bdttimespec

Specify time structure for Black-Derman-Toy 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; 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.

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

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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 = '01-01-2000'; Maturity = ['01-01-2001'; '01-01-2002'; '01-01-2003'; '01-01-2004'; '01-01-2005']; TimeSpec = bdttimespec(ValuationDate, Maturity, Compounding) ```
```TimeSpec = FinObj: 'BDTTimeSpec' ValuationDate: 730486 Maturity: [5x1 double] Compounding: 1 Basis: 0 EndMonthRule: 1 ```