Doubly Robust Mean-CVaR Portfolio ArXiv ID: 2309.11693 “View on arXiv” Authors: Unknown Abstract In this study, we address the challenge of portfolio optimization, a critical aspect of managing investment risks and maximizing returns. The mean-CVaR portfolio is considered a promising method due to today’s unstable financial market crises like the COVID-19 pandemic. It incorporates expected returns into the CVaR, which considers the expected value of losses exceeding a specified probability level. However, the instability associated with the input parameter changes and estimation errors can deteriorate portfolio performance. Therefore in this study, we propose a Doubly Robust mean-CVaR Portfolio refined approach to the mean-CVaR portfolio optimization. Our method can solve the instability problem to simultaneously optimize the multiple levels of CVaRs and define uncertainty sets for the mean parameter to perform robust optimization. Theoretically, the proposed method can be formulated as a second-order cone programming problem which is the same formulation as traditional mean-variance portfolio optimization. In addition, we derive an estimation error bound of the proposed method for the finite-sample case. Finally, experiments with benchmark and real market data show that our proposed method exhibits better performance compared to existing portfolio optimization strategies. ...

Improving Portfolio Performance Using a Novel Method for Predicting Financial Regimes ArXiv ID: 2310.04536 “View on arXiv” Authors: Unknown Abstract This work extends a previous work in regime detection, which allowed trading positions to be profitably adjusted when a new regime was detected, to ex ante prediction of regimes, leading to substantial performance improvements over the earlier model, over all three asset classes considered (equities, commodities, and foreign exchange), over a test period of four years. The proposed new model is also benchmarked over this same period against a hidden Markov model, the most popular current model for financial regime prediction, and against an appropriate index benchmark for each asset class, in the case of the commodities model having a test period cost-adjusted cumulative return over four times higher than that expected from the index. Notably, the proposed model makes use of a contrarian trading strategy, not uncommon in the financial industry but relatively unexplored in machine learning models. The model also makes use of frequent short positions, something not always desirable to investors due to issues of both financial risk and ethics; however, it is discussed how further work could remove this reliance on shorting and allow the construction of a long-only version of the model. ...

Transformers versus LSTMs for electronic trading ArXiv ID: 2309.11400 “View on arXiv” Authors: Unknown Abstract With the rapid development of artificial intelligence, long short term memory (LSTM), one kind of recurrent neural network (RNN), has been widely applied in time series prediction. Like RNN, Transformer is designed to handle the sequential data. As Transformer achieved great success in Natural Language Processing (NLP), researchers got interested in Transformer’s performance on time series prediction, and plenty of Transformer-based solutions on long time series forecasting have come out recently. However, when it comes to financial time series prediction, LSTM is still a dominant architecture. Therefore, the question this study wants to answer is: whether the Transformer-based model can be applied in financial time series prediction and beat LSTM. To answer this question, various LSTM-based and Transformer-based models are compared on multiple financial prediction tasks based on high-frequency limit order book data. A new LSTM-based model called DLSTM is built and new architecture for the Transformer-based model is designed to adapt for financial prediction. The experiment result reflects that the Transformer-based model only has the limited advantage in absolute price sequence prediction. The LSTM-based models show better and more robust performance on difference sequence prediction, such as price difference and price movement. ...

Comparing effects of price limit and circuit breaker in stock exchanges by an agent-based model ArXiv ID: 2309.10220 “View on arXiv” Authors: Unknown Abstract The prevention of rapidly and steeply falling market prices is vital to avoid financial crisis. To this end, some stock exchanges implement a price limit or a circuit breaker, and there has been intensive investigation into which regulation best prevents rapid and large variations in price. In this study, we examine this question using an artificial market model that is an agent-based model for a financial market. Our findings show that the price limit and the circuit breaker basically have the same effect when the parameters, limit price range and limit time range, are the same. However, the price limit is less effective when limit the time range is smaller than the cancel time range. With the price limit, many sell orders are accumulated around the lower limit price, and when the lower limit price is changed before the accumulated sell orders are cancelled, it leads to the accumulation of sell orders of various prices. These accumulated sell orders essentially act as a wall against buy orders, thereby preventing price from rising. Caution should be taken in the sense that these results pertain to a limited situation. Specifically, our finding that the circuit breaker is better than the price limit should be adapted only in cases where the reason for falling prices is erroneous orders and when individual stocks are regulated. ...

