Over-the-Counter Market Making via Reinforcement Learning ArXiv ID: 2307.01816 “View on arXiv” Authors: Unknown Abstract The over-the-counter (OTC) market is characterized by a unique feature that allows market makers to adjust bid-ask spreads based on order size. However, this flexibility introduces complexity, transforming the market-making problem into a high-dimensional stochastic control problem that presents significant challenges. To address this, this paper proposes an innovative solution utilizing reinforcement learning techniques to tackle the OTC market-making problem. By assuming a linear inverse relationship between market order arrival intensity and bid-ask spreads, we demonstrate the optimal policy for bid-ask spreads follows a Gaussian distribution. We apply two reinforcement learning algorithms to conduct a numerical analysis, revealing the resulting return distribution and bid-ask spreads under different time and inventory levels. ...

Some challenges of calibrating differentiable agent-based models ArXiv ID: 2307.01085 “View on arXiv” Authors: Unknown Abstract Agent-based models (ABMs) are a promising approach to modelling and reasoning about complex systems, yet their application in practice is impeded by their complexity, discrete nature, and the difficulty of performing parameter inference and optimisation tasks. This in turn has sparked interest in the construction of differentiable ABMs as a strategy for combatting these difficulties, yet a number of challenges remain. In this paper, we discuss and present experiments that highlight some of these challenges, along with potential solutions. ...

Principal Component Analysis and Hidden Markov Model for Forecasting Stock Returns ArXiv ID: 2307.00459 “View on arXiv” Authors: Unknown Abstract This paper presents a method for predicting stock returns using principal component analysis (PCA) and the hidden Markov model (HMM) and tests the results of trading stocks based on this approach. Principal component analysis is applied to the covariance matrix of stock returns for companies listed in the S&P 500 index, and interpreting principal components as factor returns, we apply the HMM model on them. Then we use the transition probability matrix and state conditional means to forecast the factors returns. Reverting the factor returns forecasts to stock returns using eigenvectors, we obtain forecasts for the stock returns. We find that, with the right hyperparameters, our model yields a strategy that outperforms the buy-and-hold strategy in terms of the annualized Sharpe ratio. ...

Blockchain scaling and liquidity concentration on decentralized exchanges ArXiv ID: 2306.17742 “View on arXiv” Authors: Unknown Abstract Liquidity providers (LPs) on decentralized exchanges (DEXs) can protect themselves from adverse selection risk by updating their positions more frequently. However, repositioning is costly, because LPs have to pay gas fees for each update. We analyze the causal relation between repositioning and liquidity concentration around the market price, using the entry of blockchain scaling solutions, Arbitrum and Polygon, as our instruments. Lower gas fees on scaling solutions allow LPs to update more frequently than on Ethereum. Our results demonstrate that higher repositioning intensity and precision lead to greater liquidity concentration, which benefits small trades by reducing their slippage. ...

Decomposing cryptocurrency high-frequency price dynamics into recurring and noisy components ArXiv ID: 2306.17095 “View on arXiv” Authors: Unknown Abstract This paper investigates the temporal patterns of activity in the cryptocurrency market with a focus on Bitcoin, Ethereum, Dogecoin, and WINkLink from January 2020 to December 2022. Market activity measures - logarithmic returns, volume, and transaction number, sampled every 10 seconds, were divided into intraday and intraweek periods and then further decomposed into recurring and noise components via correlation matrix formalism. The key findings include the distinctive market behavior from traditional stock markets due to the nonexistence of trade opening and closing. This was manifest in three enhanced-activity phases aligning with Asian, European, and U.S. trading sessions. An intriguing pattern of activity surge in 15-minute intervals, particularly at full hours, was also noticed, implying the potential role of algorithmic trading. Most notably, recurring bursts of activity in bitcoin and ether were identified to coincide with the release times of significant U.S. macroeconomic reports such as Nonfarm payrolls, Consumer Price Index data, and Federal Reserve statements. The most correlated daily patterns of activity occurred in 2022, possibly reflecting the documented correlations with U.S. stock indices in the same period. Factors that are external to the inner market dynamics are found to be responsible for the repeatable components of the market dynamics, while the internal factors appear to be substantially random, which manifests itself in a good agreement between the empirical eigenvalue distributions in their bulk and the random matrix theory predictions expressed by the Marchenko-Pastur distribution. The findings reported support the growing integration of cryptocurrencies into the global financial markets. ...

Analysis of Indian foreign exchange markets: A Multifractal Detrended Fluctuation Analysis (MFDFA) approach ArXiv ID: 2306.16162 “View on arXiv” Authors: Unknown Abstract The multifractal spectra of daily foreign exchange rates for US dollar (USD), the British Pound (GBP), the Euro (Euro) and the Japanese Yen (Yen) with respect to the Indian Rupee are analysed for the period 6th January 1999 to 24th July 2018. We observe that the time series of logarithmic returns of all the four exchange rates exhibit features of multifractality. Next, we research the source of the observed multifractality. For this, we transform the return series in two ways: a) We randomly shuffle the original time series of logarithmic returns and b) We apply the process of phase randomisation on the unchanged series. Our results indicate in the case of the US dollar the source of multifractality is mainly the fat tail. For the British Pound and the Euro, we see the long-range correlations between the observations and the thick tails of the probability distribution give rise to the observed multifractal features, while in the case of the Japanese Yen, the origin of the multifractal nature of the return series is mostly due to the broad tail. ...

