Autonomous Sparse Mean-CVaR Portfolio Optimization ArXiv ID: 2405.08047 “View on arXiv” Authors: Unknown Abstract The $\ell_0$-constrained mean-CVaR model poses a significant challenge due to its NP-hard nature, typically tackled through combinatorial methods characterized by high computational demands. From a markedly different perspective, we propose an innovative autonomous sparse mean-CVaR portfolio model, capable of approximating the original $\ell_0$-constrained mean-CVaR model with arbitrary accuracy. The core idea is to convert the $\ell_0$ constraint into an indicator function and subsequently handle it through a tailed approximation. We then propose a proximal alternating linearized minimization algorithm, coupled with a nested fixed-point proximity algorithm (both convergent), to iteratively solve the model. Autonomy in sparsity refers to retaining a significant portion of assets within the selected asset pool during adjustments in pool size. Consequently, our framework offers a theoretically guaranteed approximation of the $\ell_0$-constrained mean-CVaR model, improving computational efficiency while providing a robust asset selection scheme. ...

Comparative Study of Bitcoin Price Prediction ArXiv ID: 2405.08089 “View on arXiv” Authors: Unknown Abstract Prediction of stock prices has been a crucial and challenging task, especially in the case of highly volatile digital currencies such as Bitcoin. This research examineS the potential of using neural network models, namely LSTMs and GRUs, to forecast Bitcoin’s price movements. We employ five-fold cross-validation to enhance generalization and utilize L2 regularization to reduce overfitting and noise. Our study demonstrates that the GRUs models offer better accuracy than LSTMs model for predicting Bitcoin’s price. Specifically, the GRU model has an MSE of 4.67, while the LSTM model has an MSE of 6.25 when compared to the actual prices in the test set data. This finding indicates that GRU models are better equipped to process sequential data with long-term dependencies, a characteristic of financial time series data such as Bitcoin prices. In summary, our results provide valuable insights into the potential of neural network models for accurate Bitcoin price prediction and emphasize the importance of employing appropriate regularization techniques to enhance model performance. ...

Data-driven measures of high-frequency trading ArXiv ID: 2405.08101 “View on arXiv” Authors: Unknown Abstract High-frequency trading (HFT) accounts for almost half of equity trading volume, yet it is not identified in public data. We develop novel data-driven measures of HFT activity that separate strategies that supply and demand liquidity. We train machine learning models to predict HFT activity observed in a proprietary dataset using concurrent public intraday data. Once trained on the dataset, these models generate HFT measures for the entire U.S. stock universe from 2010 to 2023. Our measures outperform conventional proxies, which struggle to capture HFT’s time dynamics. We further validate them using shocks to HFT activity, including latency arbitrage, exchange speed bumps, and data feed upgrades. Finally, our measures reveal how HFT affects fundamental information acquisition. Liquidity-supplying HFTs improve price discovery around earnings announcements while liquidity-demanding strategies impede it. ...

Kernel Three Pass Regression Filter ArXiv ID: 2405.07292 “View on arXiv” Authors: Unknown Abstract We forecast a single time series using a high-dimensional set of predictors. When these predictors share common underlying dynamics, an approximate latent factor model provides a powerful characterization of their co-movements Bai(2003). These latent factors succinctly summarize the data and can also be used for prediction, alleviating the curse of dimensionality in high-dimensional prediction exercises, see Stock & Watson (2002a). However, forecasting using these latent factors suffers from two potential drawbacks. First, not all pervasive factors among the set of predictors may be relevant, and using all of them can lead to inefficient forecasts. The second shortcoming is the assumption of linear dependence of predictors on the underlying factors. The first issue can be addressed by using some form of supervision, which leads to the omission of irrelevant information. One example is the three-pass regression filter proposed by Kelly & Pruitt (2015). We extend their framework to cases where the form of dependence might be nonlinear by developing a new estimator, which we refer to as the Kernel Three-Pass Regression Filter (K3PRF). This alleviates the aforementioned second shortcoming. The estimator is computationally efficient and performs well empirically. The short-term performance matches or exceeds that of established models, while the long-term performance shows significant improvement. ...

Trade execution games in a Markovian environment ArXiv ID: 2405.07184 “View on arXiv” Authors: Unknown Abstract This paper examines a trade execution game for two large traders in a generalized price impact model. We incorporate a stochastic and sequentially dependent factor that exogenously affects the market price into financial markets. Our model accounts for how strategic and environmental uncertainties affect the large traders’ execution strategies. We formulate an expected utility maximization problem for two large traders as a Markov game model. Applying the backward induction method of dynamic programming, we provide an explicit closed-form execution strategy at a Markov perfect equilibrium. Our theoretical results reveal that the execution strategy generally lies in a dynamic and non-randomized class; it becomes deterministic if the Markovian environment is also deterministic. In addition, our simulation-based numerical experiments suggest that the execution strategy captures various features observed in financial markets. ...

