Fuzzy Random Option Pricing in Continuous Time: A Systematic Review and an Extension of Vasicek’s Equilibrium Model of the Term Structure

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Abstract
Fuzzy random option pricing in continuous time (FROPCT) has emerged as an active research field over the past two decades; thus, there is a need for a comprehensive review that provides a broad perspective on the literature and identifies research gaps. In this regard, we conducted a structure review of the literature by using the WoS and SCOPUS databases while following the PRISMA criteria. With this review, we outline the primary research streams, publication outlets, and notable authors in this domain. Furthermore, the literature review revealed a lack of advancements for the equilibrium models of the yield curve. This finding serves as a primary motivation for the second contribution of this paper, which involves an extension of Vasicek’s yield curve equilibrium model. Specifically, we introduce the existence of fuzzy uncertainty in the parameters governing interest rate movements, including the speed of reversion, equilibrium short-term interest rate, and volatility. By incorporating fuzzy uncertainty, we enhance the model’s ability to capture the complexities of real-world interest rate dynamics. Moreover, this paper presents an empirical application of the proposed extension to the term structure of fixed-income public bonds in European Union. The empirical analysis suggests the suitability of the proposed extension of Vasicek’s model for practical applications.

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