Theoretical Economics as Successive Approximations of Statistical Moments ArXiv ID: 2310.05971 “View on arXiv” Authors: Unknown Abstract This paper studies the links between the descriptions of macroeconomic variables and statistical moments of market trade, price, and return. The randomness of market trade values and volumes during the averaging interval Δ results in the random properties of price and return. We describe how averages and volatilities of price and return depend on the averages, volatilities, and correlations of market trade values and volumes. The averages, volatilities, and correlations of market trade, price, and return can behave randomly during the long interval Δ2»Δ. To describe their statistical properties during the long interval Δ2, we introduce the secondary averaging procedure of trade, price, and return. We explain why, in the coming years, predictions of market-based probabilities of price and return will be limited by Gaussian distributions. We discuss the roots of the internal weakness of the commonly used hedging tool, Value-at-Risk, that cannot be solved and remains the source of additional risks and losses. One should consider theoretical economics as a set of successive approximations, each of which describes the next array of the n-th statistical moments of market trades, price, return, and macroeconomic variables, which are repeatedly averaged during the sequence of increasing time intervals. ...

Hedging Properties of Algorithmic Investment Strategies using Long Short-Term Memory and Time Series models for Equity Indices ArXiv ID: 2309.15640 “View on arXiv” Authors: Unknown Abstract This paper proposes a novel approach to hedging portfolios of risky assets when financial markets are affected by financial turmoils. We introduce a completely novel approach to diversification activity not on the level of single assets but on the level of ensemble algorithmic investment strategies (AIS) built based on the prices of these assets. We employ four types of diverse theoretical models (LSTM - Long Short-Term Memory, ARIMA-GARCH - Autoregressive Integrated Moving Average - Generalized Autoregressive Conditional Heteroskedasticity, momentum, and contrarian) to generate price forecasts, which are then used to produce investment signals in single and complex AIS. In such a way, we are able to verify the diversification potential of different types of investment strategies consisting of various assets (energy commodities, precious metals, cryptocurrencies, or soft commodities) in hedging ensemble AIS built for equity indices (S&P 500 index). Empirical data used in this study cover the period between 2004 and 2022. Our main conclusion is that LSTM-based strategies outperform the other models and that the best diversifier for the AIS built for the S&P 500 index is the AIS built for Bitcoin. Finally, we test the LSTM model for a higher frequency of data (1 hour). We conclude that it outperforms the results obtained using daily data. ...

Implementing portfolio risk management and hedging in practice ArXiv ID: 2309.15767 “View on arXiv” Authors: Unknown Abstract In academic literature portfolio risk management and hedging are often versed in the language of stochastic control and Hamilton–Jacobi–Bellman~(HJB) equations in continuous time. In practice the continuous-time framework of stochastic control may be undesirable for various business reasons. In this work we present a straightforward approach for thinking of cross-asset portfolio risk management and hedging, providing some implementation details, while rarely venturing outside the convex optimisation setting of (approximate) quadratic programming~(QP). We pay particular attention to the correspondence between the economic concepts and their mathematical representations; the abstractions enabling us to handle multiple asset classes and risk models at once; the dimensional analysis of the resulting equations; and the assumptions inherent in our derivations. We demonstrate how to solve the resulting QPs with CVXOPT. ...

Optimal Entry and Exit with Signature in Statistical Arbitrage ArXiv ID: 2309.16008 “View on arXiv” Authors: Unknown Abstract In this paper, we explore an optimal timing strategy for the trading of price spreads exhibiting mean-reverting characteristics. A sequential optimal stopping framework is formulated to analyze the optimal timings for both entering and subsequently liquidating positions, all while considering the impact of transaction costs. Then we leverages a refined signature optimal stopping method to resolve this sequential optimal stopping problem, thereby unveiling the precise entry and exit timings that maximize gains. Our framework operates without any predefined assumptions regarding the dynamics of the underlying mean-reverting spreads, offering adaptability to diverse scenarios. Numerical results are provided to demonstrate its superior performance when comparing with conventional mean reversion trading rules. ...

Startup success prediction and VC portfolio simulation using CrunchBase data ArXiv ID: 2309.15552 “View on arXiv” Authors: Unknown Abstract Predicting startup success presents a formidable challenge due to the inherently volatile landscape of the entrepreneurial ecosystem. The advent of extensive databases like Crunchbase jointly with available open data enables the application of machine learning and artificial intelligence for more accurate predictive analytics. This paper focuses on startups at their Series B and Series C investment stages, aiming to predict key success milestones such as achieving an Initial Public Offering (IPO), attaining unicorn status, or executing a successful Merger and Acquisition (M&A). We introduce novel deep learning model for predicting startup success, integrating a variety of factors such as funding metrics, founder features, industry category. A distinctive feature of our research is the use of a comprehensive backtesting algorithm designed to simulate the venture capital investment process. This simulation allows for a robust evaluation of our model’s performance against historical data, providing actionable insights into its practical utility in real-world investment contexts. Evaluating our model on Crunchbase’s, we achieved a 14 times capital growth and successfully identified on B round high-potential startups including Revolut, DigitalOcean, Klarna, Github and others. Our empirical findings illuminate the importance of incorporating diverse feature sets in enhancing the model’s predictive accuracy. In summary, our work demonstrates the considerable promise of deep learning models and alternative unstructured data in predicting startup success and sets the stage for future advancements in this research area. ...

