Optimal portfolio under ratio-type periodic evaluation in incomplete markets with stochastic factors ArXiv ID: 2401.14672 “View on arXiv” Authors: Unknown Abstract This paper studies a type of periodic utility maximization for portfolio management in an incomplete market model, where the underlying price diffusion process depends on some external stochastic factors. The portfolio performance is periodically evaluated on the relative ratio of two adjacent wealth levels over an infinite horizon. For both power and logarithmic utilities, we formulate the auxiliary one-period optimization problems with modified utility functions, for which we develop the martingale duality approach to establish the existence of the optimal portfolio processes and the dual minimizers can be identified as the “least favorable” completion of the market. With the help of the duality results in the auxiliary problems and some fixed point arguments, we further derive and verify the optimal portfolio processes in a periodic manner for the original periodic evaluation problems over an infinite horizon. ...

Tweet Influence on Market Trends: Analyzing the Impact of Social Media Sentiment on Biotech Stocks ArXiv ID: 2402.03353 “View on arXiv” Authors: Unknown Abstract This study investigates the relationship between tweet sentiment across diverse categories: news, company opinions, CEO opinions, competitor opinions, and stock market behavior in the biotechnology sector, with a focus on understanding the impact of social media discourse on investor sentiment and decision-making processes. We analyzed historical stock market data for ten of the largest and most influential pharmaceutical companies alongside Twitter data related to COVID-19, vaccines, the companies, and their respective CEOs. Using VADER sentiment analysis, we examined the sentiment scores of tweets and assessed their relationships with stock market performance. We employed ARIMA (AutoRegressive Integrated Moving Average) and VAR (Vector AutoRegression) models to forecast stock market performance, incorporating sentiment covariates to improve predictions. Our findings revealed a complex interplay between tweet sentiment, news, biotech companies, their CEOs, and stock market performance, emphasizing the importance of considering diverse factors when modeling and predicting stock prices. This study provides valuable insights into the influence of social media on the financial sector and lays a foundation for future research aimed at refining stock price prediction models. ...

Higher order approximation of option prices in Barndorff-Nielsen and Shephard models ArXiv ID: 2401.14390 “View on arXiv” Authors: Unknown Abstract We present an approximation method based on the mixing formula (Hull & White 1987, Romano & Touzi 1997) for pricing European options in Barndorff-Nielsen and Shephard models. This approximation is based on a Taylor expansion of the option price. It is implemented using a recursive algorithm that allows us to obtain closed form approximations of the option price of any order (subject to technical conditions on the background driving Lévy process). This method can be used for any type of Barndorff-Nielsen and Shephard stochastic volatility model. Explicit results are presented in the case where the stationary distribution of the background driving Lévy process is inverse Gaussian or gamma. In both of these cases, the approximation compares favorably to option prices produced by the characteristic function. In particular, we also perform an error analysis of the approximation, which is partially based on the results of Das & Langrené (2022). We obtain asymptotic results for the error of the $N^{"\text{th"}}$ order approximation and error bounds when the variance process satisfies an inverse Gaussian Ornstein-Uhlenbeck process or a gamma Ornstein-Uhlenbeck process. ...

MTRGL:Effective Temporal Correlation Discerning through Multi-modal Temporal Relational Graph Learning ArXiv ID: 2401.14199 “View on arXiv” Authors: Unknown Abstract In this study, we explore the synergy of deep learning and financial market applications, focusing on pair trading. This market-neutral strategy is integral to quantitative finance and is apt for advanced deep-learning techniques. A pivotal challenge in pair trading is discerning temporal correlations among entities, necessitating the integration of diverse data modalities. Addressing this, we introduce a novel framework, Multi-modal Temporal Relation Graph Learning (MTRGL). MTRGL combines time series data and discrete features into a temporal graph and employs a memory-based temporal graph neural network. This approach reframes temporal correlation identification as a temporal graph link prediction task, which has shown empirical success. Our experiments on real-world datasets confirm the superior performance of MTRGL, emphasizing its promise in refining automated pair trading strategies. ...

Self and mutually exciting point process embedding flexible residuals and intensity with discretely Markovian dynamics ArXiv ID: 2401.13890 “View on arXiv” Authors: Unknown Abstract This work introduces a self and mutually exciting point process that embeds flexible residuals and intensity with discretely Markovian dynamics. By allowing the integration of diverse residual distributions, this model serves as an extension of the Hawkes process, facilitating intensity modeling. This model’s nature enables a filtered historical simulation that more accurately incorporates the properties of the original time series. Furthermore, the process extends to multivariate models with manageable estimation and simulation implementations. We investigate the impact of a flexible residual distribution on the estimation of high-frequency financial data, comparing it with the Hawkes process. ...

