Finding the nonnegative minimal solutions of Cauchy PDEs in a volatility-stabilized market ArXiv ID: 2411.13558 “View on arXiv” Authors: Unknown Abstract The strong relative arbitrage problem in Stochastic Portfolio Theory seeks an investment strategy that almost surely outperforms a benchmark portfolio at the end of a given time horizon. The highest relative return in relative arbitrage opportunities is characterized by the smallest nonnegative continuous solution of a Cauchy problem for a partial differential equation (PDE). However, solving this type of PDE poses analytical and numerical challenges, due to the high dimensionality and its non-unique solutions. In this paper, we discuss numerical methods to address the relative arbitrage problem and the associated PDE in a volatility-stabilized market, using time-changed Bessel bridges. We present a practical algorithm and demonstrate numerical results through an example in volatility-stabilized markets. ...

Market efficiency, informational asymmetry and pseudo-collusion of adaptively learning agents ArXiv ID: 2411.05032 “View on arXiv” Authors: Unknown Abstract We examine the dynamics of informational efficiency in a market with asymmetrically informed, boundedly rational traders who adaptively learn optimal strategies using simple multiarmed bandit (MAB) algorithms. The strategies available to the traders have two dimensions: on the one hand, the traders must endogenously choose whether to acquire a costly information signal, on the other, they must determine how aggressively they trade by choosing the share of their wealth to be invested in the risky asset. Our study contributes to two strands of literature: the literature comparing the effects of competitive and strategic behavior on asset price efficiency under costly information as well as the actively growing literature on algorithmic tacit collusion and pseudo-collusion in financial markets. We find that for certain market environments (with low information costs) our model reproduces the results of Kyle [“1989”] in that the ability of traders to trade strategically leads to worse price efficiency compared to the purely competitive case. For other environments (with high information costs), on the other hand, our results show that a market with strategically acting traders can be more efficient than a purely competitive one. Furthermore, we obtain novel results on the ability of independently learning traders to coordinate on a pseudo-collusive behavior, leading to non-competitive pricing. Contrary to some recent contributions (see e.g. [“Cartea et al. 2022”]), we find that the pseudo-collusive behavior in our model is robust to a large number of agents, demonstrating that even in the setting of financial markets with a large number of independently learning traders non-competitive pricing and pseudo-collusive behavior can frequently arise. ...

Robust and Fast Bass local volatility ArXiv ID: 2411.04321 “View on arXiv” Authors: Unknown Abstract The Bass Local Volatility Model (Bass-LV), as studied in [“Conze and Henry-Labordere, 2021”], stands out for its ability to eliminate the need for interpolation between maturities. This offers a significant advantage over traditional LV models. However, its performance highly depends on accurate construction of state price densities and the corresponding marginal distributions and efficient numerical convolutions which are necessary when solving the associated fixed point problems. In this paper, we propose a new approach combining local quadratic estimation and lognormal mixture tails for the construction of state price densities. We investigate computational efficiency of trapezoidal rule based schemes for numerical convolutions and show that they outperform commonly used Gauss-Hermite quadrature. We demonstrate the performance of the proposed method, both in standard option pricing models, as well as through a detailed market case study. ...

Supervised Autoencoders with Fractionally Differentiated Features and Triple Barrier Labelling Enhance Predictions on Noisy Data ArXiv ID: 2411.12753 “View on arXiv” Authors: Unknown Abstract This paper investigates the enhancement of financial time series forecasting with the use of neural networks through supervised autoencoders (SAE), to improve investment strategy performance. Using the Sharpe and Information Ratios, it specifically examines the impact of noise augmentation and triple barrier labeling on risk-adjusted returns. The study focuses on Bitcoin, Litecoin, and Ethereum as the traded assets from January 1, 2016, to April 30, 2022. Findings indicate that supervised autoencoders, with balanced noise augmentation and bottleneck size, significantly boost strategy effectiveness. However, excessive noise and large bottleneck sizes can impair performance. ...

Zero-Coupon Treasury Rates and Returns using the Volatility Index ArXiv ID: 2411.03699 “View on arXiv” Authors: Unknown Abstract We study a multivariate autoregressive stochastic volatility model for the first 3 principal components (level, slope, curvature) of 10 series of zero-coupon Treasury bond rates with maturities from 1 to 10 years. We fit this model using monthly data from 1990. Unlike classic models with hidden stochastic volatility, here it is observed as VIX: the volatility index for the S&P 500 stock market index. Surprisingly, this stock index volatility works for Treasury bonds, too. Next, we prove long-term stability and the Law of Large Numbers. We express total returns of zero-coupon bonds using these principal components. We prove the Law of Large Numbers for these returns. All results are done for discrete and continuous time. ...

