Global Neural Networks and The Data Scaling Effect in Financial Time Series Forecasting ArXiv ID: 2309.02072 “View on arXiv” Authors: Unknown Abstract Neural networks have revolutionized many empirical fields, yet their application to financial time series forecasting remains controversial. In this study, we demonstrate that the conventional practice of estimating models locally in data-scarce environments may underlie the mixed empirical performance observed in prior work. By focusing on volatility forecasting, we employ a dataset comprising over 10,000 global stocks and implement a global estimation strategy that pools information across cross-sections. Our econometric analysis reveals that forecasting accuracy improves markedly as the training dataset becomes larger and more heterogeneous. Notably, even with as little as 12 months of data, globally trained networks deliver robust predictions for individual stocks and portfolios that are not even in the training dataset. Furthermore, our interpretation of the model dynamics shows that these networks not only capture key stylized facts of volatility but also exhibit resilience to outliers and rapid adaptation to market regime changes. These findings underscore the importance of leveraging extensive and diverse datasets in financial forecasting and advocate for a shift from traditional local training approaches to integrated global estimation methods. ...

On statistical arbitrage under a conditional factor model of equity returns ArXiv ID: 2309.02205 “View on arXiv” Authors: Unknown Abstract We consider a conditional factor model for a multivariate portfolio of United States equities in the context of analysing a statistical arbitrage trading strategy. A state space framework underlies the factor model whereby asset returns are assumed to be a noisy observation of a linear combination of factor values and latent factor risk premia. Filter and state prediction estimates for the risk premia are retrieved in an online way. Such estimates induce filtered asset returns that can be compared to measurement observations, with large deviations representing candidate mean reversion trades. Further, in that the risk premia are modelled as time-varying quantities, non-stationarity in returns is de facto captured. We study an empirical trading strategy respectful of transaction costs, and demonstrate performance over a long history of 29 years, for both a linear and a non-linear state space model. Our results show that the model is competitive relative to the results of other methods, including simple benchmarks and other cutting-edge approaches as published in the literature. Also of note, while strategy performance degradation is noticed through time – especially for the most recent years – the strategy continues to offer compelling economics, and has scope for further advancement. ...

Optimal Management of DC Pension Plan with Inflation Risk and Tail VaR Constraint ArXiv ID: 2309.01936 “View on arXiv” Authors: Unknown Abstract This paper investigates an optimal investment problem under the tail Value at Risk (tail VaR, also known as expected shortfall, conditional VaR, average VaR) and portfolio insurance constraints confronted by a defined-contribution pension member. The member’s aim is to maximize the expected utility from the terminal wealth exceeding the minimum guarantee by investing his wealth in a cash bond, an inflation-linked bond and a stock. Due to the presence of the tail VaR constraint, the problem cannot be tackled by standard control tools. We apply the Lagrange method along with quantile optimization techniques to solve the problem. Through delicate analysis, the optimal investment output in closed-form and optimal investment strategy are derived. A numerical analysis is also provided to show how the constraints impact the optimal investment output and strategy. ...

FinDiff: Diffusion Models for Financial Tabular Data Generation ArXiv ID: 2309.01472 “View on arXiv” Authors: Unknown Abstract The sharing of microdata, such as fund holdings and derivative instruments, by regulatory institutions presents a unique challenge due to strict data confidentiality and privacy regulations. These challenges often hinder the ability of both academics and practitioners to conduct collaborative research effectively. The emergence of generative models, particularly diffusion models, capable of synthesizing data mimicking the underlying distributions of real-world data presents a compelling solution. This work introduces ‘FinDiff’, a diffusion model designed to generate real-world financial tabular data for a variety of regulatory downstream tasks, for example economic scenario modeling, stress tests, and fraud detection. The model uses embedding encodings to model mixed modality financial data, comprising both categorical and numeric attributes. The performance of FinDiff in generating synthetic tabular financial data is evaluated against state-of-the-art baseline models using three real-world financial datasets (including two publicly available datasets and one proprietary dataset). Empirical results demonstrate that FinDiff excels in generating synthetic tabular financial data with high fidelity, privacy, and utility. ...

INTAGS: Interactive Agent-Guided Simulation ArXiv ID: 2309.01784 “View on arXiv” Authors: Unknown Abstract In many applications involving multi-agent system (MAS), it is imperative to test an experimental (Exp) autonomous agent in a high-fidelity simulator prior to its deployment to production, to avoid unexpected losses in the real-world. Such a simulator acts as the environmental background (BG) agent(s), called agent-based simulator (ABS), aiming to replicate the complex real MAS. However, developing realistic ABS remains challenging, mainly due to the sequential and dynamic nature of such systems. To fill this gap, we propose a metric to distinguish between real and synthetic multi-agent systems, which is evaluated through the live interaction between the Exp and BG agents to explicitly account for the systems’ sequential nature. Specifically, we characterize the system/environment by studying the effect of a sequence of BG agents’ responses to the environment state evolution and take such effects’ differences as MAS distance metric; The effect estimation is cast as a causal inference problem since the environment evolution is confounded with the previous environment state. Importantly, we propose the Interactive Agent-Guided Simulation (INTAGS) framework to build a realistic ABS by optimizing over this novel metric. To adapt to any environment with interactive sequential decision making agents, INTAGS formulates the simulator as a stochastic policy in reinforcement learning. Moreover, INTAGS utilizes the policy gradient update to bypass differentiating the proposed metric such that it can support non-differentiable operations of multi-agent environments. Through extensive experiments, we demonstrate the effectiveness of INTAGS on an equity stock market simulation example. We show that using INTAGS to calibrate the simulator can generate more realistic market data compared to the state-of-the-art conditional Wasserstein Generative Adversarial Network approach. ...

