The Volatility Index (VIX) is a real-time index that has been used as the first measure to quantify market expectations for volatility, which affects the financial market as a main actor of the overall economy that is sensitive to the environmental and social aspects of investors and companies. The VIX is calculated using option prices for the S&P 500 Index (SPX) and is expressed as a percentage. Taking into account that VIX only shows the implicit volatility of the S&P 500 for the next 30 days, the authors develop a model for a near-optimal state trying to avoid uncertainty and insufficient accuracy. The researchers are trying to make a contribution to the theory of socially responsible portfolio management. The developed approach allows potential investments to make decisions regarding such important topics as ethical investing, performance analysis, as well as sustainable investment strategies. The approach of this research allows to use deep probabilistic convolutional neural networks based on conditional variance as a linear function of errors with the aim of estimating and predicting the VIX. For this purpose, the use of technical indicators and economic indexes such as Chicago Board Options Exchange (CBOE) VIX and S&P 500 is considered. The results of estimating and predicting the VIX with the proposed method indicate high precision and create a certainty in modeling to achieve the goals.
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