An iterative algorithm to determine the number of time steps in path generation methods. (29th January 2016)

• Record Type: Journal Article
• Authors: Fan, Chenxi; Wu, Qingbiao
• Is Part Of: Mathematical methods in the applied sciences. Volume 39:Number 9(2016:Jun. 15)
• Page Start: 2182
• Page End: 2192
• Publication Date: 2016-01-29
• Subjects: Monte Carlo methods -- applications to actuarial sciences and financial mathematics -- quasi‐Monte Carlo methods -- Brownian bridge methods -- option pricing -- path generation methods; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.3632
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : 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.