PRIME: A Price-Reverting Impact Model of a cryptocurrency Exchange ArXiv ID: 2305.07559 “View on arXiv” Authors: Unknown Abstract In a financial exchange, market impact is a measure of the price change of an asset following a transaction. This is an important element of market microstructure, which determines the behaviour of the market following a trade. In this paper, we first provide a discussion on the market impact observed in the BTC/USD Futures market, then we present a novel multi-agent market simulation that can follow an underlying price series, whilst maintaining the ability to reproduce the market impact observed in the market in an explainable manner. This simulation of the financial exchange allows the model to interact realistically with market participants, helping its users better estimate market slippage as well as the knock-on consequences of their market actions. In turn, it allows various stakeholders such as industrial practitioners, governments and regulators to test their market hypotheses, without deploying capital or destabilising the system. ...

Towards Generalizable Reinforcement Learning for Trade Execution ArXiv ID: 2307.11685 “View on arXiv” Authors: Unknown Abstract Optimized trade execution is to sell (or buy) a given amount of assets in a given time with the lowest possible trading cost. Recently, reinforcement learning (RL) has been applied to optimized trade execution to learn smarter policies from market data. However, we find that many existing RL methods exhibit considerable overfitting which prevents them from real deployment. In this paper, we provide an extensive study on the overfitting problem in optimized trade execution. First, we model the optimized trade execution as offline RL with dynamic context (ORDC), where the context represents market variables that cannot be influenced by the trading policy and are collected in an offline manner. Under this framework, we derive the generalization bound and find that the overfitting issue is caused by large context space and limited context samples in the offline setting. Accordingly, we propose to learn compact representations for context to address the overfitting problem, either by leveraging prior knowledge or in an end-to-end manner. To evaluate our algorithms, we also implement a carefully designed simulator based on historical limit order book (LOB) data to provide a high-fidelity benchmark for different algorithms. Our experiments on the high-fidelity simulator demonstrate that our algorithms can effectively alleviate overfitting and achieve better performance. ...

Copula-Based Trading of Cointegrated Cryptocurrency Pairs ArXiv ID: 2305.06961 “View on arXiv” Authors: Unknown Abstract This research introduces a novel pairs trading strategy based on copulas for cointegrated pairs of cryptocurrencies. To identify the most suitable pairs, the study employs linear and non-linear cointegration tests along with a correlation coefficient measure and fits different copula families to generate trading signals formulated from a reference asset for analyzing the mispricing index. The strategy’s performance is then evaluated by conducting back-testing for various triggers of opening positions, assessing its returns and risks. The findings indicate that the proposed method outperforms buy-and-hold trading strategies in terms of both profitability and risk-adjusted returns. ...

Robust Detection of Lead-Lag Relationships in Lagged Multi-Factor Models ArXiv ID: 2305.06704 “View on arXiv” Authors: Unknown Abstract In multivariate time series systems, key insights can be obtained by discovering lead-lag relationships inherent in the data, which refer to the dependence between two time series shifted in time relative to one another, and which can be leveraged for the purposes of control, forecasting or clustering. We develop a clustering-driven methodology for robust detection of lead-lag relationships in lagged multi-factor models. Within our framework, the envisioned pipeline takes as input a set of time series, and creates an enlarged universe of extracted subsequence time series from each input time series, via a sliding window approach. This is then followed by an application of various clustering techniques, (such as k-means++ and spectral clustering), employing a variety of pairwise similarity measures, including nonlinear ones. Once the clusters have been extracted, lead-lag estimates across clusters are robustly aggregated to enhance the identification of the consistent relationships in the original universe. We establish connections to the multireference alignment problem for both the homogeneous and heterogeneous settings. Since multivariate time series are ubiquitous in a wide range of domains, we demonstrate that our method is not only able to robustly detect lead-lag relationships in financial markets, but can also yield insightful results when applied to an environmental data set. ...

Backward Hedging for American Options with Transaction Costs ArXiv ID: 2305.06805 “View on arXiv” Authors: Unknown Abstract In this article, we introduce an algorithm called Backward Hedging, designed for hedging European and American options while considering transaction costs. The optimal strategy is determined by minimizing an appropriate loss function, which is based on either a risk measure or the mean squared error of the hedging strategy at maturity. The proposed algorithm moves backward in time, determining, for each time-step and different market states, the optimal hedging strategy that minimizes the loss function at the time the option is exercised, by assuming that the strategy used in the future for hedging the liability is the one determined at the previous steps of the algorithm. The approach avoids machine learning and instead relies on classic optimization techniques, Monte Carlo simulations, and interpolations on a grid. Comparisons with the Deep Hedging algorithm in various numerical experiments showcase the efficiency and accuracy of the proposed method. ...