Beyond the Traditional VIX: A Novel Approach to Identifying Uncertainty Shocks in Financial Markets ArXiv ID: 2411.02804 “View on arXiv” Authors: Unknown Abstract We introduce a new identification strategy for uncertainty shocks to explain macroeconomic volatility in financial markets. The Chicago Board Options Exchange Volatility Index (VIX) measures market expectations of future volatility, but traditional methods based on second-moment shocks and time-varying volatility of the VIX often fail to capture the non-Gaussian, heavy-tailed nature of asset returns. To address this, we construct a revised VIX by fitting a double-subordinated Normal Inverse Gaussian Levy process to S&P 500 option prices, providing a more comprehensive measure of volatility that reflects the extreme movements and heavy tails observed in financial data. Using an axiomatic approach, we introduce a general family of risk-reward ratios, computed with our revised VIX and fitted over a fractional time series to more accurately identify uncertainty shocks in financial markets. ...

Blending Ensemble for Classification with Genetic-algorithm generated Alpha factors and Sentiments (GAS) ArXiv ID: 2411.03035 “View on arXiv” Authors: Unknown Abstract With the increasing maturity and expansion of the cryptocurrency market, understanding and predicting its price fluctuations has become an important issue in the field of financial engineering. This article introduces an innovative Genetic Algorithm-generated Alpha Sentiment (GAS) blending ensemble model specifically designed to predict Bitcoin market trends. The model integrates advanced ensemble learning methods, feature selection algorithms, and in-depth sentiment analysis to effectively capture the complexity and variability of daily Bitcoin trading data. The GAS framework combines 34 Alpha factors with 8 news economic sentiment factors to provide deep insights into Bitcoin price fluctuations by accurately analyzing market sentiment and technical indicators. The core of this study is using a stacked model (including LightGBM, XGBoost, and Random Forest Classifier) for trend prediction which demonstrates excellent performance in traditional buy-and-hold strategies. In addition, this article also explores the effectiveness of using genetic algorithms to automate alpha factor construction as well as enhancing predictive models through sentiment analysis. Experimental results show that the GAS model performs competitively in daily Bitcoin trend prediction especially when analyzing highly volatile financial assets with rich data. ...

Climate AI for Corporate Decarbonization Metrics Extraction ArXiv ID: 2411.03402 “View on arXiv” Authors: Unknown Abstract Corporate Greenhouse Gas (GHG) emission targets are important metrics in sustainable investing [“12, 16”]. To provide a comprehensive view of company emission objectives, we propose an approach to source these metrics from company public disclosures. Without automation, curating these metrics manually is a labor-intensive process that requires combing through lengthy corporate sustainability disclosures that often do not follow a standard format. Furthermore, the resulting dataset needs to be validated thoroughly by Subject Matter Experts (SMEs), further lengthening the time-to-market. We introduce the Climate Artificial Intelligence for Corporate Decarbonization Metrics Extraction (CAI) model and pipeline, a novel approach utilizing Large Language Models (LLMs) to extract and validate linked metrics from corporate disclosures. We demonstrate that the process improves data collection efficiency and accuracy by automating data curation, validation, and metric scoring from public corporate disclosures. We further show that our results are agnostic to the choice of LLMs. This framework can be applied broadly to information extraction from textual data. ...

Time-Causal VAE: Robust Financial Time Series Generator ArXiv ID: 2411.02947 “View on arXiv” Authors: Unknown Abstract We build a time-causal variational autoencoder (TC-VAE) for robust generation of financial time series data. Our approach imposes a causality constraint on the encoder and decoder networks, ensuring a causal transport from the real market time series to the fake generated time series. Specifically, we prove that the TC-VAE loss provides an upper bound on the causal Wasserstein distance between market distributions and generated distributions. Consequently, the TC-VAE loss controls the discrepancy between optimal values of various dynamic stochastic optimization problems under real and generated distributions. To further enhance the model’s ability to approximate the latent representation of the real market distribution, we integrate a RealNVP prior into the TC-VAE framework. Finally, extensive numerical experiments show that TC-VAE achieves promising results on both synthetic and real market data. This is done by comparing real and generated distributions according to various statistical distances, demonstrating the effectiveness of the generated data for downstream financial optimization tasks, as well as showcasing that the generated data reproduces stylized facts of real financial market data. ...

Utilizing RNN for Real-time Cryptocurrency Price Prediction and Trading Strategy Optimization ArXiv ID: 2411.05829 “View on arXiv” Authors: Unknown Abstract This study explores the use of Recurrent Neural Networks (RNN) for real-time cryptocurrency price prediction and optimized trading strategies. Given the high volatility of the cryptocurrency market, traditional forecasting models often fall short. By leveraging RNNs’ capability to capture long-term patterns in time-series data, this research aims to improve accuracy in price prediction and develop effective trading strategies. The project follows a structured approach involving data collection, preprocessing, and model refinement, followed by rigorous backtesting for profitability and risk assessment. This work contributes to both the academic and practical fields by providing a robust predictive model and optimized trading strategies that address the challenges of cryptocurrency trading. ...