# cvtree

Convert inverse-discount tree to interest-rate tree

## Syntax

``RateTree = cvtree(Tree)``

## Description

example

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

## Examples

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

```load deriv.mat; HWTree```
```HWTree = struct with fields: 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: {[1.0279] [1.0528 1.0356 1.0186] [1x5 double] [1x5 double]} ```
`HWTree.FwdTree{1}`
```ans = 1.0279 ```
`HWTree.FwdTree{2}`
```ans = 1×3 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 = struct with fields: 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: {[0.0275] [0.0514 0.0349 0.0185] [1x5 double] [1x5 double]} ```
`RTree.RateTree{1}`
```ans = 0.0275 ```
`RTree.RateTree{2}`
```ans = 1×3 0.0514 0.0349 0.0185 ```

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

`treeviewer(RTree)`

## Input Arguments

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Tree structure, specified by Heath-Jarrow-Morton, Black-Derman-Toy, Hull-White, Black-Karasinski, or Cox-Ingersoll-Ross tree structure that uses inverse-discount notation for forward rates.

Data Types: `struct`

## Output Arguments

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Tree structure using rate notation for forward rates, returned as a tree structure.