fixedbybk

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

Syntax

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

Input 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.

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

NINST-by-1 of notional principal amounts or NINST-by-1 cell array where each element is a NumDates-by-2 cell array where the first column is dates and the second column is associated principal amount. The date indicates the last day that the principal value is valid.

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. 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] = fixedbybk(BKTree, CouponRate, Settle,
Maturity)
computes the price of a fixed-rate note from a Black-Karasinski tree.

[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 using optional input arguments.

[Price, PriceTree] = fixedbybk(BKTree, CouponRate, Settle,
Maturity, Name,Value)
computes the price of a price of a fixed-rate note from a Black-Karasinski 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 BK tree. The fixed-rate note argument Settle is ignored.

Examples

expand all

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)
Warning: Fixed rate notes are valued at Tree ValuationDate rather than Settle 

Price =

  103.5126

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