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
This paper has a twofold objective. The first aim is to present a comprehensive bibliographical analysis of journal articles and book chapters on fuzzy-random option pricing (FROP) over the WoS and SCOPUS databases. It follows PRISMA criteria and takes special care of developments in continuous time. Thus, we described the principal findings about the research streams, outlets and authors of this topic and lets us suggest further research. The second contribution is motivated by the fact that the bibliographical revision has identified a lack of developments on equilibrium models on the yield curve. This question motivates extending Vasicek’s yield curve equilibrium model to introduce fuzziness in the parameters that govern interest rate movements (speed of reversion, equilibrium short-term interest rate, and volatility). Likewise, this paper develops an empirical application on the term structure of fixed income public bonds with the highest credit rating in the Euro area.

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