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An iterative algorithm to determine the number of time steps in path generation methods
Author(s) -
Fan Chenxi,
Wu Qingbiao
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3632
Subject(s) - discretization , mathematics , brownian bridge , mathematical optimization , convergence (economics) , path (computing) , valuation (finance) , monte carlo method , interval (graph theory) , valuation of options , context (archaeology) , algorithm , iterative method , brownian motion , computer science , mathematical analysis , finance , statistics , programming language , paleontology , combinatorics , economics , econometrics , biology , economic growth
The construction of Brownian motion paths is the most important part of simulation methods for option pricing. Particularly, there are several commonly used path generation methods in the context of quasi‐Monte Carlo, including the standard method and the Brownian bridge method. To apply each method, an inevitable step is to decide how many points are used to discretize the time interval. This paper implements an iterative algorithm to select a suitable number of time steps by successively adding discretization nodes until a specific convergence criterion is met. Numerical results with this algorithm are presented in the valuation of Asian options. Copyright © 2016 John Wiley & Sons, Ltd.