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bondbyhjm - Price bond from 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 `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 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) 13 = BUS/252
`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 before 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`	(Optional) Date when a bond actually starts (the date from which a bond cash flow is considered). To make an instrument forward-starting, specify this date as a future date. If you do not specify `StartDate`, the effective start date is the `Settle` date.
`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 from 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. The HJMTree structure contains the time and forward-rate information needed to price the bond.

load deriv.mat;

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

bondbyhjm - Price bond from HJM interest-rate tree

Syntax

Arguments

Description

Examples

See Also