bdttimespec

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

Syntax

TimeSpec = bdttimespec(ValuationDate,Maturity)

TimeSpec = bdttimespec(___,Compounding)

Description

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.

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

Examples

Specify a Five-Period Tree with Annual Nodes

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

ValuationDate — Pricing date and first observation in the tree

datetime scalar | string scalar | date character vector

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.

Maturity — Dates marking the cash flow dates of the tree

datetime array | string array | date character vector

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.

Compounding — Rate at which the input zero rates were compounded when annualized

1 (default) | integer with value of 1, 2, 3, 4, 6, 12, 365, or -1

(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

TimeSpec — Specification for the time layout for bdttree

structure

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

R2022b: Serial date numbers not recommended

Although bdttimespec supports serial date numbers, datetime values are recommended instead. The datetime data type provides flexible date and time formats, storage out to nanosecond precision, and properties to account for time zones and daylight saving time.

To convert serial date numbers or text to datetime values, use the datetime function. For example:

t = datetime(738427.656845093,"ConvertFrom","datenum");
y = year(t)

y =

        2021

There are no plans to remove support for serial date number inputs.