Why didn’t I know this already?

Since the binomial tree pricing is a backward induction process, the tree resolution can be adjusted locally to improve the accuracy of the option price. The tree can be divided over the time axis and each sub-tree can have a different resolution. This is like using varying time steps in the finite difference method.

example

For example, the figure above shows how one could increase the resolution of the tree between time step 8 and 10 by factor of 3.

  • From time step 10 to 8: use the black tree
  • At time step 8, sample the option value at the red nodes
  • From time step 8 to 0: use the red tree