PRICING OF HIGH-DIMENSIONAL AMERICAN OPTIONS BY NEURAL NETWORKS

Michael Köhler · Adam Krzyżak · Neboǰsa Todorović

92 citations0/0 files storedMathematical Finance

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Stochastic processes and financial applications Neural Networks and Applications Adaptive Dynamic Programming Control

Abstract

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.

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References

2003Monte Carlo Methods in Financial Engineering 2001Valuing American Options by Simulation: A Simple Least-Squares Approach 2001Regression methods for pricing complex American-style options 2002Monte Carlo valuation of American options 1999Applications of Malliavin calculus to Monte Carlo methods in finance 1996Valuation of the early-exercise price for options using simulations and nonparametric regression 2004MaxWeight scheduling in a generalized switch: State space collapse and workload minimization in heavy traffic 2004Pricing American Options: A Duality Approach

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