bondbybdt (Financial Derivatives Toolbox)

Price bond by BDT interest rate tree

Syntax

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

Arguments

BDTTree
Interest rate tree structure created by bdttree.

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 is 100.

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

`BDTTree`	Interest rate tree structure created by `bdttree`.
`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 is `100`.
Options	(Optional) Derivatives pricing options structure created with `derivset`.

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

Description

[Price, PriceTree] = bondbybdt(BDTTree, CouponRate, Settle, Maturity, Period, Basis, EndMonthRule, IssueDate, FirstCouponDate, LastCouponDate, StartDate, Face, Options) computes the price of a bond by a BDT interest rate tree.

Price is a number of instruments (NINST)-by-1 matrix of expected prices at time 0.

PriceTree is a MATLAB structure of trees containing vectors of instrument prices and accrued interest, and a vector of observation times for each node. Within PriceTree:

PriceTree.PTree contains the clean prices.
PriceTree.AITree contains the accrued interest.
PriceTree.tObs contains the observation times.

Examples

Price a 10% bond using a BDT interest rate tree.

Load the file deriv.mat, which provides BDTTree. BDTTree contains the time and interest rate information needed to price the bond.

```
load deriv 
```

Set the required values. Other arguments will use defaults.

CouponRate = 0.10;
Settle = '01-Jan-2000';
Maturity = '01-Jan-2003';
Period = 1;

Use bondbybdt to compute the price of the bond.

Price = bondbybdt(BDTTree, CouponRate, Settle, Maturity, Period)

Price =

  95.5030

See Also

bdttree, bdtprice, instbond

bdtvolspec bondbyhjm