Non-parametric cumulants approach for outlier detection of multivariate financial data ArXiv ID: 2305.10911 “View on arXiv” Authors: Unknown Abstract In this paper, we propose an outlier detection algorithm for multivariate data based on their projections on the directions that maximize the Cumulant Generating Function (CGF). We prove that CGF is a convex function, and we characterize the CGF maximization problem on the unit n-circle as a concave minimization problem. Then, we show that the CGF maximization approach can be interpreted as an extension of the standard principal component technique. Therefore, for validation and testing, we provide a thorough comparison of our methodology with two other projection-based approaches both on artificial and real-world financial data. Finally, we apply our method as an early detector for financial crises. ...

Risk Budgeting Allocation for Dynamic Risk Measures ArXiv ID: 2305.11319 “View on arXiv” Authors: Unknown Abstract We define and develop an approach for risk budgeting allocation - a risk diversification portfolio strategy - where risk is measured using a dynamic time-consistent risk measure. For this, we introduce a notion of dynamic risk contributions that generalise the classical Euler contributions and which allow us to obtain dynamic risk contributions in a recursive manner. We prove that, for the class of coherent dynamic distortion risk measures, the risk allocation problem may be recast as a sequence of strictly convex optimisation problems. Moreover, we show that self-financing dynamic risk budgeting strategies with initial wealth of 1 are scaled versions of the solution of the sequence of convex optimisation problems. Furthermore, we develop an actor-critic approach, leveraging the elicitability of dynamic risk measures, to solve for risk budgeting strategies using deep learning. ...

Support for Stock Trend Prediction Using Transformers and Sentiment Analysis ArXiv ID: 2305.14368 “View on arXiv” Authors: Unknown Abstract Stock trend analysis has been an influential time-series prediction topic due to its lucrative and inherently chaotic nature. Many models looking to accurately predict the trend of stocks have been based on Recurrent Neural Networks (RNNs). However, due to the limitations of RNNs, such as gradient vanish and long-term dependencies being lost as sequence length increases, in this paper we develop a Transformer based model that uses technical stock data and sentiment analysis to conduct accurate stock trend prediction over long time windows. This paper also introduces a novel dataset containing daily technical stock data and top news headline data spanning almost three years. Stock prediction based solely on technical data can suffer from lag caused by the inability of stock indicators to effectively factor in breaking market news. The use of sentiment analysis on top headlines can help account for unforeseen shifts in market conditions caused by news coverage. We measure the performance of our model against RNNs over sequence lengths spanning 5 business days to 30 business days to mimic different length trading strategies. This reveals an improvement in directional accuracy over RNNs as sequence length is increased, with the largest improvement being close to 18.63% at 30 business days. ...

Short-Term Stock Price Forecasting using exogenous variables and Machine Learning Algorithms ArXiv ID: 2309.00618 “View on arXiv” Authors: Unknown Abstract Creating accurate predictions in the stock market has always been a significant challenge in finance. With the rise of machine learning as the next level in the forecasting area, this research paper compares four machine learning models and their accuracy in forecasting three well-known stocks traded in the NYSE in the short term from March 2020 to May 2022. We deploy, develop, and tune XGBoost, Random Forest, Multi-layer Perceptron, and Support Vector Regression models. We report the models that produce the highest accuracies from our evaluation metrics: RMSE, MAPE, MTT, and MPE. Using a training data set of 240 trading days, we find that XGBoost gives the highest accuracy despite running longer (up to 10 seconds). Results from this study may improve by further tuning the individual parameters or introducing more exogenous variables. ...

Finite-Difference Solution Ansatz approach in Least-Squares Monte Carlo ArXiv ID: 2305.09166 “View on arXiv” Authors: Unknown Abstract This article presents a simple but effective and efficient approach to improve the accuracy and stability of Least-Squares Monte Carlo. The key idea is to construct the ansatz of conditional expected continuation payoff using the finite-difference solution from one dimension, to be used in linear regression. This approach bridges between solving backward partial differential equations and Monte Carlo simulation, aiming at achieving the best of both worlds. In a general setting encompassing both local and stochastic volatility models, the ansatz is proven to act as a control variate, reducing the mean squared error, thereby leading to a reduction of the final pricing error. We illustrate the technique with realistic examples including Bermudan options, worst of issuer callable notes and expected positive exposure on European options under valuation adjustments. ...

Convex optimization over a probability simplex ArXiv ID: 2305.09046 “View on arXiv” Authors: Unknown Abstract We propose a new iteration scheme, the Cauchy-Simplex, to optimize convex problems over the probability simplex ${“w\in\mathbb{R”}^n\ |\ \sum_i w_i=1\ \textrm{“and”}\ w_i\geq0}$. Specifically, we map the simplex to the positive quadrant of a unit sphere, envisage gradient descent in latent variables, and map the result back in a way that only depends on the simplex variable. Moreover, proving rigorous convergence results in this formulation leads inherently to tools from information theory (e.g., cross-entropy and KL divergence). Each iteration of the Cauchy-Simplex consists of simple operations, making it well-suited for high-dimensional problems. In continuous time, we prove that $f(x_T)-f(x^) = {“O”}(1/T)$ for differentiable real-valued convex functions, where $T$ is the number of time steps and $w^$ is the optimal solution. Numerical experiments of projection onto convex hulls show faster convergence than similar algorithms. Finally, we apply our algorithm to online learning problems and prove the convergence of the average regret for (1) Prediction with expert advice and (2) Universal Portfolios. ...

