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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)
```