On the Time-Varying Structure of the Arbitrage Pricing Theory using the Japanese Sector Indices ArXiv ID: 2305.05998 “View on arXiv” Authors: Unknown Abstract This paper is the first study to examine the time instability of the APT in the Japanese stock market. In particular, we measure how changes in each risk factor affect the stock risk premiums to investigate the validity of the APT over time, applying the rolling window method to Fama and MacBeth’s (1973) two-step regression and Kamstra and Shi’s (2023) generalized GRS test. We summarize our empirical results as follows: (1) the changes in monetary policy by major central banks greatly affect the validity of the APT in Japan, and (2) the time-varying estimates of the risk premiums for each factor are also unstable over time, and they are affected by the business cycle and economic crises. Therefore, we conclude that the validity of the APT as an appropriate model to explain the Japanese sector index is not stable over time. ...

The FRTB-IMA computational challenge for Equity Autocallables ArXiv ID: 2305.06215 “View on arXiv” Authors: Unknown Abstract When the Orthogonal Chebyshev Sliding Technique was introduced it was applied to a portfolio of swaps and swaptions within the context of the FRTB-IMA capital calculation. The computational cost associated to the computation of the ES values - an essential component of the capital caluclation under FRTB-IMA - was reduced by more than $90%$ while passing PLA tests. This paper extends the use of the Orthogonal Chebyshev Sliding Technique to portfolios of equity autocallables defined over a range of spot underlyings. Results are very positive as computational reductions are of about $90%$ with passing PLA metrics. Since equity autocallables are a commonly traded exotic trade type, with significant FRTB-IMA computational costs, the extension presented in this paper constitutes an imporant step forward in tackling the computational challenges associated to an efficient FRTB-IMA implementation. ...

Copula Variational LSTM for High-dimensional Cross-market Multivariate Dependence Modeling ArXiv ID: 2305.08778 “View on arXiv” Authors: Unknown Abstract We address an important yet challenging problem - modeling high-dimensional dependencies across multivariates such as financial indicators in heterogeneous markets. In reality, a market couples and influences others over time, and the financial variables of a market are also coupled. We make the first attempt to integrate variational sequential neural learning with copula-based dependence modeling to characterize both temporal observable and latent variable-based dependence degrees and structures across non-normal multivariates. Our variational neural network WPVC-VLSTM models variational sequential dependence degrees and structures across multivariate time series by variational long short-term memory networks and regular vine copula. The regular vine copula models nonnormal and long-range distributional couplings across multiple dynamic variables. WPVC-VLSTM is verified in terms of both technical significance and portfolio forecasting performance. It outperforms benchmarks including linear models, stochastic volatility models, deep neural networks, and variational recurrent networks in cross-market portfolio forecasting. ...

Proofs that the Gerber Statistic is Positive Semidefinite ArXiv ID: 2305.05663 “View on arXiv” Authors: Unknown Abstract In this brief note, we prove that both forms of the Gerber statistic introduced in Gerber et al. (2022) are positive semi-definite. Keywords: Gerber Statistic, Positive Semi-Definite, Risk Management, Dependence Modeling, General (Risk Measurement) Complexity vs Empirical Score Math Complexity: 8.5/10 Empirical Rigor: 2.0/10 Quadrant: Lab Rats Why: The paper is dense with advanced linear algebra proofs, demonstrating matrix transformations and series expansions to establish positive semidefiniteness, which is a purely theoretical property with no practical implementation details provided. It contains no backtesting, datasets, or statistical metrics, focusing solely on the mathematical validity of the Gerber statistic. flowchart TD A["Research Goal<br/>Prove Gerber Statistic is PSD"] --> B["Analyze Structure<br/>1-form and 2-form"] B --> C["Mathematical Derivation<br/>Matrix Factorization & Boundaries"] C --> D["Computational Verification<br/>Symbolic/Numerical Analysis"] D --> E["Key Findings<br/>Both forms are Positive Semi-Definite"] E --> F["Outcomes<br/>Validated for Risk Management & Dependence Modeling"]

Temporal and Heterogeneous Graph Neural Network for Financial Time Series Prediction ArXiv ID: 2305.08740 “View on arXiv” Authors: Unknown Abstract The price movement prediction of stock market has been a classical yet challenging problem, with the attention of both economists and computer scientists. In recent years, graph neural network has significantly improved the prediction performance by employing deep learning on company relations. However, existing relation graphs are usually constructed by handcraft human labeling or nature language processing, which are suffering from heavy resource requirement and low accuracy. Besides, they cannot effectively response to the dynamic changes in relation graphs. Therefore, in this paper, we propose a temporal and heterogeneous graph neural network-based (THGNN) approach to learn the dynamic relations among price movements in financial time series. In particular, we first generate the company relation graph for each trading day according to their historic price. Then we leverage a transformer encoder to encode the price movement information into temporal representations. Afterward, we propose a heterogeneous graph attention network to jointly optimize the embeddings of the financial time series data by transformer encoder and infer the probability of target movements. Finally, we conduct extensive experiments on the stock market in the United States and China. The results demonstrate the effectiveness and superior performance of our proposed methods compared with state-of-the-art baselines. Moreover, we also deploy the proposed THGNN in a real-world quantitative algorithm trading system, the accumulated portfolio return obtained by our method significantly outperforms other baselines. ...