bdttimespec (Financial Derivatives Toolbox)

Specify time structure for BDT interest rate tree

Syntax

TimeSpec = bdttimespec(ValuationDate, Maturity, Compounding)

Arguments

ValuationDate
Scalar date marking the pricing date and first observation in the tree. Specify as serial date number or date string

Maturity
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.

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

`ValuationDate`	Scalar date marking the pricing date and first observation in the tree. Specify as serial date number or date string
`Maturity`	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.
`Compounding`	(Optional) Scalar value representing the rate at which the input zero rates were compounded when annualized. Default = `1`. This argument determines the formula for the discount factors: `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, e.g. `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.

Description

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

TimeSpec is a structure specifying the time layout for bdttree. 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.

Examples

Specify a four period tree with annual nodes. 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'];
Volatility = [.2; .19; .18; .17; .16];

TimeSpec = bdttimespec(ValuationDate, Maturity, Compounding)

TimeSpec = 

           FinObj: 'BDTTimeSpec'
    ValuationDate: 730486
         Maturity: [5x1 double]
      Compounding: 1
            Basis: 0
     EndMonthRule: 1

See Also

bdttree, bdtvolspec

bdtsens bdttree