Understanding the worst-kept secret of high-frequency trading ArXiv ID: 2307.15599 “View on arXiv” Authors: Unknown Abstract Volume imbalance in a limit order book is often considered as a reliable indicator for predicting future price moves. In this work, we seek to analyse the nuances of the relationship between prices and volume imbalance. To this end, we study a market-making problem which allows us to view the imbalance as an optimal response to price moves. In our model, there is an underlying efficient price driving the mid-price, which follows the model with uncertainty zones. A single market maker knows the underlying efficient price and consequently the probability of a mid-price jump in the future. She controls the volumes she quotes at the best bid and ask prices. Solving her optimization problem allows us to understand endogenously the price-imbalance connection and to confirm in particular that it is optimal to quote a predictive imbalance. Our model can also be used by a platform to select a suitable tick size, which is known to be a crucial topic in financial regulation. The value function of the market maker’s control problem can be viewed as a family of functions, indexed by the level of the market maker’s inventory, solving a coupled system of PDEs. We show existence and uniqueness of classical solutions to this coupled system of equations. In the case of a continuous inventory, we also prove uniqueness of the market maker’s optimal control policy. ...

An Ensemble Method of Deep Reinforcement Learning for Automated Cryptocurrency Trading ArXiv ID: 2309.00626 “View on arXiv” Authors: Unknown Abstract We propose an ensemble method to improve the generalization performance of trading strategies trained by deep reinforcement learning algorithms in a highly stochastic environment of intraday cryptocurrency portfolio trading. We adopt a model selection method that evaluates on multiple validation periods, and propose a novel mixture distribution policy to effectively ensemble the selected models. We provide a distributional view of the out-of-sample performance on granular test periods to demonstrate the robustness of the strategies in evolving market conditions, and retrain the models periodically to address non-stationarity of financial data. Our proposed ensemble method improves the out-of-sample performance compared with the benchmarks of a deep reinforcement learning strategy and a passive investment strategy. ...

Machine Learning-powered Pricing of the Multidimensional Passport Option ArXiv ID: 2307.14887 “View on arXiv” Authors: Unknown Abstract Introduced in the late 90s, the passport option gives its holder the right to trade in a market and receive any positive gain in the resulting traded account at maturity. Pricing the option amounts to solving a stochastic control problem that for $d>1$ risky assets remains an open problem. Even in a correlated Black-Scholes (BS) market with $d=2$ risky assets, no optimal trading strategy has been derived in closed form. In this paper, we derive a discrete-time solution for multi-dimensional BS markets with uncorrelated assets. Moreover, inspired by the success of deep reinforcement learning in, e.g., board games, we propose two machine learning-powered approaches to pricing general options on a portfolio value in general markets. These approaches prove to be successful for pricing the passport option in one-dimensional and multi-dimensional uncorrelated BS markets. ...

Option Smile Volatility and Implied Probabilities: Implications of Concavity in IV Curves ArXiv ID: 2307.15718 “View on arXiv” Authors: Unknown Abstract Earnings announcements (EADs) are corporate events that provide investors with fundamentally important information. The prospect of stock price rises may also contribute to EADs increased volatility. Using data on extremely short term options, we study that bimodality in the risk neutral distribution and concavity in the IV smiles are ubiquitous characteristics before an earnings announcement day. This study compares the returns between concave and non concave IV smiles to see if the concavity in the IV curve leads to any information about the risk in the market and showcases how investors hedge against extreme volatility during earnings announcements. In fact, our paper shows in the presence of concave IV smiles; investors pay a significant premium to hedge against the uncertainty caused by the forthcoming announcement. ...

American options in time-dependent one-factor models: Semi-analytic pricing, numerical methods and ML support ArXiv ID: 2307.13870 “View on arXiv” Authors: Unknown Abstract Semi-analytical pricing of American options in a time-dependent Ornstein-Uhlenbeck model was presented in [“Carr, Itkin, 2020”]. It was shown that to obtain these prices one needs to solve (numerically) a nonlinear Volterra integral equation of the second kind to find the exercise boundary (which is a function of the time only). Once this is done, the option prices follow. It was also shown that computationally this method is as efficient as the forward finite difference solver while providing better accuracy and stability. Later this approach called “the Generalized Integral transform” method has been significantly extended by the authors (also, in cooperation with Peter Carr and Alex Lipton) to various time-dependent one factor, and stochastic volatility models as applied to pricing barrier options. However, for American options, despite possible, this was not explicitly reported anywhere. In this paper our goal is to fill this gap and also discuss which numerical method (including those in machine learning) could be efficient to solve the corresponding Volterra integral equations. ...

