Estimating the roughness exponent of stochastic volatility from discrete observations of the integrated variance ArXiv ID: 2307.02582 “View on arXiv” Authors: Unknown Abstract We consider the problem of estimating the roughness of the volatility process in a stochastic volatility model that arises as a nonlinear function of fractional Brownian motion with drift. To this end, we introduce a new estimator that measures the so-called roughness exponent of a continuous trajectory, based on discrete observations of its antiderivative. The estimator has a very simple form and can be computed with great efficiency on large data sets. It is not derived from distributional assumptions but from strictly pathwise considerations. We provide conditions on the underlying trajectory under which our estimator converges in a strictly pathwise sense. Then we verify that these conditions are satisfied by almost every sample path of fractional Brownian motion (with drift). As a consequence, we obtain strong consistency theorems in the context of a large class of rough volatility models, such as the rough fractional volatility model and the rough Bergomi model. We also demonstrate that our estimator is robust with respect to proxy errors between the integrated and realized variance, and that it can be applied to estimate the roughness exponent directly from the price trajectory. Numerical simulations show that our estimation procedure performs well after passing to a scale-invariant modification of our estimator. ...

LOB-Based Deep Learning Models for Stock Price Trend Prediction: A Benchmark Study ArXiv ID: 2308.01915 “View on arXiv” Authors: Unknown Abstract The recent advancements in Deep Learning (DL) research have notably influenced the finance sector. We examine the robustness and generalizability of fifteen state-of-the-art DL models focusing on Stock Price Trend Prediction (SPTP) based on Limit Order Book (LOB) data. To carry out this study, we developed LOBCAST, an open-source framework that incorporates data preprocessing, DL model training, evaluation and profit analysis. Our extensive experiments reveal that all models exhibit a significant performance drop when exposed to new data, thereby raising questions about their real-world market applicability. Our work serves as a benchmark, illuminating the potential and the limitations of current approaches and providing insight for innovative solutions. ...

Noise reduction for functional time series ArXiv ID: 2307.02154 “View on arXiv” Authors: Unknown Abstract A novel method for noise reduction in the setting of curve time series with error contamination is proposed, based on extending the framework of functional principal component analysis (FPCA). We employ the underlying, finite-dimensional dynamics of the functional time series to separate the serially dependent dynamical part of the observed curves from the noise. Upon identifying the subspaces of the signal and idiosyncratic components, we construct a projection of the observed curve time series along the noise subspace, resulting in an estimate of the underlying denoised curves. This projection is optimal in the sense that it minimizes the mean integrated squared error. By applying our method to similated and real data, we show the denoising estimator is consistent and outperforms existing denoising techniques. Furthermore, we show it can be used as a pre-processing step to improve forecasting. ...

Online Learning of Order Flow and Market Impact with Bayesian Change-Point Detection Methods ArXiv ID: 2307.02375 “View on arXiv” Authors: Unknown Abstract Financial order flow exhibits a remarkable level of persistence, wherein buy (sell) trades are often followed by subsequent buy (sell) trades over extended periods. This persistence can be attributed to the division and gradual execution of large orders. Consequently, distinct order flow regimes might emerge, which can be identified through suitable time series models applied to market data. In this paper, we propose the use of Bayesian online change-point detection (BOCPD) methods to identify regime shifts in real-time and enable online predictions of order flow and market impact. To enhance the effectiveness of our approach, we have developed a novel BOCPD method using a score-driven approach. This method accommodates temporal correlations and time-varying parameters within each regime. Through empirical application to NASDAQ data, we have found that: (i) Our newly proposed model demonstrates superior out-of-sample predictive performance compared to existing models that assume i.i.d. behavior within each regime; (ii) When examining the residuals, our model demonstrates good specification in terms of both distributional assumptions and temporal correlations; (iii) Within a given regime, the price dynamics exhibit a concave relationship with respect to time and volume, mirroring the characteristics of actual large orders; (iv) By incorporating regime information, our model produces more accurate online predictions of order flow and market impact compared to models that do not consider regimes. ...

Robust Hedging GANs ArXiv ID: 2307.02310 “View on arXiv” Authors: Unknown Abstract The availability of deep hedging has opened new horizons for solving hedging problems under a large variety of realistic market conditions. At the same time, any model - be it a traditional stochastic model or a market generator - is at best an approximation of market reality, prone to model-misspecification and estimation errors. This raises the question, how to furnish a modelling setup with tools that can address the risk of discrepancy between anticipated distribution and market reality, in an automated way. Automated robustification is currently attracting increased attention in numerous investment problems, but it is a delicate task due to its imminent implications on risk management. Hence, it is beyond doubt that more activity can be anticipated on this topic to converge towards a consensus on best practices. This paper presents a natural extension of the original deep hedging framework to address uncertainty in the data generating process via an adversarial approach inspired by GANs to automate robustification in our hedging objective. This is achieved through an interplay of three modular components: (i) a (deep) hedging engine, (ii) a data-generating process (that is model agnostic permitting a large variety of classical models as well as machine learning-based market generators), and (iii) a notion of distance on model space to measure deviations between our market prognosis and reality. We do not restrict the ambiguity set to a region around a reference model, but instead penalize deviations from the anticipated distribution. Our suggested choice for each component is motivated by model agnosticism, allowing a seamless transition between settings. Since all individual components are already used in practice, we believe that our framework is easily adaptable to existing functional settings. ...