An Explicit Scheme for Pathwise XVA Computations ArXiv ID: 2401.13314 “View on arXiv” Authors: Unknown Abstract Motivated by the equations of cross valuation adjustments (XVAs) in the realistic case where capital is deemed fungible as a source of funding for variation margin, we introduce a simulation/regression scheme for a class of anticipated BSDEs, where the coefficient entails a conditional expected shortfall of the martingale part of the solution. The scheme is explicit in time and uses neural network least-squares and quantile regressions for the embedded conditional expectations and expected shortfall computations. An a posteriori Monte Carlo validation procedure allows assessing the regression error of the scheme at each time step. The superiority of this scheme with respect to Picard iterations is illustrated in a high-dimensional and hybrid market/default risks XVA use-case. ...

From Numbers to Words: Multi-Modal Bankruptcy Prediction Using the ECL Dataset ArXiv ID: 2401.12652 “View on arXiv” Authors: Unknown Abstract In this paper, we present ECL, a novel multi-modal dataset containing the textual and numerical data from corporate 10K filings and associated binary bankruptcy labels. Furthermore, we develop and critically evaluate several classical and neural bankruptcy prediction models using this dataset. Our findings suggest that the information contained in each data modality is complementary for bankruptcy prediction. We also see that the binary bankruptcy prediction target does not enable our models to distinguish next year bankruptcy from an unhealthy financial situation resulting in bankruptcy in later years. Finally, we explore the use of LLMs in the context of our task. We show how GPT-based models can be used to extract meaningful summaries from the textual data but zero-shot bankruptcy prediction results are poor. All resources required to access and update the dataset or replicate our experiments are available on github.com/henriarnoUG/ECL. ...

New approximate stochastic dominance approaches for Enhanced Indexation models ArXiv ID: 2401.12669 “View on arXiv” Authors: Unknown Abstract In this paper, we discuss portfolio selection strategies for Enhanced Indexation (EI), which are based on stochastic dominance relations. The goal is to select portfolios that stochastically dominate a given benchmark but that, at the same time, must generate some excess return with respect to a benchmark index. To achieve this goal, we propose a new methodology that selects portfolios using the ordered weighted average (OWA) operator, which generalizes previous approaches based on minimax selection rules and still leads to solving linear programming models. We also introduce a new type of approximate stochastic dominance rule and show that it implies the almost Second-order Stochastic Dominance (SSD) criterion proposed by Lizyayev and Ruszczynski (2012). We prove that our EI model based on OWA selects portfolios that dominate a given benchmark through this new form of stochastic dominance criterion. We test the performance of the obtained portfolios in an extensive empirical analysis based on real-world datasets. The computational results show that our proposed approach outperforms several SSD-based strategies widely used in the literature, as well as the global minimum variance portfolio. ...

Optimizing Transition Strategies for Small to Medium Sized Portfolios ArXiv ID: 2401.13126 “View on arXiv” Authors: Unknown Abstract This work discusses the benefits of constrained portfolio turnover strategies for small to medium-sized portfolios. We propose a dynamic multi-period model that aims to minimize transaction costs and maximize terminal wealth levels whilst adhering to strict portfolio turnover constraints. Our results demonstrate that using our framework in combination with a reasonable forecast, can lead to higher portfolio values and lower transaction costs on average when compared to a naive, single-period model. Such results were maintained given different problem cases, such as, trading horizon, assets under management, wealth levels, etc. In addition, the proposed model lends itself to a reformulation that makes use of the column generation algorithm which can be strategically leveraged to reduce complexity and solving times. ...

Transformers with Attentive Federated Aggregation for Time Series Stock Forecasting ArXiv ID: 2402.06638 “View on arXiv” Authors: Unknown Abstract Recent innovations in transformers have shown their superior performance in natural language processing (NLP) and computer vision (CV). The ability to capture long-range dependencies and interactions in sequential data has also triggered a great interest in time series modeling, leading to the widespread use of transformers in many time series applications. However, being the most common and crucial application, the adaptation of transformers to time series forecasting has remained limited, with both promising and inconsistent results. In contrast to the challenges in NLP and CV, time series problems not only add the complexity of order or temporal dependence among input sequences but also consider trend, level, and seasonality information that much of this data is valuable for decision making. The conventional training scheme has shown deficiencies regarding model overfitting, data scarcity, and privacy issues when working with transformers for a forecasting task. In this work, we propose attentive federated transformers for time series stock forecasting with better performance while preserving the privacy of participating enterprises. Empirical results on various stock data from the Yahoo! Finance website indicate the superiority of our proposed scheme in dealing with the above challenges and data heterogeneity in federated learning. ...