The BlackScholesTrinomialTree($S_0$, 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($S_0$, r, d, v, T, N) command is similar except that in this case a uniform time grid with step size $\frac{T}{N}$ is used instead of G.

$\mathrm{with}\left(\mathrm{Finance}\right)\:$

$\mathrm{S0}≔100\:$

$r≔0.1\:$

$d≔0.05\:$

$v≔0.15\:$

$\mathrm{T0}≔\mathrm{BlackScholesTrinomialTree}\left(\mathrm{S0}\,r\,d\,v\,3\,10\right)\:$

$\mathrm{TreePlot}\left(\mathrm{T0}\,\mathrm{thickness}=2\,\mathrm{axes}=\mathrm{BOXED}\,\mathrm{gridlines}=\mathrm{true}\right)$

$\mathrm{TreePlot}\left(\mathrm{T0}\,\mathrm{thickness}=2\,\mathrm{axes}=\mathrm{BOXED}\,\mathrm{gridlines}=\mathrm{true}\,\mathrm{color}=\mathrm{red}\,\mathrm{scale}=\mathrm{logarithmic}\right)$

$\mathrm{GetUnderlying}\left(\mathrm{T0}\,2\,1\right)$

$112.3208700$

$\mathrm{GetUnderlying}\left(\mathrm{T0}\,2\,2\right)$

$99.99999998$

$\mathrm{GetProbabilities}\left(\mathrm{T0}\,1\,1\right)$

$\left[0.3027600400\,0.4949526183\,0.2022873417\right]$

$v≔\mathrm{LocalVolatilitySurface}\left(0.15-t\cdot 0.01\,t\,K\right)\:$

$\mathrm{T1}≔\mathrm{BlackScholesTrinomialTree}\left(\mathrm{S0}\,r\,d\,v\,3\,10\right)\:$

$\mathrm{TreePlot}\left(\mathrm{T1}\,\mathrm{thickness}=2\,\mathrm{axes}=\mathrm{BOXED}\,\mathrm{gridlines}=\mathrm{true}\right)$

$\mathrm{TreePlot}\left(\mathrm{T1}\,\mathrm{thickness}=2\,\mathrm{axes}=\mathrm{BOXED}\,\mathrm{gridlines}=\mathrm{true}\,\mathrm{color}=\mathrm{red}\,\mathrm{scale}=\mathrm{logarithmic}\right)$

$\mathrm{GetUnderlying}\left(\mathrm{T1}\,2\,1\right)$

$112.0601630$

$\mathrm{GetUnderlying}\left(\mathrm{T1}\,2\,2\right)$

$100.$

$\mathrm{GetUnderlying}\left(\mathrm{T1}\,2\,3\right)$

$89.23777849$

$\mathrm{GetProbabilities}\left(\mathrm{T1}\,1\,1\right)$

$\left[0.3027600400\,0.2022873417\,0.4949526183\right]$

$\mathrm{GetProbabilities}\left(\mathrm{T1}\,2\,2\right)$

$\left[0.3045379854\,0.2008387776\,0.4946232370\right]$

$\mathrm{P1}≔\mathrm{TreePlot}\left(\mathrm{T0}\,\mathrm{thickness}=2\,\mathrm{axes}=\mathrm{BOXED}\,\mathrm{gridlines}=\mathrm{true}\,\mathrm{color}=\mathrm{blue}\right)\:$

$\mathrm{P2}≔\mathrm{TreePlot}\left(\mathrm{T1}\,\mathrm{thickness}=2\,\mathrm{axes}=\mathrm{BOXED}\,\mathrm{gridlines}=\mathrm{true}\,\mathrm{color}=\mathrm{red}\right)\:$

$\mathrm{plots}\left[\mathrm{display}\right]\left(\mathrm{P1}\,\mathrm{P2}\right)$

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

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

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