Affiliations: Department of Business Management, Social and Business Research Laboratory, Rovira i Virgili University, Avinguda Universitat, Reus, Spain
Correspondence:
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Corresponding author. Jorge de Andrés-Sánchez, Department of Business Management, Social and Business Research Laboratory, Rovira i Virgili University, Avinguda Universitat, 1 43204 Reus, Spain. E-mail: [email protected].
Abstract: The main objective of this paper is assessing the empirical performance of fuzzy extension to Black-Scholes option pricing formula (FBS). Concretely we evaluate the goodness of the FBS predictions for traded prices of options on the Spanish stock index IBEX35 during March 2017. We firstly propose a procedure to fit, from real data, the fuzzy parameters to implement FBS in stock options: price of the subjacent asset, free discount rate and stock volatility. Subsequently we evaluate the capability of FBS to include actual traded prices and whether this capability depends on option moneyness and expiration date. We find that FBS fits quite well actual traded prices. However, generally most representative market prices (closing and medium) are not better fitted than those more extreme (minimum and maximum). We have also check that the goodness of the FBS predictions often depends on the moneyness grade and the expiration date of options.
Keywords: Fuzzy numbers, fuzzy regression, expected interval of fuzzy numbers, finance, option pricing, Black-Scholes formula