Capital Structure Theories and its Practice, A study with reference to select NSE listed public sectors banks, India ArXiv ID: 2307.14049 “View on arXiv” Authors: Unknown Abstract Among the various factors affecting the firms positioning and performance in modern day markets, capital structure of the firm has its own way of expressing itself as a crucial one. With the rapid changes in technology, firms are being pushed onto a paradigm that is burdening the capital management process. Hence the study of capital structure changes gives the investors an insight into firm’s behavior and intrinsic goals. These changes will vary for firms in different sectors. This work considers the banking sector, which has a unique capital structure for the given regulations of its operations in India. The capital structure behavioral changes in a few public sector banks are studied in this paper. A theoretical framework has been developed from the popular capital structure theories and hypotheses are derived from them accordingly. The main idea is to validate different theories with real time performance of the select banks from 2011 to 2022. Using statistical techniques like regression and correlation, tested hypotheses have resulted in establishing the relation between debt component and financial performance variables of the select banks which are helping in understanding the theories in practice. ...

Derivative Pricing using Quantum Signal Processing ArXiv ID: 2307.14310 “View on arXiv” Authors: Unknown Abstract Pricing financial derivatives on quantum computers typically includes quantum arithmetic components which contribute heavily to the quantum resources required by the corresponding circuits. In this manuscript, we introduce a method based on Quantum Signal Processing (QSP) to encode financial derivative payoffs directly into quantum amplitudes, alleviating the quantum circuits from the burden of costly quantum arithmetic. Compared to current state-of-the-art approaches in the literature, we find that for derivative contracts of practical interest, the application of QSP significantly reduces the required resources across all metrics considered, most notably the total number of T-gates by $\sim 16$x and the number of logical qubits by $\sim 4$x. Additionally, we estimate that the logical clock rate needed for quantum advantage is also reduced by a factor of $\sim 5$x. Overall, we find that quantum advantage will require $4.7$k logical qubits, and quantum devices that can execute $10^9$ T-gates at a rate of $45$MHz. While in this work we focus specifically on the payoff component of the derivative pricing process where the method we present is most readily applicable, similar techniques can be employed to further reduce the resources in other applications, such as state preparation. ...

Financial Machine Learning ArXiv ID: ssrn-4520856 “View on arXiv” Authors: Unknown Abstract Click link for full abstract. Keywords: Unknown Complexity vs Empirical Score Math Complexity: 7.0/10 Empirical Rigor: 3.0/10 Quadrant: Lab Rats Why: The paper is a survey of financial machine learning literature, featuring advanced mathematical concepts (e.g., econometric formulations, expectation operators, and probability theory) throughout, but it lacks original backtests, datasets, or implementation code, focusing instead on theoretical frameworks and methodological reviews. flowchart TD A["Research Goal: Apply ML to Financial Markets"] --> B["Data: Asset Prices & Economic Indicators"] B --> C["Preprocessing: Feature Engineering & Normalization"] C --> D["Model Selection: Supervised & Unsupervised Algorithms"] D --> E["Computational Process: Backtesting & Cross-Validation"] E --> F["Outcomes: Alpha Generation & Risk Metrics"] F --> G["Key Finding: Trade-off between Complexity and Overfitting"]

Macroscopic Market Making ArXiv ID: 2307.14129 “View on arXiv” Authors: Unknown Abstract We propose a macroscopic market making model à la Avellaneda-Stoikov, using continuous processes for orders instead of discrete point processes. The model intends to bridge the gap between market making and optimal execution problems, while shedding light on the influence of order flows on the optimal strategies. We demonstrate our model through three problems. The study provides a comprehensive analysis from Markovian to non-Markovian noises and from linear to non-linear intensity functions, encompassing both bounded and unbounded coefficients. Mathematically, the contribution lies in the existence and uniqueness of the optimal control, guaranteed by the well-posedness of the strong solution to the Hamilton-Jacobi-Bellman equation and the (non-)Lipschitz forward-backward stochastic differential equation. Finally, the model’s applications to price impact and optimal execution are discussed. ...

Modeling Inverse Demand Function with Explainable Dual Neural Networks ArXiv ID: 2307.14322 “View on arXiv” Authors: Unknown Abstract Financial contagion has been widely recognized as a fundamental risk to the financial system. Particularly potent is price-mediated contagion, wherein forced liquidations by firms depress asset prices and propagate financial stress, enabling crises to proliferate across a broad spectrum of seemingly unrelated entities. Price impacts are currently modeled via exogenous inverse demand functions. However, in real-world scenarios, only the initial shocks and the final equilibrium asset prices are typically observable, leaving actual asset liquidations largely obscured. This missing data presents significant limitations to calibrating the existing models. To address these challenges, we introduce a novel dual neural network structure that operates in two sequential stages: the first neural network maps initial shocks to predicted asset liquidations, and the second network utilizes these liquidations to derive resultant equilibrium prices. This data-driven approach can capture both linear and non-linear forms without pre-specifying an analytical structure; furthermore, it functions effectively even in the absence of observable liquidation data. Experiments with simulated datasets demonstrate that our model can accurately predict equilibrium asset prices based solely on initial shocks, while revealing a strong alignment between predicted and true liquidations. Our explainable framework contributes to the understanding and modeling of price-mediated contagion and provides valuable insights for financial authorities to construct effective stress tests and regulatory policies. ...