# Documentation

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# hwvolspec

Specify Hull-White interest-rate volatility process

## Syntax

```Volspec = hwvolspec(ValuationDate,VolDates,VolCurve,AlphaDates,AlphaCurve,InterpMethod) ```

## Arguments

 `ValuationDate` Scalar value representing the observation date of the investment horizon. `VolDates` Number of points (`NPOINTS`-by-`1`) vector of yield volatility end dates. `VolCurve` `NPOINTS`-by-`1` vector or scalar of yield volatility values in decimal form. The term structure of `VolCurve` is the yield volatility represented by the value of the volatility of the yield from time `t` = 0 to time `t` + i, where i is any point within the volatility curve. `AlphaDates` `MPOINTS`-by-`1` vector of mean reversion end dates. `AlphaCurve` `MPOINTS`-by-`1` vector of positive mean reversion values or scalar in decimal form. `InterpMethod` (Optional) Interpolation method. Default is `'linear'`. See `interp1` for more information.

### Note

The number of points in `VolCurve` and `AlphaCurve` do not have to be the same.

## Description

`Volspec = hwvolspec(ValuationDate,VolDates,VolCurve,AlphaDates,AlphaCurve,InterpMethod)` creates a structure specifying the volatility for `hwtree`.

The volatility process is such that the variance of r(t + dt) - r(t) is defined as follows: ```V = (Volatility.^2 .* (1 - exp(-2*Alpha .* dt))) ./ (2 * Alpha)```. For more information on using Hull-White interest rate trees, see Hull-White (HW) and Black-Karasinski (BK) Modeling.

## Examples

collapse all

This example shows how to create a Hull-White volatility specification (`VolSpec`) using the following data.

```ValuationDate = '01-01-2004'; StartDate = ValuationDate; VolDates = ['12-31-2004'; '12-31-2005'; '12-31-2006'; '12-31-2007']; VolCurve = 0.01; AlphaDates = '01-01-2008'; AlphaCurve = 0.1; HWVolSpec = hwvolspec(ValuationDate, VolDates, VolCurve,... AlphaDates, AlphaCurve)```
```HWVolSpec = struct with fields: FinObj: 'HWVolSpec' ValuationDate: 731947 VolDates: [4x1 double] VolCurve: [4x1 double] AlphaCurve: 0.1000 AlphaDates: 733408 VolInterpMethod: 'linear' ```