Equities

Quantitative statistical analysis of order-splitting behaviour of individual trading accounts in the Japanese stock market over nine years ArXiv ID: 2308.01112 “View on arXiv” Authors: Unknown Abstract In this research, we focus on the order-splitting behavior. The order splitting is a trading strategy to execute their large potential metaorder into small pieces to reduce transaction cost. This strategic behavior is believed to be important because it is a promising candidate for the microscopic origin of the long-range correlation (LRC) in the persistent order flow. Indeed, in 2005, Lillo, Mike, and Farmer (LMF) introduced a microscopic model of the order-splitting traders to predict the asymptotic behavior of the LRC from the microscopic dynamics, even quantitatively. The plausibility of this scenario has been qualitatively investigated by Toth et al. 2015. However, no solid support has been presented yet on the quantitative prediction by the LMF model in the lack of large microscopic datasets. In this report, we have provided the first quantitative statistical analysis of the order-splitting behavior at the level of each trading account. We analyse a large dataset of the Tokyo stock exchange (TSE) market over nine years, including the account data of traders (called virtual servers). The virtual server is a unit of trading accounts in the TSE market, and we can effectively define the trader IDs by an appropriate preprocessing. We apply a strategy clustering to individual traders to identify the order-splitting traders and the random traders. For most of the stocks, we find that the metaorder length distribution obeys power laws with exponent $α$, such that $P(L)\propto L^{"-α-1"}$ with the metaorder length $L$. By analysing the sign correlation $C(τ)\propto τ^{"-γ"}$, we directly confirmed the LMF prediction $γ\approx α-1$. Furthermore, we discuss how to estimate the total number of the splitting traders only from public data via the ACF prefactor formula in the LMF model. Our work provides the first quantitative evidence of the LMF model. ...

Graph Neural Networks for Forecasting Multivariate Realized Volatility with Spillover Effects ArXiv ID: 2308.01419 “View on arXiv” Authors: Unknown Abstract We present a novel methodology for modeling and forecasting multivariate realized volatilities using customized graph neural networks to incorporate spillover effects across stocks. The proposed model offers the benefits of incorporating spillover effects from multi-hop neighbors, capturing nonlinear relationships, and flexible training with different loss functions. Our empirical findings provide compelling evidence that incorporating spillover effects from multi-hop neighbors alone does not yield a clear advantage in terms of predictive accuracy. However, modeling nonlinear spillover effects enhances the forecasting accuracy of realized volatilities, particularly for short-term horizons of up to one week. Moreover, our results consistently indicate that training with the Quasi-likelihood loss leads to substantial improvements in model performance compared to the commonly-used mean squared error. A comprehensive series of empirical evaluations in alternative settings confirm the robustness of our results. ...

An exploration of the mathematical structure and behavioural biases of 21st century financial crises ArXiv ID: 2307.15402 “View on arXiv” Authors: Unknown Abstract In this paper we contrast the dynamics of the 2022 Ukraine invasion financial crisis with notable financial crises of the 21st century - the dot-com bubble, global financial crisis and COVID-19. We study the similarity in market dynamics and associated implications for equity investors between various financial market crises and we introduce new mathematical techniques to do so. First, we study the strength of collective dynamics during different market crises, and compare suitable portfolio diversification strategies with respect to the unique number of sectors and stocks for optimal systematic risk reduction. Next, we introduce a new linear operator method to quantify distributional distance between equity returns during various crises. Our method allows us to fairly compare underlying stock and sector performance during different time periods, normalising for those collective dynamics driven by the overall market. Finally, we introduce a new combinatorial portfolio optimisation framework driven by random sampling to investigate whether particular equities and equity sectors are more effective in maximising investor risk-adjusted returns during market crises. ...

Option Smile Volatility and Implied Probabilities: Implications of Concavity in IV Curves ArXiv ID: 2307.15718 “View on arXiv” Authors: Unknown Abstract Earnings announcements (EADs) are corporate events that provide investors with fundamentally important information. The prospect of stock price rises may also contribute to EADs increased volatility. Using data on extremely short term options, we study that bimodality in the risk neutral distribution and concavity in the IV smiles are ubiquitous characteristics before an earnings announcement day. This study compares the returns between concave and non concave IV smiles to see if the concavity in the IV curve leads to any information about the risk in the market and showcases how investors hedge against extreme volatility during earnings announcements. In fact, our paper shows in the presence of concave IV smiles; investors pay a significant premium to hedge against the uncertainty caused by the forthcoming announcement. ...

Capital Structure Theories and its Practice, A study with reference to select NSE listed public sectors banks, India ArXiv ID: 2307.14049 “View on arXiv” Authors: Unknown Abstract Among the various factors affecting the firms positioning and performance in modern day markets, capital structure of the firm has its own way of expressing itself as a crucial one. With the rapid changes in technology, firms are being pushed onto a paradigm that is burdening the capital management process. Hence the study of capital structure changes gives the investors an insight into firm’s behavior and intrinsic goals. These changes will vary for firms in different sectors. This work considers the banking sector, which has a unique capital structure for the given regulations of its operations in India. The capital structure behavioral changes in a few public sector banks are studied in this paper. A theoretical framework has been developed from the popular capital structure theories and hypotheses are derived from them accordingly. The main idea is to validate different theories with real time performance of the select banks from 2011 to 2022. Using statistical techniques like regression and correlation, tested hypotheses have resulted in establishing the relation between debt component and financial performance variables of the select banks which are helping in understanding the theories in practice. ...

