Vol.:(0123456789) Computational Economics https://doi.org/10.1007/s10614-020-10030-4 1 3 A Markov Decision Process Model for Optimal Trade of Options Using Statistical Data Ali Nasir 1  · Ambreen Khursheed 1  · Kazim Ali 1  · Faisal Mustafa 1 Accepted: 16 July 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020 Abstract This paper presents a Markov decision process model for calculating optimal deci- sion policy regarding the trade of options assuming the American options trading system. The proposed model incorporates the conditional probabilities of option prices given various features (or factors) that afect those prices. The generation of such probabilities requires statistical data of the feature values as well as the option price values. Given the availability of statistical data, the paper explains how the Markov decision process model can be formulated and solved using ‘value iteration’ to calculate optimal decision policy that maximizes the accumulative return. The model has been applied to the data of Microsoft and Coca Cola options. Analysis in the case study reveals how optimal decision policy can be interpreted and used for making sales or purchase decisions regarding various options at hand. The results indicate that there are signifcant advantages for the fnancial community including, but not limited to the investors who utilize our proposed approach. Keywords Markov chain · American options · Optimal policy 1 Introduction Options provide the ability to sell or purchase a principle asset at a specifc price (strike price) within a certain period (Jiang et al. 2019). One of the major challenges raised concerning the trading of options is to fnd the option’s ‘fair price’ (Ciosek and Silver 2015). This challenge can be dealt with by implementing an optimal exer- cise strategy that is the feedback rule that directs when to exercise an option at a strike price to maximize the accumulative return. Determination of such a feedback rule that works is not straight forward because many factors afect the dynamics of the strike price. For example, the fuctuations in strike price for a share of a com- pany, e.g., Microsoft may depend upon the variations in operational expenses of * Ali Nasir a.nasir@ucp.edu.pk 1 University of Central Punjab, Lahore, Pakistan