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
(Optional) 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
(Optional) 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 is followed only by the bond's maturity cash flow date.

StartDate
Ignored.

Face
(Optional) Face value. Default = 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`	(Optional) 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`	(Optional) 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 is followed only by the bond's maturity cash flow date.
`StartDate`	Ignored.
`Face`	(Optional) Face value. Default = `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

[Price, PriceTree] = bondbyhjm(HJMTree, CouponRate, Settle, Maturity, Period, Basis, EndMonthRule, IssueDate, FirstCouponDate, LastCouponDate, StartDate, Face, Options) computes the price of a bond by an HJM forward rate tree.

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. Within PriceTree:

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 =

  97.5280

See Also

hjmtree, hjmprice, instbond

bondbybdt bondbyzero