A derivative valuation method which was developed by Figlewski and Gao (1999). It is a very flexible approach that helps enhance efficiency in trinomial trees to a great extent.
It uses coarse time and price steps in most the tree, but small sections of finer mesh are built up to improve resolution in critical areas. In other words, the model is based on a lattice-like numerical process in which regions of high resolution are embedded in critical regions of a lower resolution mesh. The model explains how the so-called truncation error arises and presents a new approach that sharply reduces it by grafting one or more small sections of fine high-resolution lattice onto a tree with coarser time and price steps. Three different structures of the adaptive mesh model (AMM) were introduced: one for pricing vanilla options, one for barrier options, and one for calculating delta and gamma efficiently. The AMM approach can be extended to cater to a wide variety of contingent claims, allowing fro significantly higher efficiency with very trivial increase in computational effort.
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