A Conformable Heston option pricing model

In the aftermath of the proposal of the Black-Scholes-Merton model in 1973, a considerable number of research groups issued substantial criticisms of the model. An initial observation revealed a discontinuity in stock returns, a phenomenon referred to as the jump diffusion model. A multitude of efforts have been made to develop alternative models that can adequately capture the leptokurtic nature of returns, as evidenced by data observed in financial markets. A substantial proportion of these models presuppose that volatility manifests as a stochastic process; a notable illustration of this is the Heston model, which was proposed in 1993. Over the course of several decades, researchers have proposed a variety of modifications to the BS model. Among these modifications, there have been proposals to incorporate fractional and conformable derivatives into the solution of the partial differential equation. In contrast, the extant literature concerning the modification of the traditional Heston model is limited. Consequently, the present study exclusively focuses on the traditional Heston model and its modifications, specifically the Heston model augmented by He and Zhu (HZ), as well as the novel model developed within this research. The incorporation of conformable derivatives from Khalil et al. and Anderson et al. into this model has yielded the Conformable Heston model, a derivative that significantly outperforms the approximation of European call options’ price. Furthermore, an empirical analysis was conducted, encompassing two base samples and a third out-of-sample. The findings of our study suggest that the Heston Conformable model exhibits a significantly superior ability to approximate the market price of the contracts in the three samples when compared with the traditional Heston model and with the model proposed by HZ. In the empirical analysis section, the stability and positivity of the Conformable Heston model on Mexican stock contracts was tested. It has been demonstrated that the magnitude of error is negligible. This is substantiated by the observation that the median value is equivalent to 0.00, the maximum absolute error is approximately 0.33, and the number of observations that fall outside the 95th percentile is minimal. Furthermore, in Section 5, we employed the Diebold-Mariano test with the intention of validating the results. To this end, a comparison was made between the He and Zhu model and the Heston Conformable model. To this end, we employed samples of option contracts from international companies, in addition to out-of-sample data. The findings of this investigation indicate that the General Conformable model is to be preferred for every maturity date, as evidenced by the results of the Diebold-Mariano test, with significance levels tending towards 0.99. It is important to note, however, that these significance levels must be interpreted with caution, particularly in the context of maturities for which observations are scarce. In summary, the Conformable Heston model, and the conformable parameters are positive and stable, and the price of the model that meets the criteria is in close agreement with the prevailing market price. A further investigation was conducted by examining the option contracts of international companies, which resulted in the calculation of the mean square error of implied volatility. This analysis also yielded the conclusion that the Conformable Heston model provides the lowest value.