Quasi-Montecarlo Methods for Evaluating Asian Options
by
Maria Giuseppina Bruno
Dipartimento di Matematica per le Decisioni Economiche, Finanziarie ed Assicurative, Facoltà di Economia, Università degli Studi di Roma "La Sapienza", Italy

The evaluation of the most recent financial instruments generally leads to multidimensional models which, even if provided with analytical expressions or solutions, need the employment of some numerical calculation procedures.

The financial literature (but not only this one) has recently shown a renewed interest in the numerical procedures based on the Montecarlo method for the greatest flexibility revealed by this method (with respect to the others such as the finite difference method and the lattice-type ones) in managing high dimentional problems. In the present paper, we illustrate an alternative technique for calculating multiple integrals, the so called Quasi-Montecarlo method, and we apply it for pricing asian options. The idea underlying the Quasi-Montecarlo method is very simple: to replace the random number sequences of the traditional Montecarlo method - which, even those sampled by more recent generators, show a general tendency to cluster into some space regions - with deterministic sequences of points generated so as to ensure a certain uniformity degree or, better, a given level of discrepancy.

It is suffice to construct deterministic sequences with a lower discrepancy than the expected one of a random sequence in order to improve the efficiency of the traditional Montecarlo method. Sequences of this type are called "low discrepancy sequences".

In this paper, we use the low discrepancy sequences, in particular the Halton sequence (1960) and the Sobol one (1967), to evaluate both a "geometric mean" asian option and an "arithmetic mean" one. In both cases, the two sequences used accelerate the convergence process to the solution and improve the accuracy of the results of the traditional Montecarlo method.

Date received: February 1, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacq-02.