The Adaptive Mesh Model: a new approach to efficient option pricing

Most derivative securities must be priced by numerical techniques. These mo dels contain "distribution error" and "nonlinearity error". The Adaptive Me sh Model (AMM) sharply reduces nonlinearity error by grafting one or more s mall sections of fine high-resolution lattice onto a tree with coarser time and price steps. Three different AMM structures are presented, one for pri cing ordinary options, one for barrier options, and one for computing delta and gamma efficiently. The AMM approach can be adapted to a wide variety o f contingent claims. For some common problems, accuracy increases by severa l orders of magnitude with no increase in execution time. (C) 1999 Elsevier Science S.A. All rights reserved.