Portfolio Optimization Rules beyond the Mean-Variance Approach ArXiv ID: 2305.08530 “View on arXiv” Authors: Unknown Abstract In this paper, we revisit the relationship between investors’ utility functions and portfolio allocation rules. We derive portfolio allocation rules for asymmetric Laplace distributed $ALD(μ,σ,κ)$ returns and compare them with the mean-variance approach, which is based on Gaussian returns. We reveal that in the limit of small $\fracμσ$, the Markowitz contribution is accompanied by a skewness term. We also obtain the allocation rules when the expected return is a random normal variable in an average and worst-case scenarios, which allows us to take into account uncertainty of the predicted returns. An optimal worst-case scenario solution smoothly approximates between equal weights and minimum variance portfolio, presenting an attractive convex alternative to the risk parity portfolio. We address the issue of handling singular covariance matrices by imposing conditional independence structure on the precision matrix directly. Finally, utilizing a microscopic portfolio model with random drift and analytical expression for the expected utility function with log-normal distributed cross-sectional returns, we demonstrate the influence of model parameters on portfolio construction. This comprehensive approach enhances allocation weight stability, mitigates instabilities associated with the mean-variance approach, and can prove valuable for both short-term traders and long-term investors. ...

Hybrid Quantum Algorithms integrating QAOA, Penalty Dephasing and Zeno Effect for Solving Binary Optimization Problems with Multiple Constraints ArXiv ID: 2305.08056 “View on arXiv” Authors: Unknown Abstract When tackling binary optimization problems using quantum algorithms, the conventional Ising representation and Quantum Approximate Optimization Algorithm (QAOA) encounter difficulties in efficiently handling errors for large-scale problems involving multiple constraints. To address these challenges, this paper presents a hybrid framework that combines the use of standard Ising Hamiltonians to solve a subset of the constraints, while employing non-Ising formulations to represent and address the remaining constraints. The resolution of these non-Ising constraints is achieved through either penalty dephasing or the quantum Zeno effect. This innovative approach leads to a collection of quantum circuits with adaptable structures, depending on the chosen representation for each constraint. Furthermore, this paper introduces a novel technique that utilizes the quantum Zeno effect by frequently measuring the constraint flag, enabling the resolution of any optimization constraint. Theoretical properties of these algorithms are discussed, and their performance in addressing practical aircraft loading problems is highly promising, showcasing significant potential for a wide range of industrial applications. ...

NYSE Price Correlations Are Abitrageable Over Hours and Predictable Over Years ArXiv ID: 2305.08241 “View on arXiv” Authors: Unknown Abstract Trade prices of about 1000 New York Stock Exchange-listed stocks are studied at one-minute time resolution over the continuous five year period 2018–2022. For each stock, in dollar-volume-weighted transaction time, the discrepancy from a Brownian-motion martingale is measured on timescales of minutes to several days. The result is well fit by a power-law shot-noise (or Gaussian) process with Hurst exponent 0.465, that is, slightly mean-reverting. As a check, we execute an arbitrage strategy on simulated Hurst-exponent data, and a comparable strategy in backtesting on the actual data, obtaining similar results (annualized returns $\sim 60$% if zero transaction costs). Next examining the cross-correlation structure of the $\sim 1000$ stocks, we find that, counterintuitively, correlations increase with time lag in the range studied. We show that this behavior that can be quantitatively explained if the mean-reverting Hurst component of each stock is uncorrelated, i.e., does not share that stock’s overall correlation with other stocks. Overall, we find that $\approx 45$% of a stock’s 1-hour returns variance is explained by its particular correlations to other stocks, but that most of this is simply explained by the movement of all stocks together. Unexpectedly, the fraction of variance explained is greatest when price volatility is high, for example during COVID-19 year 2020. An arbitrage strategy with cross-correlations does significantly better than without (annualized returns $\sim 100$% if zero transaction costs). Measured correlations from any single year in 2018–2022 are about equally good in predicting all the other years, indicating that an overall correlation structure is persistent over the whole period. ...

Trillion Dollar Words: A New Financial Dataset, Task & Market Analysis ArXiv ID: 2305.07972 “View on arXiv” Authors: Unknown Abstract Monetary policy pronouncements by Federal Open Market Committee (FOMC) are a major driver of financial market returns. We construct the largest tokenized and annotated dataset of FOMC speeches, meeting minutes, and press conference transcripts in order to understand how monetary policy influences financial markets. In this study, we develop a novel task of hawkish-dovish classification and benchmark various pre-trained language models on the proposed dataset. Using the best-performing model (RoBERTa-large), we construct a measure of monetary policy stance for the FOMC document release days. To evaluate the constructed measure, we study its impact on the treasury market, stock market, and macroeconomic indicators. Our dataset, models, and code are publicly available on Huggingface and GitHub under CC BY-NC 4.0 license. ...