A systematic review of the interactions of fuzzy set theory and option pricing

Identifier:  imarina:9294649

Handle: https://hdl.handle.net/20.500.11797/imarina9294649

Authors:  de Andrés-Sánchez J

Abstract:
This paper makes a systematic bibliographical analysis of the contributions of fuzzy set theory (FST) on option pricing to state principal mainstream focuses and exposes the basic questions of the analytical foundation of the reviewed approaches. It performs a bibliographical analysis of journal articles and book chapters by applying PRISMA guidelines to the SCOPUS and WoS databases. We subsequently present a structured report of principal findings about research fields, outlets and authors of this topic. Once we have identified the ways in which FST has contributed to option pricing, we outline basics about their mathematic and conceptual grounds. We have identified four main approaches to fuzzy option pricing (FOP). The mainstream of papers, based on the so-called fuzzy-random approach, consists of fuzzifying option pricing formulas under the hypothesis that the parameters governing the stochastic movement of prices are not crisp but fuzzy numbers. The second stream of the literature also superposes FST to conventional option pricing models, but this is made by means of the distortion of neutral to risk probabilities with fuzzy measures. The third approach, so called fuzzy pay-off, is devoted to evaluating real options and uses strictly fuzzy number concepts. The fourth approach embeds tools such as fuzzy controllers or fuzzy neural networks, taking advantage of their capability to obtain good numerical approximations to any function from empirical data. Principal outlets of FOP are journals devoted to fuzzy mathematics and soft computing, and the evolution of contributions throughout time reveals that it has become a well-stablished topic in fuzzy mathematics. The bibliographical research developed in this paper provides a wide panoramic perspective about what the principal mainstreams of FOP research are, what is done, and thus, future research lines are suggested.