Continuous-time q-learning for mean-field control problems ArXiv ID: 2306.16208 “View on arXiv” Authors: Unknown Abstract This paper studies the q-learning, recently coined as the continuous time counterpart of Q-learning by Jia and Zhou (2023), for continuous time Mckean-Vlasov control problems in the setting of entropy-regularized reinforcement learning. In contrast to the single agent’s control problem in Jia and Zhou (2023), the mean-field interaction of agents renders the definition of the q-function more subtle, for which we reveal that two distinct q-functions naturally arise: (i) the integrated q-function (denoted by $q$) as the first-order approximation of the integrated Q-function introduced in Gu, Guo, Wei and Xu (2023), which can be learnt by a weak martingale condition involving test policies; and (ii) the essential q-function (denoted by $q_e$) that is employed in the policy improvement iterations. We show that two q-functions are related via an integral representation under all test policies. Based on the weak martingale condition and our proposed searching method of test policies, some model-free learning algorithms are devised. In two examples, one in LQ control framework and one beyond LQ control framework, we can obtain the exact parameterization of the optimal value function and q-functions and illustrate our algorithms with simulation experiments. ...

Evaluation of Reinforcement Learning Techniques for Trading on a Diverse Portfolio ArXiv ID: 2309.03202 “View on arXiv” Authors: Unknown Abstract This work seeks to answer key research questions regarding the viability of reinforcement learning over the S&P 500 index. The on-policy techniques of Value Iteration (VI) and State-action-reward-state-action (SARSA) are implemented along with the off-policy technique of Q-Learning. The models are trained and tested on a dataset comprising multiple years of stock market data from 2000-2023. The analysis presents the results and findings from training and testing the models using two different time periods: one including the COVID-19 pandemic years and one excluding them. The results indicate that including market data from the COVID-19 period in the training dataset leads to superior performance compared to the baseline strategies. During testing, the on-policy approaches (VI and SARSA) outperform Q-learning, highlighting the influence of bias-variance tradeoff and the generalization capabilities of simpler policies. However, it is noted that the performance of Q-learning may vary depending on the stability of future market conditions. Future work is suggested, including experiments with updated Q-learning policies during testing and trading diverse individual stocks. Additionally, the exploration of alternative economic indicators for training the models is proposed. ...

The Implied Views of Bond Traders on the Spot Equity Market ArXiv ID: 2306.16522 “View on arXiv” Authors: Unknown Abstract This study delves into the temporal dynamics within the equity market through the lens of bond traders. Recognizing that the riskless interest rate fluctuates over time, we leverage the Black-Derman-Toy model to trace its temporal evolution. To gain insights from a bond trader’s perspective, we focus on a specific type of bond: the zero-coupon bond. This paper introduces a pricing algorithm for this bond and presents a formula that can be used to ascertain its real value. By crafting an equation that juxtaposes the theoretical value of a zero-coupon bond with its actual value, we can deduce the risk-neutral probability. It is noteworthy that the risk-neutral probability correlates with variables like the instantaneous mean return, instantaneous volatility, and inherent upturn probability in the equity market. Examining these relationships enables us to discern the temporal shifts in these parameters. Our findings suggest that the mean starts at a negative value, eventually plateauing at a consistent level. The volatility, on the other hand, initially has a minimal positive value, peaks swiftly, and then stabilizes. Lastly, the upturn probability is initially significantly high, plunges rapidly, and ultimately reaches equilibrium. ...

Trend patterns statistics for assessing irreversibility in cryptocurrencies: time-asymmetry versus inefficiency ArXiv ID: 2307.08612 “View on arXiv” Authors: Unknown Abstract In this paper, we present a measure of time irreversibility using trend pattern statistics. We define the irreversibility index as the Kullback-Leibler divergence between the distribution of uptrends subsequences (increasing trends) and the corresponding downtrends subsequences distribution (decreasing trends) in a time series. We use this index to analyze the degree of irreversibility in log return series over time, specifically focusing on five cryptocurrencies: Bitcoin, Ethereum, Ripple, Litecoin, and Bitcoin Cash. Our analysis reveals a strong indication of irreversibility in all these cryptocurrencies and the characteristic evolves over time. We additionally evaluate the market efficiency for these cryptocurrencies based on a recently proposed information-theoretic measure. By comparing inefficiency and irreversibility, we explore the relationship between these statistical features. This comparison provides insight into the non-trivial relationship between inefficiency and irreversibility. ...