Complex network analysis of cryptocurrency market during crashes ArXiv ID: 2405.05642 “View on arXiv” Authors: Unknown Abstract This paper identifies the cryptocurrency market crashes and analyses its dynamics using the complex network. We identify three distinct crashes during 2017-20, and the analysis is carried out by dividing the time series into pre-crash, crash, and post-crash periods. Partial correlation based complex network analysis is carried out to study the crashes. Degree density ($ρ_D$), average path length ($\bar{“l”}$), and average clustering coefficient ($\overline{“cc”}$) are estimated from these networks. We find that both $ρ_D$ and $\overline{“cc”}$ are smallest during the pre-crash period, and spike during the crash suggesting the network is dense during a crash. Although $ρ_D$ and $\overline{“cc”}$ decrease in the post-crash period, they remain higher than pre-crash levels for the 2017-18 and 2018-19 crashes suggesting a market attempt to return to normalcy. We get $\bar{“l”}$ is minimal during the crash period, suggesting a rapid flow of information. A dense network and rapid information flow suggest that during a crash uninformed synchronized panic sell-off happens. However, during the 2019-20 crash, the values of $ρ_D$, $\overline{“cc”}$, and $\bar{“l”}$ did not vary significantly, indicating minimal change in dynamics compared to other crashes. The findings of this study may guide investors in making decisions during market crashes. ...

High-Frequency Stock Market Order Transitions during the US-China Trade War 2018: A Discrete-Time Markov Chain Analysis ArXiv ID: 2405.05634 “View on arXiv” Authors: Unknown Abstract Statistical analysis of high-frequency stock market order transaction data is conducted to understand order transition dynamics. We employ a first-order time-homogeneous discrete-time Markov chain model to the sequence of orders of stocks belonging to six different sectors during the USA-China trade war of 2018. The Markov property of the order sequence is validated by the Chi-square test. We estimate the transition probability matrix of the sequence using maximum likelihood estimation. From the heat-map of these matrices, we found the presence of active participation by different types of traders during high volatility days. On such days, these traders place limit orders primarily with the intention of deleting the majority of them to influence the market. These findings are supported by high stationary distribution and low mean recurrence values of add and delete orders. Further, we found similar spectral gap and entropy rate values, which indicates that similar trading strategies are employed on both high and low volatility days during the trade war. Among all the sectors considered in this study, we observe that there is a recurring pattern of full execution orders in Finance & Banking sector. This shows that the banking stocks are resilient during the trade war. Hence, this study may be useful in understanding stock market order dynamics and devise trading strategies accordingly on high and low volatility days during extreme macroeconomic events. ...

Neural Network Learning of Black-Scholes Equation for Option Pricing ArXiv ID: 2405.05780 “View on arXiv” Authors: Unknown Abstract One of the most discussed problems in the financial world is stock option pricing. The Black-Scholes Equation is a Parabolic Partial Differential Equation which provides an option pricing model. The present work proposes an approach based on Neural Networks to solve the Black-Scholes Equations. Real-world data from the stock options market were used as the initial boundary to solve the Black-Scholes Equation. In particular, times series of call options prices of Brazilian companies Petrobras and Vale were employed. The results indicate that the network can learn to solve the Black-Sholes Equation for a specific real-world stock options time series. The experimental results showed that the Neural network option pricing based on the Black-Sholes Equation solution can reach an option pricing forecasting more accurate than the traditional Black-Sholes analytical solutions. The experimental results making it possible to use this methodology to make short-term call option price forecasts in options markets. ...

Markowitz Meets Bellman: Knowledge-distilled Reinforcement Learning for Portfolio Management ArXiv ID: 2405.05449 “View on arXiv” Authors: Unknown Abstract Investment portfolios, central to finance, balance potential returns and risks. This paper introduces a hybrid approach combining Markowitz’s portfolio theory with reinforcement learning, utilizing knowledge distillation for training agents. In particular, our proposed method, called KDD (Knowledge Distillation DDPG), consist of two training stages: supervised and reinforcement learning stages. The trained agents optimize portfolio assembly. A comparative analysis against standard financial models and AI frameworks, using metrics like returns, the Sharpe ratio, and nine evaluation indices, reveals our model’s superiority. It notably achieves the highest yield and Sharpe ratio of 2.03, ensuring top profitability with the lowest risk in comparable return scenarios. ...

Generalization of the Alpha-Stable Distribution with the Degree of Freedom ArXiv ID: 2405.04693 “View on arXiv” Authors: Unknown Abstract A Wright function based framework is proposed to combine and extend several distribution families. The $α$-stable distribution is generalized by adding the degree of freedom parameter. The PDF of this two-sided super distribution family subsumes those of the original $α$-stable, Student’s t distributions, as well as the exponential power distribution and the modified Bessel function of the second kind. Its CDF leads to a fractional extension of the Gauss hypergeometric function. The degree of freedom makes possible for valid variance, skewness, and kurtosis, just like Student’s t. The original $α$-stable distribution is viewed as having one degree of freedom, that explains why it lacks most of the moments. A skew-Gaussian kernel is derived from the characteristic function of the $α$-stable law, which maximally preserves the law in the new framework. To facilitate such framework, the stable count distribution is generalized as the fractional extension of the generalized gamma distribution. It provides rich subordination capabilities, one of which is the fractional $χ$ distribution that supplies the needed ‘degree of freedom’ parameter. Hence, the “new” $α$-stable distribution is a “ratio distribution” of the skew-Gaussian kernel and the fractional $χ$ distribution. Mathematically, it is a new form of higher transcendental function under the Wright function family. Last, the new univariate symmetric distribution is extended to the multivariate elliptical distribution successfully. ...