create a recombining trinomial tree approximating a Black-Scholes process

Finance[BlackScholesTrinomialTree] - create a recombining trinomial tree approximating a Black-Scholes process

	Calling Sequence
	BlackScholesTrinomialTree(, r, d, v, T, N) BlackScholesTrinomialTree(, r, d, v, G)

Parameters

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

Compatibility

•	The Finance[BlackScholesTrinomialTree] command was introduced in Maple 15.

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

Examples

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

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

Inspect the tree.

(1)

(2)

(3)

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

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

Inspect the second tree.

(4)

(5)

(6)

(7)

(8)

Compare the two trees.

	See Also
	Finance[BinomialTree], Finance[BlackScholesBinomialTree], Finance[GetDescendants], Finance[GetProbabilities], Finance[GetUnderlying], Finance[ImpliedBinomialTree], Finance[ImpliedTrinomialTree], Finance[LatticeMethods], Finance[MultinomialTree], Finance[SetDescendants], Finance[SetProbabilities], Finance[SetUnderlying], Finance[StochasticProcesses], Finance[TreePlot], Finance[TrinomialTree]