A Systematic Overview of Fuzzy Random Option Pricing in Discrete Time and a Binomial Extension to Temporal Structure of Interest Rates

Abstract

This paper makes a bibliographical analysis of fuzzy set theory (FST) contributions to option pricing with a fuzzy-random approach with detailed attention to those based in the binomial lattice. Likewise, we extend the fuzzy-random approach to yield curve binomial modelling. The bibliographical analysis was performed by applying PRISMA guidelines in the SCOPUS and WoS databases. We first present a structured report of papers about the more general fuzzy-random option pricing (FROP) field and identify principal outlets. Within FROP, we focus on the more concrete fuzzy random discrete time option pricing (FROPDT) in binomial and trinomial lattices, which is developed in greater detail. We detect that this groundwork has been extended to price options on stocks, stock indexes and real options, but no work has been done in the field of the term structure of interest rates and fixed income securities. Thus, we propose a fuzzy extension of the Ho-Lee model that we apply to the European interbank market and to price caplets.