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Finance

  

BlackScholesTrinomialTree

  

create a recombining trinomial tree approximating a Black-Scholes process

 

Calling Sequence

Parameters

Description

Examples

References

Compatibility

Calling Sequence

BlackScholesTrinomialTree(S0, r, d, v, T, N)

BlackScholesTrinomialTree(S0, r, d, v, G)

Parameters

S0

-

positive constant; the inital value of the underlying asset

r

-

non-negative constant or yield term structure; annual risk-free rate function for the underlying asset

d

-

non-negative constant or yield term structure; annual dividend rate function for the underlying asset

v

-

non-negative constant or a volatility term structure; local volatility

T

-

positive constant; time to maturity date (in years)

N

-

positive integer; number of steps

G

-

the number of steps used in the trinomial tree

Description

• 

The BlackScholesTrinomialTree(S0, r, d, v, G) command returns a trinomial tree approximating a Black-Scholes process with the specified parameters. Each step of this tree is obtained by combining two steps of the corresponding binomial tree (see Finance[BlackScholesBinomialTree] for more details).

• 

The BlackScholesTrinomialTree(S0, r, d, v, T, N) command is similar except that in this case a uniform time grid with step size TN is used instead of G.

Examples

withFinance:

First you construct a trinomial tree for a Black-Scholes process with constant drift and volatility.

S0100:

r0.1:

d0.05:

v0.15:

T0BlackScholesTrinomialTreeS0,r,d,v,3,10:

Here are two different views of the same tree; the first one uses the standard scale, the second one uses the logarithmic scale.

TreePlotT0,thickness=2,axes=BOXED,gridlines=true

TreePlotT0,thickness=2,axes=BOXED,gridlines=true,color=red,scale=logarithmic

Inspect the tree.

GetUnderlyingT0,2,1

112.3208700

(1)

GetUnderlyingT0,2,2

99.99999998

(2)

GetProbabilitiesT0,1,1

0.3027600400,0.4949526183,0.2022873417

(3)

Here is an example of a Black-Scholes process with time-dependent drift and volatility.

vLocalVolatilitySurface0.15t0.01,t,K:

T1BlackScholesTrinomialTreeS0,r,d,v,3,10:

Again, you have two different views of the same tree. The first one uses the standard scale, the second one uses the logarithmic scale.

TreePlotT1,thickness=2,axes=BOXED,gridlines=true

TreePlotT1,thickness=2,axes=BOXED,gridlines=true,color=red,scale=logarithmic

Inspect the second tree.

GetUnderlyingT1,2,1

112.0601630

(4)

GetUnderlyingT1,2,2

100.

(5)

GetUnderlyingT1,2,3

89.23777849

(6)

GetProbabilitiesT1,1,1

0.3027600400,0.2022873417,0.4949526183

(7)

GetProbabilitiesT1,2,2

0.3045379854,0.2008387776,0.4946232370

(8)

Compare the two trees.

P1TreePlotT0,thickness=2,axes=BOXED,gridlines=true,color=blue:

P2TreePlotT1,thickness=2,axes=BOXED,gridlines=true,color=red:

plots[display]P1,P2

References

  

Hull, J., Options, Futures, and Other Derivatives, 5th. edition. Upper Saddle River, New Jersey: Prentice Hall, 2003.

Compatibility

• 

The Finance[BlackScholesTrinomialTree] 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[GetDescendants]

Finance[GetProbabilities]

Finance[GetUnderlying]

Finance[ImpliedBinomialTree]

Finance[ImpliedTrinomialTree]

Finance[LatticeMethods]

Finance[SetProbabilities]

Finance[SetUnderlying]

Finance[StochasticProcesses]

Finance[TreePlot]

Finance[TrinomialTree]

 


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