Introduction of L0 norm and application of L1 and C1 norm in the study of time-series ArXiv ID: 2401.05423 “View on arXiv” Authors: Unknown Abstract Four markets are considered: Cryptocurrencies / South American exchange rate / Spanish Banking indices and European Indices and studied using TDA (Topological Data Analysis) tools. These tools are used to predict and showcase both strengths and weakness of the current TDA tools. In this paper a new tool $L0$ norm is defined and complemented with the already existing $C1$ norm. ...

Multiple-bubble testing in the cryptocurrency market: a case study of bitcoin ArXiv ID: 2401.05417 “View on arXiv” Authors: Unknown Abstract Economic periods and financial crises have highlighted the importance of evaluating financial markets to investors and researchers in recent decades. Keywords: financial markets, economic periods, financial crises, market evaluation, General Financial Markets Complexity vs Empirical Score Math Complexity: 6.0/10 Empirical Rigor: 3.0/10 Quadrant: Lab Rats Why: The paper applies advanced statistical methods like the Right-Tail Augmented Dickey–Fuller (RTADF) test, indicating significant mathematical modeling, but the excerpt shows no implementation details, backtesting results, or data processing steps, resulting in low empirical readiness. flowchart TD A["Research Question<br>Identify & test for multiple bubbles<br>in the cryptocurrency market"] --> B["Data Input<br>Historical Bitcoin Price Data<br>across different time periods"] B --> C["Methodology<br>Advanced Bubble Testing<br>e.g., GSADF or SADF"] C --> D["Computational Process<br>Calculate Test Statistics<br>Identify Bubble Regimes"] D --> E["Key Findings<br>Detect multiple bubble periods<br>Assess crash risks<br>Market implications"]

Representation of forward performance criteria with random endowment via FBSDE and its application to forward optimized certainty equivalent ArXiv ID: 2401.00103 “View on arXiv” Authors: Unknown Abstract We extend the notion of forward performance criteria to settings with random endowment in incomplete markets. Building on these results, we introduce and develop the novel concept of \textit{“forward optimized certainty equivalent (forward OCE)”}, which offers a genuinely dynamic valuation mechanism that accommodates progressively adaptive market model updates, stochastic risk preferences, and incoming claims with arbitrary maturities. In parallel, we develop a new methodology to analyze the emerging stochastic optimization problems by directly studying the candidate optimal control processes for both the primal and dual problems. Specifically, we derive two new systems of forward-backward stochastic differential equations (FBSDEs) and establish necessary and sufficient conditions for optimality, and various equivalences between the two problems. This new approach is general and complements the existing one for forward performance criteria with random endowment based on backward stochastic partial differential equations (backward SPDEs) for the related value functions. We, also, consider representative examples for both forward performance criteria with random endowment and for forward OCE. Furthermore, for the case of exponential criteria, we investigate the connection between forward OCE and forward entropic risk measures. ...

Bayesian Analysis of High Dimensional Vector Error Correction Model ArXiv ID: 2312.17061 “View on arXiv” Authors: Unknown Abstract Vector Error Correction Model (VECM) is a classic method to analyse cointegration relationships amongst multivariate non-stationary time series. In this paper, we focus on high dimensional setting and seek for sample-size-efficient methodology to determine the level of cointegration. Our investigation centres at a Bayesian approach to analyse the cointegration matrix, henceforth determining the cointegration rank. We design two algorithms and implement them on simulated examples, yielding promising results particularly when dealing with high number of variables and relatively low number of observations. Furthermore, we extend this methodology to empirically investigate the constituents of the S&P 500 index, where low-volatility portfolios can be found during both in-sample training and out-of-sample testing periods. ...

Causal Discovery in Financial Markets: A Framework for Nonstationary Time-Series Data ArXiv ID: 2312.17375 “View on arXiv” Authors: Unknown Abstract This paper introduces a new causal structure learning method for nonstationary time series data, a common data type found in fields such as finance, economics, healthcare, and environmental science. Our work builds upon the constraint-based causal discovery from nonstationary data algorithm (CD-NOD). We introduce a refined version (CD-NOTS) which is designed specifically to account for lagged dependencies in time series data. We compare the performance of different algorithmic choices, such as the type of conditional independence test and the significance level, to help select the best hyperparameters given various scenarios of sample size, problem dimensionality, and availability of computational resources. Using the results from the simulated data, we apply CD-NOTS to a broad range of real-world financial applications in order to identify causal connections among nonstationary time series data, thereby illustrating applications in factor-based investing, portfolio diversification, and comprehension of market dynamics. ...

On the Three Demons in Causality in Finance: Time Resolution, Nonstationarity, and Latent Factors ArXiv ID: 2401.05414 “View on arXiv” Authors: Unknown Abstract Financial data is generally time series in essence and thus suffers from three fundamental issues: the mismatch in time resolution, the time-varying property of the distribution - nonstationarity, and causal factors that are important but unknown/unobserved. In this paper, we follow a causal perspective to systematically look into these three demons in finance. Specifically, we reexamine these issues in the context of causality, which gives rise to a novel and inspiring understanding of how the issues can be addressed. Following this perspective, we provide systematic solutions to these problems, which hopefully would serve as a foundation for future research in the area. ...

