Context: Forecasting stock returns is a long-standing challenge in financial economics, with significant implications for both risk management and regulatory compliance. Traditional econometric models such as GARCH (Bollerslev, 1986) capture volatility persistence but fail to fully account for key stylized facts of financial time series: fat tails, volatility clustering, and leverage effects (Glosten et al., 1993). Similarly, modern machine learning and deep learning methods, although capable of modeling nonlinear dynamics (Goodfellow et al., 2016; Tealab, 2018), tend to underperform during rare but impactful market shocks (Fawcett and Provost, 1997; Pokou, 2022). As illustrated in Figure 1, these limitations often result in systematic mispredictions of excess returns, especially in turbulent markets. These forecasting inaccuracies are critical because they directly translate into unreliable estimates of Value-at-Risk (VaR), the benchmark risk measure under Basel regulatory frameworks (on Banking Supervision, 2017). Overestimation inflates capital requirements, whereas underestimation exposes institutions to excessive losses. To mitigate these shortcomings, the recent literature has shifted from precise return forecasting to directional return prediction, reframe the task as a classification problem, determining whether returns will be positive or negative (Kanas, 2001; Nyberg, 2011; Alostad and Davulcu, 2017). Beyond the standard zero threshold, quantile and volatility-based criteria have been introduced to better isolate significant market movements (Chung and Hong, 2007; Linton and Whang, 2007).

We present a novel approach for predicting the distribution of asset returns using a quantile-based method with Long Short-Term Memory (LSTM) networks. Our model is designed in two stages: the first focuses on predicting the quantiles of normalized asset returns using asset-specific features, while the second stage incorporates market data to adjust these predictions for broader economic conditions. This results in a generalized model that can be applied across various asset classes, including commodities, cryptocurrencies, as well as synthetic datasets. The predicted quantiles are then converted into full probability distributions through kernel density estimation, allowing for more precise return distribution predictions and inferencing. The LSTM model significantly outperforms a linear quantile regression baseline by 98% and a dense neural network model by over 50%, showcasing its ability to capture complex patterns in financial return distributions across both synthetic and real-world data. By using exclusively asset-class-neutral features, our model achieves robust, generalizable results.

Forecasting with multivariate time series, which aims to predict future values given previous and current several univariate time series data, has been studied for decades, with one example being ARIMA. Because it is difficult to measure the extent to which noise is mixed with informative signals within rapidly fluctuating financial time series data, designing a good predictive model is not a simple task. Recently, many researchers have become interested in recurrent neural networks and attention-based neural networks, applying them in financial forecasting. There have been many attempts to utilize these methods for the capturing of long-term temporal dependencies and to select more important features in multivariate time series data in order to make accurate predictions. In this paper, we propose a new prediction framework based on deep neural networks and a trend filtering, which converts noisy time series data into a piecewise linear fashion. We reveal that the predictive performance of deep temporal neural networks improves when the training data is temporally processed by a trend filtering. To verify the effect of our framework, three deep temporal neural networks, state of the art models for predictions in time series finance data, are used and compared with models that contain trend filtering as an input feature. Extensive experiments on real-world multivariate time series data show that the proposed method is effective and significantly better than existing baseline methods.

We study neural networks as nonparametric estimation tools for the hedging of options. To this end, we design a network, named HedgeNet, that directly outputs a hedging strategy. This network is trained to minimise the hedging error instead of the pricing error. Applied to end-of-day and tick prices of S&P 500 and Euro Stoxx 50 options, the network is able to reduce the mean squared hedging error of the Black-Scholes benchmark significantly. We illustrate, however, that a similar benefit arises by simple linear regressions that incorporate the leverage effect. Finally, we show how a faulty training/test data split, possibly along with an additional 'tagging' of data, leads to a significant overestimation of the outperformance of neural networks.

We construct realistic equity option market simulators based on generative adversarial networks (GANs). We consider recurrent and temporal convolutional architectures, and assess the impact of state compression. Option market simulators are highly relevant because they allow us to extend the limited real-world data sets available for the training and evaluation of option trading strategies. We show that network-based generators outperform classical methods on a range of benchmark metrics, and adversarial training achieves the best performance. Our work demonstrates for the first time that GANs can be successfully applied to the task of generating multivariate financial time series.

We are going to introduce the Markov Switching Regimes (MSR) model which, as its name indicates, tries to capture when a regimen has changed to another one. This would be a change between opposite trends or it could consist in passing from "being in trend" to "not being in trend" and vice versa. The name of Markov could sound familiar to some of you as j3 introduced what the Markov chains were a couple of years ago. The main characteristic of this stochastic process is that in a stage t, the probability of occurrence only depends on what happened in the immediately previous stage, t-1. In our post we will assume that the trend of an index today will depend only on which trend was living yesterday, this means, the index will be governed by a Markov chain.

How about trying to find any use of the famous Monty Hall problem in a stock index context? First of all, some of you may be confused because neither "Monty Hall problem" nor "Let's make a deal" are familiar to you so I will refresh you what these names are concerned to. Monty Hall was a TV presenter for "Let's make a deal", a famous American show in the sixties. Suppose you're on this game show and you're given the choice of three doors: behind one door there is a prize; behind the others, there is nothing. You pick a door, say number 1, and the host, who knows what's behind the doors, opens another door, say number 3, which results to be empty.