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Finance

  

TreePlot

  

plot a binomial/trinomial tree

 

Calling Sequence

Parameters

Options

Description

Examples

Compatibility

Calling Sequence

TreePlot(tree, opts, plotopts)

Parameters

tree

-

binomial or trinomial tree data structure; tree

opts

-

(optional) equation(s) of the form option = value where option is scale; specify options for the TreePlot command

plotopts

-

(optional) options to be passed to the plots[display] command

Options

• 

scale = default, exponential, or logarithmic -- This option specifies whether the tree should be plotted using the exponential, logarithmic, or the default scale.

Description

• 

The TreePlot command plots the specified binomial/trinomial tree.

• 

The tree is displayed using the plots[display] command. All unprocessed arguments are interpreted as plot options and will be passed to the plots[display] command when the final plot data structure is generated.

Examples

with(Finance):

Construct a Cox-Ross-Rubinstein binomial tree.

S0 := 100;

S0100

(1)

r := 0.05;

r0.05

(2)

sigma := 0.3;

σ0.3

(3)

T := 3.0;

T3.0

(4)

N := 20;

N20

(5)

Su := exp(sigma*sqrt(T/N));

Su1.123208700

(6)

Sd := exp(-sigma*sqrt(T/N));

Sd0.8903064939

(7)

Pu := (exp(r*T/N)-Sd)/(Su-Sd);

Pu0.5033086765

(8)

Tree := BinomialTree(T, N, S0, Su, Pu, Sd);

Tree:=moduleend module

(9)

TreePlot(Tree, thickness = 2, axes = boxed, gridlines = true);

TreePlot(Tree, thickness = 2, axes = boxed, gridlines = true, scale = logarithmic);

Here is a Jarrow-Rudd tree approximating the same process.

Su := exp((r-sigma^2/2)*T/N+sigma*sqrt(T/N));

Su1.124051423

(10)

Sd := exp((r-sigma^2/2)*T/N-sigma*sqrt(T/N));

Sd0.8909744742

(11)

Pu := 0.5;

Pu0.5

(12)

Tree2 := BinomialTree(T, N, S0, Su, Pu, Sd);

Tree2:=moduleend module

(13)

TreePlot(Tree2, thickness = 2, axes = boxed, gridlines = true);

TreePlot(Tree2, thickness = 2, axes = boxed, gridlines = true, scale = logarithmic);

Here is a trinomial tree obtained by combining two steps of the Jarrow-Rudd tree.

Su := exp((r-sigma^2/2)*2*T/N+2*sigma*sqrt(T/N));

Su1.263491601

(14)

Sd := exp((r-sigma^2/2)*2*T/N-2*sigma*sqrt(T/N));

Sd0.7938355137

(15)

Pu := 0.25;

Pu0.25

(16)

Pd := 0.25;

Pd0.25

(17)

Tree3 := TrinomialTree(T, N/2, S0, Su, Pu, Sd, Pd);

Tree3:=moduleend module

(18)

TreePlot(Tree3, thickness = 2, axes = boxed, gridlines = true);

TreePlot(Tree3, thickness = 2, axes = boxed, gridlines = true, scale = logarithmic);

plots[display](TreePlot(Tree2, color = red), TreePlot(Tree3, transparency = 0.3), axes = boxed, thickness = 2, gridlines);

The following is a tree created for a Cox-Ingersoll-Ross short rate model.

The command to create the plot from the Plotting Guide is

M := CoxIngersollRossModel(ZeroCurve(0.03), 0.05, 0.5, 0.002, 0.1);

M:=moduleend module

(19)

T := ShortRateTree(M, 3, 15);

T:=moduleend module

(20)

TreePlot(T, axes = boxed, thickness = 3, gridlines = true, color = cyan .. blue);

Compatibility

• 

The Finance[TreePlot] command was introduced in Maple 15.

• 

For more information on Maple 15 changes, see Updates in Maple 15.

See Also

Finance[BinomialTree]

Finance[BlackScholesBinomialTree]

Finance[BlackScholesTrinomialTree]

Finance[GetDescendants]

Finance[GetProbabilities]

Finance[GetUnderlying]

Finance[ImpliedBinomialTree]

Finance[ImpliedTrinomialTree]

Finance[LatticeMethods]

Finance[SetProbabilities]

Finance[SetUnderlying]

Finance[StochasticProcesses]

Finance[TreePlot]

Finance[TrinomialTree]