  In an efficient stock market, the returns and their time-dependent volatility
are often jointly modeled by stochastic volatility models (SVMs). Over the last
few decades several SVMs have been proposed to adequately capture the defining
features of the relationship between the return and its volatility. Among one
of the earliest SVM, Taylor (1982) proposed a hierarchical model, where the
current return is a function of the current latent volatility, which is further
modeled as an auto-regressive process. In an attempt to make the SVMs more
appropriate for complex realistic market behavior, a leverage parameter was
introduced in the Taylor SVM, which however led to the violation of the
efficient market hypothesis (EMH, a necessary mean-zero condition for the
return distribution that prevents arbitrage possibilities). Subsequently, a
host of alternative SVMs had been developed and are currently in use. In this
paper, we propose mean-corrections for several generalizations of Taylor SVM
that capture the complex market behavior as well as satisfy EMH. We also
establish a few theoretical results to characterize the key desirable features
of these models, and present comparison with other popular competitors.
Furthermore, four real-life examples (Oil price, CITI bank stock price,
Euro-USD rate, and S&P 500 index returns) have been used to demonstrate the
performance of this new class of SVMs.
