| Financial Derivatives Toolbox™ | ![]() |
[Price, PriceTree] = bondbybk(BKTree,
CouponRate,
Settle, Maturity, Period, Basis,
EndMonthRule, IssueDate,
FirstCouponDate, LastCouponDate,
StartDate, Face, Options)
BKTree | Forward rate tree structure created by bktree. |
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.
|
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. |
(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 BK tree. The bond argument Settle is ignored.
[Price, PriceTree] = bondbybk(BKTree, CouponRate, Settle, Maturity, Period, Basis, EndMonthRule, IssueDate, FirstCouponDate, LastCouponDate, StartDate, Face, Options) computes the price of a bond from a Black-Karasinski interest-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.PTree contains the clean prices.
PriceTree.AITree contains the accrued interest.
PriceTree.tObs contains the observation times.
Price a 4% bond using a Black-Karasinski interest-rate tree.
Load the file deriv.mat, which provides BKTree. The BKTree structure contains the time and interest-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-2004'; Maturity = '31-Dec-2008';
Use bondbybk to compute the price of the bond.
Price = bondbybk(BKTree, CouponRate, Settle, Maturity) Warning: Not all cash flows are aligned with the tree. Result will be approximated. Price = 98.0300
bkprice, bktree, hwprice, hwtree, instbond
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