Automatic differentiation (AD) is a popular method of computing exact derivatives in complex sensitivity analyses and optimisation routines that lack closed-form solutions, posing challenges for analytical and numerical alternatives. This paper introduces a vectorised version of AD that builds...

Variations of the binomial tree model are reviewed and extensions to the two most efficient trees studied in a recent literature are proposed. Tian's modified tree is extended to a more general class of tree, and the third order tree is extended to the seventh order tree. Analysis of the error...