# Documentation

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# hwtimespec

Specify time structure for Hull-White interest-rate tree

## Syntax

```TimeSpec = hwtimespec(ValuationDate,Maturity,Compounding) ```

## Arguments

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

## Description

`TimeSpec = hwtimespec(ValuationDate,Maturity,Compounding)` sets the number of levels and node times for a Hull-White tree and determines the mapping between dates and time for rate quoting.

`TimeSpec` is a structure specifying the time layout for `hwtree`. 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`.

## Examples

collapse all

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

```ValuationDate = 'Jan-1-2004'; Maturity = ['12-31-2004'; '12-31-2005'; '12-31-2006'; '12-31-2007']; Compounding = 1; TimeSpec = hwtimespec(ValuationDate, Maturity, Compounding)```
```TimeSpec = struct with fields: FinObj: 'HWTimeSpec' ValuationDate: 731947 Maturity: [4x1 double] Compounding: 1 Basis: 0 EndMonthRule: 1 ```