Gray-box Adversarial Attack of Deep Reinforcement Learning-based Trading Agents ArXiv ID: 2309.14615 “View on arXiv” Authors: Unknown Abstract In recent years, deep reinforcement learning (Deep RL) has been successfully implemented as a smart agent in many systems such as complex games, self-driving cars, and chat-bots. One of the interesting use cases of Deep RL is its application as an automated stock trading agent. In general, any automated trading agent is prone to manipulations by adversaries in the trading environment. Thus studying their robustness is vital for their success in practice. However, typical mechanism to study RL robustness, which is based on white-box gradient-based adversarial sample generation techniques (like FGSM), is obsolete for this use case, since the models are protected behind secure international exchange APIs, such as NASDAQ. In this research, we demonstrate that a “gray-box” approach for attacking a Deep RL-based trading agent is possible by trading in the same stock market, with no extra access to the trading agent. In our proposed approach, an adversary agent uses a hybrid Deep Neural Network as its policy consisting of Convolutional layers and fully-connected layers. On average, over three simulated trading market configurations, the adversary policy proposed in this research is able to reduce the reward values by 214.17%, which results in reducing the potential profits of the baseline by 139.4%, ensemble method by 93.7%, and an automated trading software developed by our industrial partner by 85.5%, while consuming significantly less budget than the victims (427.77%, 187.16%, and 66.97%, respectively). ...

The ATM implied skew in the ADO-Heston model ArXiv ID: 2309.15044 “View on arXiv” Authors: Unknown Abstract In this paper similar to [“P. Carr, A. Itkin, 2019”] we construct another Markovian approximation of the rough Heston-like volatility model - the ADO-Heston model. The characteristic function (CF) of the model is derived under both risk-neutral and real measures which is an unsteady three-dimensional PDE with some coefficients being functions of the time $t$ and the Hurst exponent $H$. To replicate known behavior of the market implied skew we proceed with a wise choice of the market price of risk, and then find a closed form expression for the CF of the log-price and the ATM implied skew. Based on the provided example, we claim that the ADO-Heston model (which is a pure diffusion model but with a stochastic mean-reversion speed of the variance process, or a Markovian approximation of the rough Heston model) is able (approximately) to reproduce the known behavior of the vanilla implied skew at small $T$. We conclude that the behavior of our implied volatility skew curve ${"\cal S"}(T) \propto a(H) T^{“b\cdot (H-1/2)”}, , b = const$, is not exactly same as in rough volatility models since $b \ne 1$, but seems to be close enough for all practical values of $T$. Thus, the proposed Markovian model is able to replicate some properties of the corresponding rough volatility model. Similar analysis is provided for the forward starting options where we found that the ATM implied skew for the forward starting options can blow-up for any $s > t$ when $T \to s$. This result, however, contradicts to the observation of [“E. Alos, D.G. Lorite, 2021”] that Markovian approximation is not able to catch this behavior, so remains the question on which one is closer to reality. ...

Tasks Makyth Models: Machine Learning Assisted Surrogates for Tipping Points ArXiv ID: 2309.14334 “View on arXiv” Authors: Unknown Abstract We present a machine learning (ML)-assisted framework bridging manifold learning, neural networks, Gaussian processes, and Equation-Free multiscale modeling, for (a) detecting tipping points in the emergent behavior of complex systems, and (b) characterizing probabilities of rare events (here, catastrophic shifts) near them. Our illustrative example is an event-driven, stochastic agent-based model (ABM) describing the mimetic behavior of traders in a simple financial market. Given high-dimensional spatiotemporal data – generated by the stochastic ABM – we construct reduced-order models for the emergent dynamics at different scales: (a) mesoscopic Integro-Partial Differential Equations (IPDEs); and (b) mean-field-type Stochastic Differential Equations (SDEs) embedded in a low-dimensional latent space, targeted to the neighborhood of the tipping point. We contrast the uses of the different models and the effort involved in learning them. ...

Towards a Theory of Maximal Extractable Value II: Uncertainty ArXiv ID: 2309.14201 “View on arXiv” Authors: Unknown Abstract Maximal Extractable Value (MEV) is value extractable by temporary monopoly power commonly found in decentralized systems. This extraction stems from a lack of user privacy upon transaction submission and the ability of a monopolist validator to reorder, add, and/or censor transactions. There are two main directions to reduce MEV: reduce the flexibility of the miner to reorder transactions by enforcing ordering rules and/or introduce a competitive market for the right to reorder, add, and/or censor transactions. In this work, we unify these approaches via \emph{“uncertainty principles”}, akin to those found in harmonic analysis and physics. This provides a quantitative trade-off between the freedom to reorder transactions and the complexity of an economic payoff to a user in a decentralized network. This trade off is analogous to the Nyquist-Shannon sampling theorem and demonstrates that sequencing rules in blockchains need to be application specific. Our results suggest that neither so-called fair ordering techniques nor economic mechanisms can individually mitigate MEV for arbitrary payoff functions. ...

Don’t Let MEV Slip: The Costs of Swapping on the Uniswap Protocol ArXiv ID: 2309.13648 “View on arXiv” Authors: Unknown Abstract We present the first in-depth empirical characterization of the costs of trading on a decentralized exchange (DEX). Using quoted prices from the Uniswap Labs interface for two pools – USDC-ETH (5bps) and PEPE-ETH (30bps) – we evaluate the efficiency of trading on DEXs. Our main tool is slippage – the difference between the realized execution price of a trade, and its quoted price – which we breakdown into its benign and adversarial components. We also present an alternative way to quantify and identify slippage due to adversarial reordering of transactions, which we call reordering slippage, that does not require quoted prices or mempool data to calculate. We find that the composition of transaction costs varies tremendously with the trade’s characteristics. Specifically, while for small swaps, gas costs dominate costs, for large swaps price-impact and slippage account for the majority of it. Moreover, when trading PEPE, a popular ‘memecoin’, the probability of adversarial slippage is about 80% higher than when trading a mature asset like USDC. Overall, our results provide preliminary evidence that DEXs offer a compelling trust-less alternative to centralized exchanges for trading digital assets. ...