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bktimespec

Specify time structure for Black-Karasinski tree

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Syntax

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

Description

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

example

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

example

Examples

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Open Live Script

This example shows how to specify a four-period tree with annual nodes using annual compounding to report rates.

ValuationDate = datetime(2004,1,1); 
Maturity = [datetime(2004,12,31) ; datetime(2005,12,31) ; datetime(2006,12,31) ; 
datetime(2007,12,31)];
Compounding = 1;
TimeSpec = bktimespec(ValuationDate,Maturity,Compounding)
TimeSpec = struct with fields:
           FinObj: 'BKTimeSpec'
    ValuationDate: 731947
         Maturity: [4x1 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, bktimespec 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, bktimespec 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 bktree, 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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See Also

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