A Mean Field Game between Informed Traders and a Broker ArXiv ID: 2401.05257 “View on arXiv” Authors: Unknown Abstract We find closed-form solutions to the stochastic game between a broker and a mean-field of informed traders. In the finite player game, the informed traders observe a common signal and a private signal. The broker, on the other hand, observes the trading speed of each of his clients and provides liquidity to the informed traders. Each player in the game optimises wealth adjusted by inventory penalties. In the mean field version of the game, using a Gâteaux derivative approach, we characterise the solution to the game with a system of forward-backward stochastic differential equations that we solve explicitly. We find that the optimal trading strategy of the broker is linear on his own inventory, on the average inventory among informed traders, and on the common signal or the average trading speed of the informed traders. The Nash equilibrium we find helps informed traders decide how to use private information, and helps brokers decide how much of the order flow they should externalise or internalise when facing a large number of clients. ...

Boundary conditions at infinity for Black-Scholes equations ArXiv ID: 2401.05549 “View on arXiv” Authors: Unknown Abstract We propose a numerical procedure for computing the prices of European options, in which the underlying asset price is a Markovian strict local martingale. If the underlying process is a strict local martingale and the payoff is of linear growth, multiple solutions exist for the corresponding Black-Scholes equations. When numerical schemes such as finite difference methods are applied, a boundary condition at infinity must be specified, which determines a solution among the candidates. The minimal solution, which is considered as the derivative price, is obtained by our boundary condition. The stability of our procedure is supported by the fact that our numerical solution satisfies a discrete maximum principle. In addition, its accuracy is demonstrated through numerical experiments in comparison with the methods proposed in the literature. ...

CNN-DRL for Scalable Actions in Finance ArXiv ID: 2401.06179 “View on arXiv” Authors: Unknown Abstract The published MLP-based DRL in finance has difficulties in learning the dynamics of the environment when the action scale increases. If the buying and selling increase to one thousand shares, the MLP agent will not be able to effectively adapt to the environment. To address this, we designed a CNN agent that concatenates the data from the last ninety days of the daily feature vector to create the CNN input matrix. Our extensive experiments demonstrate that the MLP-based agent experiences a loss corresponding to the initial environment setup, while our designed CNN remains stable, effectively learns the environment, and leads to an increase in rewards. ...

Comparison of Markowitz Model and Single-Index Model on Portfolio Selection of Malaysian Stocks ArXiv ID: 2401.05264 “View on arXiv” Authors: Unknown Abstract Our article is focused on the application of Markowitz Portfolio Theory and the Single Index Model on 10-year historical monthly return data for 10 stocks included in FTSE Bursa Malaysia KLCI, which is also our market index, as well as a risk-free asset which is the monthly fixed deposit rate. We will calculate the minimum variance portfolio and maximum Sharpe portfolio for both the Markowitz model and Single Index model subject to five different constraints, with the results presented in the form of tables and graphs such that comparisons between the different models and constraints can be made. We hope this article will help provide useful information for future investors who are interested in the Malaysian stock market and would like to construct an efficient investment portfolio. Keywords: Markowitz Portfolio Theory, Single Index Model, FTSE Bursa Malaysia KLCI, Efficient Portfolio ...

Markowitz Portfolio Construction at Seventy ArXiv ID: 2401.05080 “View on arXiv” Authors: Unknown Abstract More than seventy years ago Harry Markowitz formulated portfolio construction as an optimization problem that trades off expected return and risk, defined as the standard deviation of the portfolio returns. Since then the method has been extended to include many practical constraints and objective terms, such as transaction cost or leverage limits. Despite several criticisms of Markowitz’s method, for example its sensitivity to poor forecasts of the return statistics, it has become the dominant quantitative method for portfolio construction in practice. In this article we describe an extension of Markowitz’s method that addresses many practical effects and gracefully handles the uncertainty inherent in return statistics forecasting. Like Markowitz’s original formulation, the extension is also a convex optimization problem, which can be solved with high reliability and speed. ...

Can ChatGPT Compute Trustworthy Sentiment Scores from Bloomberg Market Wraps? ArXiv ID: 2401.05447 “View on arXiv” Authors: Unknown Abstract We used a dataset of daily Bloomberg Financial Market Summaries from 2010 to 2023, reposted on large financial media, to determine how global news headlines may affect stock market movements using ChatGPT and a two-stage prompt approach. We document a statistically significant positive correlation between the sentiment score and future equity market returns over short to medium term, which reverts to a negative correlation over longer horizons. Validation of this correlation pattern across multiple equity markets indicates its robustness across equity regions and resilience to non-linearity, evidenced by comparison of Pearson and Spearman correlations. Finally, we provide an estimate of the optimal horizon that strikes a balance between reactivity to new information and correlation. ...