Derivatives Sensitivities Computation under Heston Model on GPU ArXiv ID: 2309.10477 “View on arXiv” Authors: Unknown Abstract This report investigates the computation of option Greeks for European and Asian options under the Heston stochastic volatility model on GPU. We first implemented the exact simulation method proposed by Broadie and Kaya and used it as a baseline for precision and speed. We then proposed a novel method for computing Greeks using the Milstein discretisation method on GPU. Our results show that the proposed method provides a speed-up up to 200x compared to the exact simulation implementation and that it can be used for both European and Asian options. However, the accuracy of the GPU method for estimating Rho is inferior to the CPU method. Overall, our study demonstrates the potential of GPU for computing derivatives sensitivies with numerical methods. ...

Mean Absolute Directional Loss as a New Loss Function for Machine Learning Problems in Algorithmic Investment Strategies ArXiv ID: 2309.10546 “View on arXiv” Authors: Unknown Abstract This paper investigates the issue of an adequate loss function in the optimization of machine learning models used in the forecasting of financial time series for the purpose of algorithmic investment strategies (AIS) construction. We propose the Mean Absolute Directional Loss (MADL) function, solving important problems of classical forecast error functions in extracting information from forecasts to create efficient buy/sell signals in algorithmic investment strategies. Finally, based on the data from two different asset classes (cryptocurrencies: Bitcoin and commodities: Crude Oil), we show that the new loss function enables us to select better hyperparameters for the LSTM model and obtain more efficient investment strategies, with regard to risk-adjusted return metrics on the out-of-sample data. ...

PAMS: Platform for Artificial Market Simulations ArXiv ID: 2309.10729 “View on arXiv” Authors: Unknown Abstract This paper presents a new artificial market simulation platform, PAMS: Platform for Artificial Market Simulations. PAMS is developed as a Python-based simulator that is easily integrated with deep learning and enabling various simulation that requires easy users’ modification. In this paper, we demonstrate PAMS effectiveness through a study using agents predicting future prices by deep learning. ...

Sizing Strategies for Algorithmic Trading in Volatile Markets: A Study of Backtesting and Risk Mitigation Analysis ArXiv ID: 2309.09094 “View on arXiv” Authors: Unknown Abstract Backtest is a way of financial risk evaluation which helps to analyze how our trading algorithm would work in markets with past time frame. The high volatility situation has always been a critical situation which creates challenges for algorithmic traders. The paper investigates different models of sizing in financial trading and backtest to high volatility situations to understand how sizing models can lower the models of VaR during crisis events. Hence it tries to show that how crisis events with high volatility can be controlled using short and long positional size. The paper also investigates stocks with AR, ARIMA, LSTM, GARCH with ETF data. ...

Decentralised Finance and Automated Market Making: Predictable Loss and Optimal Liquidity Provision ArXiv ID: 2309.08431 “View on arXiv” Authors: Unknown Abstract Constant product markets with concentrated liquidity (CL) are the most popular type of automated market makers. In this paper, we characterise the continuous-time wealth dynamics of strategic LPs who dynamically adjust their range of liquidity provision in CL pools. Their wealth results from fee income, the value of their holdings in the pool, and rebalancing costs. Next, we derive a self-financing and closed-form optimal liquidity provision strategy where the width of the LP’s liquidity range is determined by the profitability of the pool (provision fees minus gas fees), the predictable losses (PL) of the LP’s position, and concentration risk. Concentration risk refers to the decrease in fee revenue if the marginal exchange rate (akin to the midprice in a limit order book) in the pool exits the LP’s range of liquidity. When the drift in the marginal rate is stochastic, we show how to optimally skew the range of liquidity to increase fee revenue and profit from the expected changes in the marginal rate. Finally, we use Uniswap v3 data to show that, on average, LPs have traded at a significant loss, and to show that the out-of-sample performance of our strategy is superior to the historical performance of LPs in the pool we consider. ...

Dynamic Time Warping for Lead-Lag Relationships in Lagged Multi-Factor Models ArXiv ID: 2309.08800 “View on arXiv” Authors: Unknown Abstract In multivariate time series systems, lead-lag relationships reveal dependencies between time series when they are shifted in time relative to each other. Uncovering such relationships is valuable in downstream tasks, such as control, forecasting, and clustering. By understanding the temporal dependencies between different time series, one can better comprehend the complex interactions and patterns within the system. We develop a cluster-driven methodology based on dynamic time warping for robust detection of lead-lag relationships in lagged multi-factor models. 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 algorithm is able to robustly detect lead-lag relationships in financial markets, which can be subsequently leveraged in trading strategies with significant economic benefits. ...