Price predictability at ultra-high frequency: Entropy-based randomness test ArXiv ID: 2312.16637 “View on arXiv” Authors: Unknown Abstract We use the statistical properties of Shannon entropy estimator and Kullback-Leibler divergence to study the predictability of ultra-high frequency financial data. We develop a statistical test for the predictability of a sequence based on empirical frequencies. We show that the degree of randomness grows with the increase of aggregation level in transaction time. We also find that predictable days are usually characterized by high trading activity, i.e., days with unusually high trading volumes and the number of price changes. We find a group of stocks for which predictability is caused by a frequent change of price direction. We study stylized facts that cause price predictability such as persistence of order signs, autocorrelation of returns, and volatility clustering. We perform multiple testing for sub-intervals of days to identify whether there is predictability at a specific time period during the day. ...

Randomized Signature Methods in Optimal Portfolio Selection ArXiv ID: 2312.16448 “View on arXiv” Authors: Unknown Abstract We present convincing empirical results on the application of Randomized Signature Methods for non-linear, non-parametric drift estimation for a multi-variate financial market. Even though drift estimation is notoriously ill defined due to small signal to noise ratio, one can still try to learn optimal non-linear maps from data to future returns for the purposes of portfolio optimization. Randomized Signatures, in contrast to classical signatures, allow for high dimensional market dimension and provide features on the same scale. We do not contribute to the theory of Randomized Signatures here, but rather present our empirical findings on portfolio selection in real world settings including real market data and transaction costs. ...

The implied volatility surface (also) is path-dependent ArXiv ID: 2312.15950 “View on arXiv” Authors: Unknown Abstract We propose a new model for the forecasting of both the implied volatility surfaces and the underlying asset price. In the spirit of Guyon and Lekeufack (2023) who are interested in the dependence of volatility indices (e.g. the VIX) on the paths of the associated equity indices (e.g. the S&P 500), we first study how vanilla options implied volatility can be predicted using the past trajectory of the underlying asset price. Our empirical study reveals that a large part of the movements of the at-the-money-forward implied volatility for up to two years time-to-maturities can be explained using the past returns and their squares. Moreover, we show that this feedback effect gets weaker when the time-to-maturity increases. Building on this new stylized fact, we fit to historical data a parsimonious version of the SSVI parameterization (Gatheral and Jacquier, 2014) of the implied volatility surface relying on only four parameters and show that the two parameters ruling the at-the-money-forward implied volatility as a function of the time-to-maturity exhibit a path-dependent behavior with respect to the underlying asset price. Finally, we propose a model for the joint dynamics of the implied volatility surface and the underlying asset price. The latter is modelled using a variant of the path-dependent volatility model of Guyon and Lekeufack and the former is obtained by adding a feedback effect of the underlying asset price onto the two parameters ruling the at-the-money-forward implied volatility in the parsimonious SSVI parameterization and by specifying Ornstein-Uhlenbeck processes for the residuals of these two parameters and Jacobi processes for the two other parameters. Thanks to this model, we are able to simulate highly realistic paths of implied volatility surfaces that are free from static arbitrage. ...

Deep Reinforcement Learning for Quantitative Trading ArXiv ID: 2312.15730 “View on arXiv” Authors: Unknown Abstract Artificial Intelligence (AI) and Machine Learning (ML) are transforming the domain of Quantitative Trading (QT) through the deployment of advanced algorithms capable of sifting through extensive financial datasets to pinpoint lucrative investment openings. AI-driven models, particularly those employing ML techniques such as deep learning and reinforcement learning, have shown great prowess in predicting market trends and executing trades at a speed and accuracy that far surpass human capabilities. Its capacity to automate critical tasks, such as discerning market conditions and executing trading strategies, has been pivotal. However, persistent challenges exist in current QT methods, especially in effectively handling noisy and high-frequency financial data. Striking a balance between exploration and exploitation poses another challenge for AI-driven trading agents. To surmount these hurdles, our proposed solution, QTNet, introduces an adaptive trading model that autonomously formulates QT strategies through an intelligent trading agent. Incorporating deep reinforcement learning (DRL) with imitative learning methodologies, we bolster the proficiency of our model. To tackle the challenges posed by volatile financial datasets, we conceptualize the QT mechanism within the framework of a Partially Observable Markov Decision Process (POMDP). Moreover, by embedding imitative learning, the model can capitalize on traditional trading tactics, nurturing a balanced synergy between discovery and utilization. For a more realistic simulation, our trading agent undergoes training using minute-frequency data sourced from the live financial market. Experimental findings underscore the model’s proficiency in extracting robust market features and its adaptability to diverse market conditions. ...