# A New Class of Discrete-time Stochastic Volatility Model with Correlated Errors

## TL;DR

This paper introduces a new class of discrete-time stochastic volatility models that incorporate mean-corrections to better capture market behavior while satisfying the efficient market hypothesis, supported by theoretical analysis and real-world data examples.

## Contribution

It proposes mean-corrected stochastic volatility models that address limitations of previous models and demonstrate improved performance on real market data.

## Key findings

- Models satisfy EMH and capture complex market dynamics
- Theoretical properties are established for the new models
- Empirical tests show improved fit to real data

## Abstract

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.