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bdttimespec

Specify time structure for Black-Derman-Toy interest-rate tree

Syntax

TimeSpec = bdttimespec(ValuationDate,Maturity)
TimeSpec = bdttimespec(___,Compounding)

Description

example

TimeSpec = bdttimespec(ValuationDate,Maturity) sets the number of levels and node times for a bdttree and determines the mapping between dates and time for rate quoting.

example

TimeSpec = bdttimespec(___,Compounding) adds the optional argument Compounding.

Examples

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This example shows how to specify a five-period tree with annual nodes and use annual compounding to report rates.

Compounding = 1;
ValuationDate = '01-01-2000';
Maturity = ['01-01-2001'; '01-01-2002'; '01-01-2003'; 
'01-01-2004'; '01-01-2005'];

TimeSpec = bdttimespec(ValuationDate, Maturity, Compounding)
TimeSpec = struct with fields:
           FinObj: 'BDTTimeSpec'
    ValuationDate: 730486
         Maturity: [5x1 double]
      Compounding: 1
            Basis: 0
     EndMonthRule: 1

Input Arguments

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Pricing date and first observation in the tree, specified as a scalar date using a serial date number or date character vector.

Data Types: double | char

Dates marking the cash flow dates of the tree, specified as NLEVELS-by-1 vector of serial date numbers or date character vectors. Cash flows with these maturities fall on tree nodes. Maturity should be in increasing order.

Data Types: double | char | cell

(Optional) Rate at which the input zero rates were compounded when annualized, specified as a scalar integer value.

  • If Compounding = 1, 2, 3, 4, 6, 12:

    Disc = (1 + Z/F)^(-T), where F is the compounding frequency, Z is the zero rate, and T is the time in periodic units; for example, T = F is one year.

  • If Compounding = 365:

    Disc = (1 + Z/F)^(-T), where F is the number of days in the basis year and T is a number of days elapsed computed by basis.

  • If Compounding = −1:

    Disc = exp(-T*Z), where T is time in years.

Data Types: double

Output Arguments

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Specification for the time layout for bdttree, returned as a structure. The state observation dates are [ValuationDate; Maturity(1:end-1)]. Because a forward rate is stored at the last observation, the tree can value cash flows out to Maturity(end).

Introduced before R2006a