Specify time structure for Black-Karasinski tree


TimeSpec = bktimespec(ValuationDate, Maturity, Compounding)



Scalar date marking the pricing date and first observation in the tree. Specify as a serial date number or date character vector.


Number of levels (depth) of the tree. A number of levels (NLEVELS)-by-1 vector of dates marking the cash flow dates of the tree. Cash flows with these maturities fall on tree nodes. Maturity should be in increasing order.


(Optional) Scalar value representing the rate at which the input zero rates were compounded when annualized. Default = -1 (continuous compounding). This argument determines the formula for the discount factors:

Compounding = 1, 2, 3, 4, 6, 12 = F

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.

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.

Compounding = −1

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


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

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


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Specify a Four-Period Tree with Annual Nodes

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

ValuationDate = 'Jan-1-2004';
Maturity = ['12-31-2004'; '12-31-2005'; '12-31-2006';
Compounding = 1;
TimeSpec = bktimespec(ValuationDate, Maturity, Compounding)
TimeSpec = 

           FinObj: 'BKTimeSpec'
    ValuationDate: 731947
         Maturity: [4x1 double]
      Compounding: 1
            Basis: 0
     EndMonthRule: 1

Related Examples

See Also

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Introduced before R2006a

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