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Business and Management., Economics
Accelerated Trinomial Trees (ATTs) are a derivatives pricing lattice method that circumvent the restrictive time step condition inherent in standard trinomial trees and explicit finite difference methods (FDMs) in which the time step must scale with the square of the spatial step. ATTs consist of L uniform supersteps each of which contains an inner lattice/trinomial tree with N non-uniform subtime steps. Similarly to implicit FDMs, the size of the superstep in ATTs, a function of N, are constrained primarily by accuracy demands. ATTs can price options up to N times faster than standard trinomial trees (explicit FDMs). ATTs can be interpreted as using risk neutral extended probabilities; extended in the sense that values can lie outside the range [0; 1] on the substep scale but aggregate to probabilities within the range [0; 1] on the superstep scale. Hence it is only strictly at the end of each superstep that a practically meaningful solution may be extracted from the tree. We demonstrate that ATTs with L supersteps are more efficient than competing implicit methods which use L time steps in pricing Black-Scholes American put options and 2-dimensional American basket options. Crucially this performance is achieved using an algorithm that requires only a modest modification of a standard trinomial tree. This is in contrast to implicit FDMs which may be relatively complex in their implementation.
Forthcoming in the Journal of Computational Finance