A General Conformable Black–Scholes Equation for Option Pricing

Since the emergence of the Black–Scholes model (BSM) in the early 1970s, models for the pricing of financial options have been developed and evolved with mathematical tools that provide greater efficiency and accuracy in the valuation of these assets. In this research, we have used the generalized conformable derivatives associated with seven obtained conformable models with a closed-form solution that is similar to the traditional Black and Scholes. In addition, an empirical analysis was carried out to test the models with Mexican options contracts listed in 2023. Six foreign options were also tested, in particular three London options and three US options. With this sample, in addition to applying the seven generalized conformable models, we compared the results with the Heston model. We obtained much better results with the conformable models. Similarly, we decided to apply the seven conformable models to the data of the Morales et al. article, and we again determined that the conformable models greatly outperform the approximation of the Black, Scholes (BS), and Merton model with time-varying parameters and the basic Khalil conformable equation. In addition to the base sample, it was decided to test the strength of the seven generalized conformable models on 10 stock options that were out-sampled. In addition to the MSE results, for the sample of six options whose shares were traded in the London and New York stock markets, we tested the positivity and stability of the results. We plotted the values of the option contracts obtained by applying each of the seven generalized conformable models, the values of the contracts obtained by applying the traditional Heston model, and the market value of the contracts.