The skew processes have recently received much attention, owing to their capacity to describe controlled dynamics. In this paper, we employ the skew geometric Brownian motion (SGBM) to depict nine major stock index markets. The skew process not only shows us where the “support” and “resistance” levels are, but also how strong the force is. However, the densities of the skew processes make it challenging to estimate the parameters in a convenient manner. For the sake of overcoming this challenge, we adopt a Bayesian approach, which plays an important role in allowing us to estimate the parameters by conditional probability densities without having to evaluate complex integrals. Furthermore, we also propose the likelihood ratio tests and significance tests for the skew probability. In the empirical study, our findings reveal that skew phenomenon exists in the global stock markets and that the SGBM model works better than the traditional GBM model, as well as performing competitively, compared to the GBM-jump model (GBM-J) and Markov regime switching GBM model (GBM-MRS). In addition, we explore the possible reasons behind the skew phenomenon in stock markets, the price clustering phenomenon and herd behaviors can help to explain the skew phenomenon.

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In this study, we consider option pricing under a Markov regime-switching GARCH-jump (RS-GARCH-jump) model. More specifically, we derive the risk neutral dynamics and propose a lattice algorithm to price European and American options in this framework. We also provide a method of parameter estimation in our RS-GARCH-jump setting using historical data on the underlying time series. To measure the pricing performance of the proposed algorithm, we investigate the convergence of the tree-based results to the true option values and show that this algorithm exhibits good convergence. By comparing the pricing results of RS-GARCH-jump model with regime-switching GARCH (RS-GARCH) model, GARCH-jump model, GARCH model, Black–Scholes (BS) model, and Regime-Switching (RS) model, we show that accommodating jump effect and regime switching substantially changes the option prices. The empirical results also show that the RS-GARCH-jump model performs well in explaining option prices and confirm the importance of allowing for both jump components and regime switching.

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