Learn more about Financial Derivatives Toolbox

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.

cvtree - Convert inverse-discount tree to interest-rate tree

Syntax

Arguments

Description

Examples

See Also