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PRICING OF HIGH‐DIMENSIONAL AMERICAN OPTIONS BY NEURAL NETWORKS
Author(s) -
Kohler Michael,
Krzyżak Adam,
Todorovic Nebojsa
Publication year - 2010
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.2010.00404.x
Subject(s) - valuation of options , consistency (knowledge bases) , econometrics , artificial neural network , constraint (computer aided design) , monte carlo method , economics , computer science , mathematics , statistics , artificial intelligence , geometry
Pricing of American options in discrete time is considered, where the option is allowed to be based on several underlyings. It is assumed that the price processes of the underlyings are given Markov processes. We use the Monte Carlo approach to generate artificial sample paths of these price processes, and then we use the least squares neural networks regression estimates to estimate from this data the so‐called continuation values, which are defined as mean values of the American options for given values of the underlyings at time t subject to the constraint that the options are not exercised at time t . Results concerning consistency and rate of convergence of the estimates are presented, and the pricing of American options is illustrated by simulated data.