Macroscopic Market Making ArXiv ID: 2307.14129 “View on arXiv” Authors: Unknown Abstract We propose a macroscopic market making model à la Avellaneda-Stoikov, using continuous processes for orders instead of discrete point processes. The model intends to bridge the gap between market making and optimal execution problems, while shedding light on the influence of order flows on the optimal strategies. We demonstrate our model through three problems. The study provides a comprehensive analysis from Markovian to non-Markovian noises and from linear to non-linear intensity functions, encompassing both bounded and unbounded coefficients. Mathematically, the contribution lies in the existence and uniqueness of the optimal control, guaranteed by the well-posedness of the strong solution to the Hamilton-Jacobi-Bellman equation and the (non-)Lipschitz forward-backward stochastic differential equation. Finally, the model’s applications to price impact and optimal execution are discussed. ...

Efficient Multi-Change Point Analysis to decode Economic Crisis Information from the S&P500 Mean Market Correlation ArXiv ID: 2308.00087 “View on arXiv” Authors: Unknown Abstract Identifying macroeconomic events that are responsible for dramatic changes of economy is of particular relevance to understand the overall economic dynamics. We introduce an open-source available efficient Python implementation of a Bayesian multi-trend change point analysis which solves significant memory and computing time limitations to extract crisis information from a correlation metric. Therefore, we focus on the recently investigated S&P500 mean market correlation in a period of roughly 20 years that includes the dot-com bubble, the global financial crisis and the Euro crisis. The analysis is performed two-fold: first, in retrospect on the whole dataset and second, in an on-line adaptive manner in pre-crisis segments. The on-line sensitivity horizon is roughly determined to be 80 up to 100 trading days after a crisis onset. A detailed comparison to global economic events supports the interpretation of the mean market correlation as an informative macroeconomic measure by a rather good agreement of change point distributions and major crisis events. Furthermore, the results hint to the importance of the U.S. housing bubble as trigger of the global financial crisis, provide new evidence for the general reasoning of locally (meta)stable economic states and could work as a comparative impact rating of specific economic events. ...

Transfer Learning for Portfolio Optimization ArXiv ID: 2307.13546 “View on arXiv” Authors: Unknown Abstract In this work, we explore the possibility of utilizing transfer learning techniques to address the financial portfolio optimization problem. We introduce a novel concept called “transfer risk”, within the optimization framework of transfer learning. A series of numerical experiments are conducted from three categories: cross-continent transfer, cross-sector transfer, and cross-frequency transfer. In particular, 1. a strong correlation between the transfer risk and the overall performance of transfer learning methods is established, underscoring the significance of transfer risk as a viable indicator of “transferability”; 2. transfer risk is shown to provide a computationally efficient way to identify appropriate source tasks in transfer learning, enhancing the efficiency and effectiveness of the transfer learning approach; 3. additionally, the numerical experiments offer valuable new insights for portfolio management across these different settings. ...

VolTS: A Volatility-based Trading System to forecast Stock Markets Trend using Statistics and Machine Learning ArXiv ID: 2307.13422 “View on arXiv” Authors: Unknown Abstract Volatility-based trading strategies have attracted a lot of attention in financial markets due to their ability to capture opportunities for profit from market dynamics. In this article, we propose a new volatility-based trading strategy that combines statistical analysis with machine learning techniques to forecast stock markets trend. The method consists of several steps including, data exploration, correlation and autocorrelation analysis, technical indicator use, application of hypothesis tests and statistical models, and use of variable selection algorithms. In particular, we use the k-means++ clustering algorithm to group the mean volatility of the nine largest stocks in the NYSE and NasdaqGS markets. The resulting clusters are the basis for identifying relationships between stocks based on their volatility behaviour. Next, we use the Granger Causality Test on the clustered dataset with mid-volatility to determine the predictive power of a stock over another stock. By identifying stocks with strong predictive relationships, we establish a trading strategy in which the stock acting as a reliable predictor becomes a trend indicator to determine the buy, sell, and hold of target stock trades. Through extensive backtesting and performance evaluation, we find the reliability and robustness of our volatility-based trading strategy. The results suggest that our approach effectively captures profitable trading opportunities by leveraging the predictive power of volatility clusters, and Granger causality relationships between stocks. The proposed strategy offers valuable insights and practical implications to investors and market participants who seek to improve their trading decisions and capitalize on market trends. It provides valuable insights and practical implications for market participants looking to. ...

Memory Effects, Multiple Time Scales and Local Stability in Langevin Models of the S&P500 Market Correlation ArXiv ID: 2307.12744 “View on arXiv” Authors: Unknown Abstract The analysis of market correlations is crucial for optimal portfolio selection of correlated assets, but their memory effects have often been neglected. In this work, we analyse the mean market correlation of the S&P500 which corresponds to the main market mode in principle component analysis. We fit a generalised Langevin equation (GLE) to the data whose memory kernel implies that there is a significant memory effect in the market correlation ranging back at least three trading weeks. The memory kernel improves the forecasting accuracy of the GLE compared to models without memory and hence, such a memory effect has to be taken into account for optimal portfolio selection to minimise risk or for predicting future correlations. Moreover, a Bayesian resilience estimation provides further evidence for non-Markovianity in the data and suggests the existence of a hidden slow time scale that operates on much slower times than the observed daily market data. Assuming that such a slow time scale exists, our work supports previous research on the existence of locally stable market states. ...