will 
be approximated.

Price =

  107.6773

See Also

hjmtree, hjmprice, instbond

Alphabetical List of Functions bondbyzero