Introducing the $σ$-Cell: Unifying GARCH, Stochastic Fluctuations and Evolving Mechanisms in RNN-based Volatility Forecasting ArXiv ID: 2309.01565 “View on arXiv” Authors: Unknown Abstract This paper introduces the $σ$-Cell, a novel Recurrent Neural Network (RNN) architecture for financial volatility modeling. Bridging traditional econometric approaches like GARCH with deep learning, the $σ$-Cell incorporates stochastic layers and time-varying parameters to capture dynamic volatility patterns. Our model serves as a generative network, approximating the conditional distribution of latent variables. We employ a log-likelihood-based loss function and a specialized activation function to enhance performance. Experimental results demonstrate superior forecasting accuracy compared to traditional GARCH and Stochastic Volatility models, making the next step in integrating domain knowledge with neural networks. ...

Mutual information maximizing quantum generative adversarial networks ArXiv ID: 2309.01363 “View on arXiv” Authors: Unknown Abstract One of the most promising applications in the era of Noisy Intermediate-Scale Quantum (NISQ) computing is quantum generative adversarial networks (QGANs), which offer significant quantum advantages over classical machine learning in various domains. However, QGANs suffer from mode collapse and lack explicit control over the features of generated outputs. To overcome these limitations, we propose InfoQGAN, a novel quantum-classical hybrid generative adversarial network that integrates the principles of InfoGAN with a QGAN architecture. Our approach employs a variational quantum circuit for data generation, a classical discriminator, and a Mutual Information Neural Estimator (MINE) to explicitly optimize the mutual information between latent codes and generated samples. Numerical simulations on synthetic 2D distributions and Iris dataset augmentation demonstrate that InfoQGAN effectively mitigates mode collapse while achieving robust feature disentanglement in the quantum generator. By leveraging these advantages, InfoQGAN not only enhances training stability but also improves data augmentation performance through controlled feature generation. These results highlight the potential of InfoQGAN as a foundational approach for advancing quantum generative modeling in the NISQ era. ...

iCOS: Option-Implied COS Method ArXiv ID: 2309.00943 “View on arXiv” Authors: Unknown Abstract This paper proposes the option-implied Fourier-cosine method, iCOS, for non-parametric estimation of risk-neutral densities, option prices, and option sensitivities. The iCOS method leverages the Fourier-based COS technique, proposed by Fang and Oosterlee (2008), by utilizing the option-implied cosine series coefficients. Notably, this procedure does not rely on any model assumptions about the underlying asset price dynamics, it is fully non-parametric, and it does not involve any numerical optimization. These features make it rather general and computationally appealing. Furthermore, we derive the asymptotic properties of the proposed non-parametric estimators and study their finite-sample behavior in Monte Carlo simulations. Our empirical analysis using S&P 500 index options and Amazon equity options illustrates the effectiveness of the iCOS method in extracting valuable information from option prices under different market conditions. Additionally, we apply our methodology to dissect and quantify observation and discretization errors in the VIX index. ...

Chance or Chaos? Fractal geometry aimed to inspect the nature of Bitcoin ArXiv ID: 2309.00390 “View on arXiv” Authors: Unknown Abstract The aim of this paper is to analyse the Bitcoin in order to shed some light on its nature and behaviour. We select 9 cryptocurrencies that account for almost 75% of total market capitalisation and compare their evolution with that of a wide variety of traditional assets: commodities with spot and futures contracts, treasury bonds, stock indices, growth and value stocks. Fractal geometry will be applied to carry out a careful statistical analysis of the performance of the Bitcoin returns. As a main conclusion, we have detected a high degree of persistence in its prices, which decreases the efficiency but increases its predictability. Moreover, we observe that the underlying technology influences price dynamics, with fully decentralised cryptocurrencies being the only ones to exhibit self-similarity features at any time scale. ...

Instabilities of Super-Time-Stepping Methods on the Heston Stochastic Volatility Model ArXiv ID: 2309.00540 “View on arXiv” Authors: Unknown Abstract This note explores in more details instabilities of explicit super-time-stepping schemes, such as the Runge-Kutta-Chebyshev or Runge-Kutta-Legendre schemes, noticed in the litterature, when applied to the Heston stochastic volatility model. The stability remarks are relevant beyond the scope of super-time-stepping schemes. Keywords: super-time-stepping schemes, Heston stochastic volatility model, Runge-Kutta-Chebyshev, numerical stability, stochastic differential equations, Equity (Derivatives Pricing) ...