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Low-Discrepancy Sequences: Monte Carlo Simulation of Option Prices

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Intellectual Contribution by Alan Jung

Contribution Title

Low-Discrepancy Sequences: Monte Carlo Simulation of Option Prices

Publication

The Journal of Derivatives

Co-author

S. Galanti

Year

1997

Description

This paper examines the use of Monte Carlo simulation with low discrepancy sequences (or quasi-Monte Carlo) for numerically valuing complex derivative contracts. Comparisons are made with the more traditional Monte Carlo method using random sequences. Unlike the latter, low discrepancy sequences (or quasi-random) are deterministic. Recent research has hinted that low discrepancy sequences improve the rate of convergence of the Monte Carlo simulation. However depending on the number of discrete time intervals involved and smoothness of the problem, the results to date are inconclusive and even contradictory. This paper attempts to clarify and to shed some light on the use of low discrepancy sequences. In addition to an in-depth discussion on the implementation of low discrepancy sequences, several examples using complex path dependent options are provided. These include, barrier, Asian, and lookback options.

Complete Citation

Low-Discrepancy Sequences: Monte Carlo Simulation of Option Prices, co-authored with S. Galanti. The Journal of Derivatives, Fall 1997, Vol. 5, No. 1.

Website

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