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)

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

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 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

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

See Also

hjmtree, hjmprice, instbond

  


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