# Documentation

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# cvtree

Convert inverse-discount tree to interest-rate tree

## Syntax

```RateTree = cvtree(Tree) ```

## Arguments

 `Tree` Heath-Jarrow-Morton, Black-Derman-Toy, Hull-White, or Black-Karasinski tree structure using inverse-discount notation for forward rates.

## Description

`RateTree = cvtree(Tree)` converts a tree structure using inverse-discount notation to a tree structure using rate notation for forward rates.

## Examples

Convert a Hull-White tree using inverse-discount notation to a Hull-White tree displaying interest-rate notation.

```load deriv.mat; HWTree```
```HWTree = FinObj: 'HWFwdTree' VolSpec: [1x1 struct] TimeSpec: [1x1 struct] RateSpec: [1x1 struct] tObs: [0 1 2 3] dObs: [731947 732313 732678 733043] CFlowT: {[4x1 double] [3x1 double] [2x1 double] [4]} Probs: {[3x1 double] [3x3 double] [3x5 double]} Connect: {[2] [2 3 4] [2 2 3 4 4]} FwdTree: {1x4 cell} ```
`HWTree.FwdTree{1}`
```ans = 1.0279 ```
`HWTree.FwdTree{2}`
```ans = 1.0528 1.0356 1.0186```

Use `treeviewer` to display the path of interest rates expressed in inverse-discount notation.

`treeviewer(HWTree)`

Use `cvtree` to convert the inverse-discount notation to interest-rate notation.

`RTree = cvtree(HWTree)`
```RTree = FinObj: 'HWRateTree' VolSpec: [1x1 struct] TimeSpec: [1x1 struct] RateSpec: [1x1 struct] tObs: [0 1 2 3] dObs: [731947 732313 732678 733043] CFlowT: {[4x1 double] [3x1 double] [2x1 double] [4]} Probs: {[3x1 double] [3x3 double] [3x5 double]} Connect: {[2] [2 3 4] [2 2 3 4 4]} RateTree: {1x4 cell}```
`RTree.RateTree{1}`
```ans = 0.0275 ```
`RTree.RateTree{2}`
```ans = 0.0514 0.0349 0.0185```

Now use `treeviewer` to display the converted tree, showing the path of interest rates expressed as forward rates.