fixedbybdt - Price fixed-rate note from Black-Derman-Toy interest-rate tree

Syntax

Input Arguments

BDTTree	Interest-rate tree structure created by bdttree.
CouponRate	Decimal annual rate.
Settle	Settlement dates. Number of instruments (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.

Ordered Input or Name-Value Pair Arguments

Enter the following optional inputs using an ordered syntax or as name-value pair arguments. You cannot mix ordered syntax with name-value pair arguments.

Reset	NINST-by-1 vector representing the frequency of payments per year. Default: 1
Basis	Day-count basis of the instrument. A vector of integers. 0 = actual/actual 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 For more information, see basis. Default: 0 (actual/actual)
Principal	The notional principal amount. Default: 100
Options	Derivatives pricing options structure created with derivset.
EndMonthRule	End-of-month rule. A NINST-by-1 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 coupon payment date is always the same numerical day of the month. 1 = Set rule on, meaning that a bond coupon payment date is always the last actual day of the month. Default: 1

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments, where Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

AdjustCashFlowsBasis	Adjust the cash flows based on the actual period day count. NINST-by-1 of logicals. Default: False
BusinessDayConvention	Require payment dates to be business dates. NINST-by-1 cell array with possible choices of business day convention: actual follow modifiedfollow previous modifiedprevious Default: actual
Holidays	Holidays used for business day convention. NHOLIDAYS-by-1 of MATLAB date numbers. Default: If no dates are specified, holidays.m is used.

Description

[Price, PriceTree] = fixedbybdt(BDTTree, CouponRate, Settle, Maturity) computes the price of a fixed-rate note from a BDT interest-rate tree.

[Price, PriceTree] = fixedbybdt(BDTTree, CouponRate, Settle, Maturity, Reset, Basis, Principal, Options, EndMonthRule) computes the price of a fixed-rate note from a BDT interest-rate tree using additional input arguments.

[Price, PriceTree] = fixedbybdt(BDTTree, CouponRate, Settle, Maturity, Name,Value) computes the price of a price of a fixed-rate note from a BDT interest-rate tree with additional options specified by one or more Name,Value pair arguments.

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 BDT tree. The fixed-rate note argument Settle is ignored.

Examples

Price a 10% fixed-rate note using a BDT interest-rate tree.

Load the file deriv.mat, which provides BDTTree. The BDTTree 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 = 0.10;
Settle = '01-Jan-2000';
Maturity = '01-Jan-2004';
Reset = 1;

Use fixedbybdt to compute the price of the note.

Price = fixedbybdt(BDTTree, CouponRate, Settle, Maturity, Reset)

Price =

  92.9974

See Also

bdttree | bondbybdt | capbybdt | cfbybdt | floatbybdt | floorbybdt | swapbybdt

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