Soft Computing

, Volume 23, Issue 24, pp 13351–13374 | Cite as

Option pricing and the Greeks under Gaussian fuzzy environments

  • Hong-Ming ChenEmail author
  • Cheng-Feng Hu
  • Wei-Chang Yeh
Methodologies and Application


This work considers pricing European call options and the study of Greek letters of options under a fuzzy environment. In the past work, stock prices are usually represented by symmetric triangular fuzzy numbers for the computational convenience while pricing options with uncertainty. It might not be enough to explain the stochastic nature of the underlining price in the option pricing formula. This work considers developing the fuzzy pattern of European call option under the assumption of the stock return being a Gaussian fuzzy number. The study of Greeks for the sensitivity analysis of the fuzzy call option price with respect to the change in the pricing variables is included. The empirical analysis and comparison on the fuzzy European option pricing based on the real market data of SPX options at CBOE are provided. Our results show that the fuzzy options are more close to the theoretical options derived from the Black–Scholes formula while employing Gaussian fuzzy stock returns for pricing European call options.


Gaussian fuzzy number Options Greeks SPX Optimization 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Applied MathematicsTunghai UniversityTaichungTaiwan
  2. 2.Department of Applied MathematicsNational Chiayi UniversityChiayi CityTaiwan
  3. 3.Department of Industrial Engineering and Engineering ManagementNational Tsing Hua UniversityHsinchuTaiwan

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