ORIGINAL ARTICLE Optimized radial basis function neural network for improving approximate dynamic programming in pricing high dimensional options Ehsan Hajizadeh 1 • Masoud Mahootchi 1 Received: 18 May 2016 / Accepted: 18 December 2016 Ó The Natural Computing Applications Forum 2016 Abstract Pricing American basket option is one of the essential problems in quantitative finance. The complexity of this type of option has motivated many practitioners and researchers to develop simulation-based methods. In this paper, we develop an optimized radial basis function neural network (RBFNN), which is optimally tuned by the particle swarm optimization algorithm to enhance the efficiency and accuracy of approximate dynamic programming (ADP) for pricing the American basket option. Additionally, for the scenario generation, a simulation-based technique using a copula-GARCH method and Extreme Value Theory is performed to tackle the nonlinearity of dependencies between variables. The prices obtained through the pro- posed approach compared with those ones achieved from pure RBFNN and ADP in different situations. This is also illustrated that the obtained prices of American basket option can outperform the results obtained through the RBFNN and ADP approaches in terms of the predefined fitness measures. Keywords Radial basis function neural network  Approximate dynamic programming  Particle swarm optimization algorithm  American basket options 1 Introduction A new recently developed type of options entitled high dimensional or multi-asset (basket) options are used in some real-world applications. These contracts can play a significant role in reducing the risk of investors and prac- titioners in the financial markets. Basket option, which could be considered as an exotic option, includes a group of securities, commodities or currencies as an underlying asset where its price and its numbers of tradable assets are officially determined at the time of issuing that option. Obviously, the value of assets or portfolio in the basket options influences the option payoff. The main advantage of having a basket option would be that it is cheaper than a portfolio including single vanilla options. Furthermore, the risk management of a portfolio having a basket option would be more com- fortable than a portfolio, including single vanilla options because of their different early exercise time. Finally, the transaction cost of trading a basket would be remarkably lower as a buyer/seller only pays a single transaction cost for trading the respective basket option, while he/she should pay multiple transaction costs for trading vanilla options. There are two main types of basket options in real-world applications in terms of the expiry time of the option: American and European basket options. Pricing and valu- ation of the American option, even the single-asset option, is a hard problem in a quantitative finance [1]. To the best of our knowledge, the closed-form solution might not be found for pricing/valuation of American options. As this type of option is practically important in the real-world problems, there is much interest in developing approxi- mations and numerical approaches for pricing/valuation of this type of option [2–4]. & Masoud Mahootchi mmahootchi@aut.ac.ir Ehsan Hajizadeh ehsanhajizadeh@aut.ac.ir 1 Department of Industrial Engineering and Management Systems, Amirkabir University of Technology (Tehran Polytechnics), 424 Hafez Ave., Tehran 15916-34311, Iran 123 Neural Comput & Applic DOI 10.1007/s00521-016-2802-x