Expiring Assets in Automated Market Makers ArXiv ID: 2401.04289 “View on arXiv” Authors: Unknown Abstract An automated market maker (AMM) is a state machine that manages pools of assets, allowing parties to buy and sell those assets according to a fixed mathematical formula. AMMs are typically implemented as smart contracts on blockchains, and its prices are kept in line with the overall market price by arbitrage: if the AMM undervalues an asset with respect to the market, an “arbitrageur” can make a risk-free profit by buying just enough of that asset to bring the AMM’s price back in line with the market. AMMs, however, are not designed for assets that expire: that is, assets that cannot be produced or resold after a specified date. As assets approach expiration, arbitrage may not be able to reconcile supply and demand, and the liquidity providers that funded the AMM may have excessive exposure to risk due to rapid price variations. This paper formally describes the design of a decentralized exchange (DEX) for assets that expire, combining aspects of AMMs and limit-order books. We ensure liveness and market clearance, providing mechanisms for liquidity providers to control their exposure to risk and adjust prices dynamically in response to situations where arbitrage may fail. ...

Scaling Laws And Statistical Properties of The Transaction Flows And Holding Times of Bitcoin ArXiv ID: 2401.04702 “View on arXiv” Authors: Unknown Abstract We study the temporal evolution of the holding-time distribution of bitcoins and find that the average distribution of holding-time is a heavy-tailed power law extending from one day to over at least $200$ weeks with an exponent approximately equal to $0.9$, indicating very long memory effects. We also report significant sample-to-sample variations of the distribution of holding times, which can be best characterized as multiscaling, with power-law exponents varying between $0.3$ and $2.5$ depending on bitcoin price regimes. We document significant differences between the distributions of book-to-market and of realized returns, showing that traders obtain far from optimal performance. We also report strong direct qualitative and quantitative evidence of the disposition effect in the Bitcoin Blockchain data. Defining age-dependent transaction flows as the fraction of bitcoins that are traded at a given time and that were born (last traded) at some specific earlier time, we document that the time-averaged transaction flow fraction has a power law dependence as a function of age, with an exponent close to $-1.5$, a value compatible with priority queuing theory. We document the existence of multifractality on the measure defined as the normalized number of bitcoins exchanged at a given time. ...

An adaptive network-based approach for advanced forecasting of cryptocurrency values ArXiv ID: 2401.05441 “View on arXiv” Authors: Unknown Abstract This paper describes an architecture for predicting the price of cryptocurrencies for the next seven days using the Adaptive Network Based Fuzzy Inference System (ANFIS). Historical data of cryptocurrencies and indexes that are considered are Bitcoin (BTC), Ethereum (ETH), Bitcoin Dominance (BTC.D), and Ethereum Dominance (ETH.D) in a daily timeframe. The methods used to teach the data are hybrid and backpropagation algorithms, as well as grid partition, subtractive clustering, and Fuzzy C-means clustering (FCM) algorithms, which are used in data clustering. The architectural performance designed in this paper has been compared with different inputs and neural network models in terms of statistical evaluation criteria. Finally, the proposed method can predict the price of digital currencies in a short time. ...

Can Large Language Models Beat Wall Street? Unveiling the Potential of AI in Stock Selection ArXiv ID: 2401.03737 “View on arXiv” Authors: Unknown Abstract This paper introduces MarketSenseAI, an innovative framework leveraging GPT-4’s advanced reasoning for selecting stocks in financial markets. By integrating Chain of Thought and In-Context Learning, MarketSenseAI analyzes diverse data sources, including market trends, news, fundamentals, and macroeconomic factors, to emulate expert investment decision-making. The development, implementation, and validation of the framework are elaborately discussed, underscoring its capability to generate actionable and interpretable investment signals. A notable feature of this work is employing GPT-4 both as a predictive mechanism and signal evaluator, revealing the significant impact of the AI-generated explanations on signal accuracy, reliability and acceptance. Through empirical testing on the competitive S&P 100 stocks over a 15-month period, MarketSenseAI demonstrated exceptional performance, delivering excess alpha of 10% to 30% and achieving a cumulative return of up to 72% over the period, while maintaining a risk profile comparable to the broader market. Our findings highlight the transformative potential of Large Language Models in financial decision-making, marking a significant leap in integrating generative AI into financial analytics and investment strategies. ...