Stochastic approximation methods for American type options

Dmitrii Silvestrov and Yanxiong Li

Communications in Statistics - Theory and Methods, 2016, vol. 45, issue 6, 1607-1631

Abstract: Stochastic approximation methods for rewards of American type options are studied. Pay-off functions are non random possibly discontinuous functions or random càdlàg functions. General conditions of convergence for binomial, trinomial, and skeleton reward approximations are formulated. Underlying log-price processes are assumed to be random walks. These processes are approximated by log-price processes given by random walks with discrete distributions of jumps. Backward recurrence algorithms for computing of reward functions for approximating log-price processes are given. These approximation algorithms and their rates of convergence are numerically tested for log-price processes represented by Gaussian and compound Gaussian random walks. Comparison of the above approximation methods is made.

Date: 2016
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DOI: 10.1080/03610926.2014.915046

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