Calibration of European option pricing model in uncertain environment: Valuation of uncertainty implied volatility

• Published in: Journal of computational and applied mathematics 2024-09, Vol.447, p.115890, Article 115890
• Main Authors: Gao, Jinwu, Jia, Ruru, Noorani, Idin, Mehrdoust, Farshid
• Format: Article
• Language: English
• Subjects: Calibration; Implied volatility; Option pricing; Uncertainty theory
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2024.115890

Uncertain differential equations have been widely used in modeling financial markets, and option pricing formulae have been obtained by employing these equations. However, according to the existing literature, the parameter estimation of the option pricing model driven by the uncertain differential equation has not been evaluated so far, and the parameters have been assumed to be arbitrary numbers for such problems. Based on the mentioned gap, this study presents an approach for parameter estimation of European option pricing model in the uncertain environment for the first time. For this purpose, some of the most common uncertain models are considered, and the corresponding empirical examples are presented. Since implied volatility as an instrument provides traders a range of prices that securities change among them, this study evaluates the implied volatility of the European option under the geometric Liu process for the first time. Empirical comparison for both in sample and out of sample dataset based on the uncertainty framework and Black–Scholes model demonstrates that the uncertain models are more accurate for evaluating the European option prices and the implied volatilities.