An interval version of Black–Scholes European option pricing model and its numerical solution

The Black–Scholes model, a powerful tool for valuation of equity options specially European equity options, is based on assumptions that are violated in some situations due to market realities. One of these cases is the instability of risk-free interest rates and the volatility of stock prices in th...

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Main Authors: S. Zangoei Zadeh, M. Azizian, M. Sarvari
Format: Article
Language:English
Published: Elsevier 2025-08-01
Series:Results in Applied Mathematics
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Online Access:http://www.sciencedirect.com/science/article/pii/S2590037425000767
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author S. Zangoei Zadeh
M. Azizian
M. Sarvari
author_facet S. Zangoei Zadeh
M. Azizian
M. Sarvari
author_sort S. Zangoei Zadeh
collection DOAJ
description The Black–Scholes model, a powerful tool for valuation of equity options specially European equity options, is based on assumptions that are violated in some situations due to market realities. One of these cases is the instability of risk-free interest rates and the volatility of stock prices in the Black–Scholes model.In this paper, in order to make the Black–Scholes model more in line with market realities, fixed parameters in the model, such as risk-free interest rates and stock price volatility, are considered with uncertainty. The obtained interval model is solved using discretization method and converting it into a minimization problem. Finally, The accuracy and efficiency of the method is tested by some numerical examples.
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spelling doaj-art-556d587ab065460eb34969efe9ecb7b42025-08-20T03:50:12ZengElsevierResults in Applied Mathematics2590-03742025-08-012710061210.1016/j.rinam.2025.100612An interval version of Black–Scholes European option pricing model and its numerical solutionS. Zangoei Zadeh0M. Azizian1M. Sarvari2Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, IranModeling in Health Research Center, Institute for Futures Studies in Health, Kerman University of Medical Sciences, Kerman, Iran; Department of General Education, Afzalipour School of Medicine, Kerman University of Medical Sciences, Kerman, Iran; Corresponding author.Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, IranThe Black–Scholes model, a powerful tool for valuation of equity options specially European equity options, is based on assumptions that are violated in some situations due to market realities. One of these cases is the instability of risk-free interest rates and the volatility of stock prices in the Black–Scholes model.In this paper, in order to make the Black–Scholes model more in line with market realities, fixed parameters in the model, such as risk-free interest rates and stock price volatility, are considered with uncertainty. The obtained interval model is solved using discretization method and converting it into a minimization problem. Finally, The accuracy and efficiency of the method is tested by some numerical examples.http://www.sciencedirect.com/science/article/pii/S2590037425000767Discretization methodBlack–Scholes modelInterval parameterOptimization
spellingShingle S. Zangoei Zadeh
M. Azizian
M. Sarvari
An interval version of Black–Scholes European option pricing model and its numerical solution
Results in Applied Mathematics
Discretization method
Black–Scholes model
Interval parameter
Optimization
title An interval version of Black–Scholes European option pricing model and its numerical solution
title_full An interval version of Black–Scholes European option pricing model and its numerical solution
title_fullStr An interval version of Black–Scholes European option pricing model and its numerical solution
title_full_unstemmed An interval version of Black–Scholes European option pricing model and its numerical solution
title_short An interval version of Black–Scholes European option pricing model and its numerical solution
title_sort interval version of black scholes european option pricing model and its numerical solution
topic Discretization method
Black–Scholes model
Interval parameter
Optimization
url http://www.sciencedirect.com/science/article/pii/S2590037425000767
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