# bdttimespec

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

## 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 = datetime(2000,1,1);
Maturity = [datetime(2001,1,1) ; datetime(2002,1,1) ; datetime(2003,1,1) ;
datetime(2004,1,1); datetime(2005,1,1)];

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 datetime, string, or date character vector.

To support existing code, bdttimespec also accepts serial date numbers as inputs, but they are not recommended.

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

To support existing code, bdttimespec also accepts serial date numbers as inputs, but they are not recommended.

(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).

## Version History

Introduced before R2006a

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