Andrés Mora-Valencia

The architecture of Bollinger Bands significantly contributes to informed decision-making in financial markets. This paper introduces two new techniques that incorporate Edgeworth correction for confidence intervals in classical Bollinger Bands (BB). In this regard, skewness and kurtosis are included to create Adjusted Bollinger Bands (ABB) with the aim of implementing a contrarian trading strategy. The performance of these techniques was evaluated on the 30 stocks of the Dow Jones Industrial Average Index and compared with performance metrics grouped by returns, risk, and riskreturn measures, including the Sharpe ratio, Omega ratio, and Information ratio, and others. Results demonstrate the outperformance of our proposal based on ABB strategies over the classical BB for different periods, such as 6 and 10 days. The effectiveness of the approach presented in this paper exhibits a significant contrast to the traditional Bollinger Band methodology. Furthermore, these results are substantiated using robust statistical tests such as the Jonckheere-Terpstra Test.

This paper introduces the moment interaction between different assets in the semi-nonparametric modeling of a multivariate distribution. We analyze bivariate portfolios where skewness and kurtosis may interact between different assets, showing that these new parameters may be significant pieces of information, particularly for measuring risk. Model performance for risk assessment is tested with backtesting techniques considering equally weighted portfolios of the S&P 500 and Nasdaq 100 indices and major cryptocurrencies (Bitcoin and Ethereum), the latter with high-frequency data. The results show adequate performance in terms of Value-at-Risk, Median Shortfall, and Expected Shortfall, especially for high confidence levels.

Environmental, social, and governance (ESG) factors have become key factors in modern portfolio management, shaping how investors think and how they allocate their assets. At the same time, the presence of asymmetric and heavy‐tailed return distributions highlights the necessity of moving beyond the classical mean–variance (MV) framework by incorporating higher‐order moments, such as skewness and kurtosis, into portfolio optimization. To address this issue, we introduce a unified mean–variance‐skewness‐kurtosis‐ESG (MVSK‐ESG) optimization model. This model uses different ESG score thresholds and focuses on ESG leaders within the Dow Jones Industrial Average and the Nasdaq 100. This model incorporates ESG scores into the objective function using a difference‐of‐convex programming framework to address the model's inherent nonconvexity. Empirical results show that MVSK‐ESG portfolios consistently outperform traditional MV and ESG‐constrained portfolios as well as their benchmarks, with higher risk‐adjusted returns. The proposed framework provides a robust approach for integrating sustainability considerations into portfolio construction.

Although Deep Neural Networks (DNNs) have repeatedly shown excellent performance, they are known to be vulnerable to adversarial attacks that contain human-imperceptible perturbations. Multiple adversarial defense strategies have been proposed to alleviate this issue, but they often demonstrate restricted practicability regarding efficiency and handling solely specific attacks. In this paper, we analyze the performance of Bayesian Neural Networks (BNNs) endowed with flexible approximate posterior distribution for detecting adversarial examples. Furthermore, we study how robust the detection method is when Bayesian layers are located at the top or throughout the DNNs to determine the role of the network's hidden layers, and we compare the results with the deterministic ones. We show how BNNs offer a powerful, and practical method of detecting adversarial examples in comparison with deterministic approaches. Finally, we discuss the impact of having well-calibrated models as detectors and how non-gaussian priors enhance the performance of the detection.

Recently, deep learning techniques are gradually replacing traditional statistical and machine learning models as the first choice for price forecasting tasks. In this paper, we leverage probabilistic deep learning for inferring the volatility index VIX. We employ the probabilistic counterpart of WaveNet, Temporal Convolutional Network (TCN), and Transformers. We show that TCN outperforms all models with an RMSE around 0.189. In addition, it has been well known that modern neural networks provide inaccurate uncertainty estimates. For solving this problem, we use the standard deviation scaling to calibrate the networks. Furthermore, we found out that MNF with Gaussian prior outperforms Reparameterization Trick and Flipout models in terms of precision and uncertainty predictions. Finally, we claim that MNF with Cauchy and LogUniform prior distributions yield well-calibrated TCN, and Transformer and WaveNet networks being the former that best infer the VIX values for one and five-step-ahead forecasting, and the probabilistic Transformer model yields an adequate forecasting for the COVID-19 pandemic period.

Real options analysis is an adequate tool with which to value companies and projects under investment uncertainty. Nevertheless, the estimation of the volatility to be employed in the valuation procedure is a challenging task. The volatility parameter not only affects the investment value, but is also important in strategic decision-making. The aim of this paper is to provide a suitable methodology for the estimation of volatility in real option project valuation, with a focus on renewable energy projects. Our procedure is a straightforward extension of the implied volatility methodology employed for financial options; however, our proposal considers the debt-to-equity ratio instead of the moneyness or strike price. Thus, the volatility of the project is the implied volatility obtained from the volatility surface of comparable firms for a certain valuation date and the given debt-to-equity relation of a renewable project. Furthermore, the natural spline model is utilized to calibrate the volatility surface for real option valuation purposes. The empirical results demonstrate that the implied volatility ranges from 3.37% to 113.78%, with median values between 16.42% and 47.10%, in the period from January 2014 to December 2020, for our research study. Finally, we consider that our proposal is a natural and straightforward manner in which to estimate the implied volatility for projects under investment uncertainty, since real option valuation is based on the same idea and tools used in financial option pricing.