# Documentation

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# hjmtree

Construct Heath-Jarrow-Morton interest-rate tree

## Syntax

```HJMTree = hjmtree(VolSpec,RateSpec,TimeSpec) ```

## Arguments

 `VolSpec` Volatility process specification. Sets the number of factors and the rules for computing the volatility $\sigma \left(t,T\right)$ for each factor. See `hjmvolspec` for information on the volatility process. `RateSpec` Interest-rate specification for the initial rate curve. See `intenvset` for information on declaring an interest-rate variable. `TimeSpec` Tree time layout specification. Defines the observation dates of the HJM tree and the compounding rule for date to time mapping and price-yield formulas. See `hjmtimespec` for information on the tree structure.

## Description

`HJMTree = hjmtree(VolSpec,RateSpec,TimeSpec)` creates a structure containing time and forward-rate information on a bushy tree.

## Examples

Using the data provided, create an HJM volatility specification (`VolSpec`), rate specification (`RateSpec`), and tree time layout specification (`TimeSpec`). Then use these specifications to create an HJM tree using `hjmtree`.

```Compounding = 1; ValuationDate = '01-01-2000'; StartDate = ['01-01-2000'; '01-01-2001'; '01-01-2002'; '01-01-2003'; '01-01-2004']; EndDates = ['01-01-2001'; '01-01-2002'; '01-01-2003'; '01-01-2004'; '01-01-2005']; Rates = [.1; .11; .12; .125; .13]; Volatility = [.2; .19; .18; .17; .16]; CurveTerm = [1; 2; 3; 4; 5]; HJMVolSpec = hjmvolspec('Stationary', Volatility , CurveTerm); RateSpec = intenvset('Compounding', Compounding,... 'ValuationDate', ValuationDate,... 'StartDates', StartDate,... 'EndDates', EndDates,... 'Rates', Rates); HJMTimeSpec = hjmtimespec(ValuationDate, EndDates, Compounding); HJMTree = hjmtree(HJMVolSpec, RateSpec, HJMTimeSpec)```
```HJMTree = FinObj: 'HJMFwdTree' VolSpec: [1x1 struct] TimeSpec: [1x1 struct] RateSpec: [1x1 struct] tObs: [0 1 2 3 4] dObs: [730486 730852 731217 731582 731947] TFwd: {[5x1 double] [4x1 double] [3x1 double] [2x1 double] [4]} CFlowT: {[5x1 double] [4x1 double] [3x1 double] [2x1 double] [5]} FwdTree: {[5x1 double] [4x1x2 double] [3x2x2 double] [2x4x2 double] [1x8x2 double]}```

Use `treeviewer` to observe the tree you have created.

```treeviewer(HJMTree) ```