Shannon entropy to quantify complexity in the financial market ArXiv ID: 2307.08666 “View on arXiv” Authors: Unknown Abstract In this paper we study the complexity in the information traffic that occurs in the peruvian financial market, using the Shannon entropy. Different series of prices of shares traded on the Lima stock exchange are used to reconstruct the unknown dynamics. We present numerical simulations on the reconstructed dynamics and we calculate the Shannon entropy to measure its complexity ...

A Scalable Reinforcement Learning-based System Using On-Chain Data for Cryptocurrency Portfolio Management ArXiv ID: 2307.01599 “View on arXiv” Authors: Unknown Abstract On-chain data (metrics) of blockchain networks, akin to company fundamentals, provide crucial and comprehensive insights into the networks. Despite their informative nature, on-chain data have not been utilized in reinforcement learning (RL)-based systems for cryptocurrency (crypto) portfolio management (PM). An intriguing subject is the extent to which the utilization of on-chain data can enhance an RL-based system’s return performance compared to baselines. Therefore, in this study, we propose CryptoRLPM, a novel RL-based system incorporating on-chain data for end-to-end crypto PM. CryptoRLPM consists of five units, spanning from information comprehension to trading order execution. In CryptoRLPM, the on-chain data are tested and specified for each crypto to solve the issue of ineffectiveness of metrics. Moreover, the scalable nature of CryptoRLPM allows changes in the portfolios’ cryptos at any time. Backtesting results on three portfolios indicate that CryptoRLPM outperforms all the baselines in terms of accumulated rate of return (ARR), daily rate of return (DRR), and Sortino ratio (SR). Particularly, when compared to Bitcoin, CryptoRLPM enhances the ARR, DRR, and SR by at least 83.14%, 0.5603%, and 2.1767 respectively. ...

Asymptotics for the Generalized Autoregressive Conditional Duration Model ArXiv ID: 2307.01779 “View on arXiv” Authors: Unknown Abstract Engle and Russell (1998, Econometrica, 66:1127–1162) apply results from the GARCH literature to prove consistency and asymptotic normality of the (exponential) QMLE for the generalized autoregressive conditional duration (ACD) model, the so-called ACD(1,1), under the assumption of strict stationarity and ergodicity. The GARCH results, however, do not account for the fact that the number of durations over a given observation period is random. Thus, in contrast with Engle and Russell (1998), we show that strict stationarity and ergodicity alone are not sufficient for consistency and asymptotic normality, and provide additional sufficient conditions to account for the random number of durations. In particular, we argue that the durations need to satisfy the stronger requirement that they have finite mean. ...

MOPO-LSI: A User Guide ArXiv ID: 2307.01719 “View on arXiv” Authors: Unknown Abstract MOPO-LSI is an open-source Multi-Objective Portfolio Optimization Library for Sustainable Investments. This document provides a user guide for MOPO-LSI version 1.0, including problem setup, workflow and the hyper-parameters in configurations. Keywords: Multi-objective portfolio optimization, Sustainable investments, Open-source library, Hyper-parameter configuration, Multi-Asset (Sustainable/ESG) Complexity vs Empirical Score Math Complexity: 6.5/10 Empirical Rigor: 4.0/10 Quadrant: Lab Rats Why: The paper introduces substantial mathematical formulation for multi-objective optimization (weighted sums, convex optimization, MOEA algorithms) but provides only a user guide and workflow description, lacking backtesting results, performance metrics, or implementation-heavy data processing details. flowchart TD A["Research Goal<br>Optimize Sustainable Investment<br>Portfolios"] --> B["Inputs: ESG Scores &<br>Financial Data"] B --> C["Methodology: Multi-Objective<br>Optimization Setup"] C --> D["Computation:<br>MOPO-LSI Engine"] D --> E["Outputs: Pareto-optimal<br>Portfolios"] E --> F["Outcomes: Trade-off Analysis<br>between Return & Sustainability"]

Option Market Making via Reinforcement Learning ArXiv ID: 2307.01814 “View on arXiv” Authors: Unknown Abstract Market making of options with different maturities and strikes is a challenging problem due to its highly dimensional nature. In this paper, we propose a novel approach that combines a stochastic policy and reinforcement learning-inspired techniques to determine the optimal policy for posting bid-ask spreads for an options market maker who trades options with different maturities and strikes. ...