fixedbybk - Price fixed-rate note from Black-Karasinski interest-rate tree

Syntax

[Price, PriceTree] = fixedbybk(BKTree, CouponRate, Settle,
Maturity, Reset, Basis, Principal, Options, EndMonthRule)

Arguments

BKTree	Interest-rate tree structure created by bktree.
CouponRate	Decimal annual rate.
Settle	Settlement dates. NINST-by-1 vector of dates representing the settlement dates of the fixed-rate note.
Maturity	NINST-by-1 vector of dates representing the maturity dates of the fixed-rate note.
Reset	(Optional) NINST-by-1 vector representing the frequency of payments per year. Default = 1.
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 (BMA) 5 = 30/360 (ISDA) 6 = 30/360 (European) 7 = actual/365 (Japanese) 8 = actual/actual (ICMA) 9 = actual/360 (ICMA) 10 = actual/365 (ICMA) 11 = 30/360E (ICMA) 12 = actual/actual (ISDA) 13 = BUS/252 For more information, see basis.
Principal	(Optional) NINST-by-1 vector of the notional principal amount. Default = 100.
Options	(Optional) Derivatives pricing options structure created with derivset.
EndMonthRule	(Optional) NINST-by-1 vector representing the End-of-month rule. Default = 1.

Description

[Price, PriceTree] = fixedbybk(BKTree, CouponRate, Settle, Maturity, Reset, Basis, Principal, Options, EndMonthRule) computes the price of a fixed-rate note from a Black-Karasinski tree.

Price is an NINST-by-1 vector of expected prices of the fixed-rate note 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.

PriceTree.PTree contains the clean prices.

PriceTree.AITree contains the accrued interest.

PriceTree.tObs contains the observation times.

The Settle date for every fixed-rate note is set to the ValuationDate of the BK tree. The fixed-rate note argument Settle is ignored.

Examples

Price a 5% fixed-rate note 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 note.

load deriv.mat; 

Set the required values. Other arguments will use defaults.

CouponRate = 0.05;
Settle = '01-Jan-2005';
Maturity = '01-Jan-2006';

Use fixedbybk to compute the price of the note.

Price = fixedbybk(BKTree, CouponRate, Settle, Maturity)

Price =

  103.5126

See Also

bktree | bondbybk | capbybk | cfbybk | floatbybk | floorbybk | swapbybk

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