CyberSec Research

The arbitrage gains or, equivalently, Loss Versus Rebalacing (LVR) for arbitrage between two imperfectly liquid markets is derived. To derive the LVR, I assume a quadratic trading cost to model the cost of trading on the more liquid exchange and discuss to which situations my model arguably applies well (long tail CEX-DEX arbitrage, DEX-DEX arbitrage) and to which not so well (CEX-DEX arbitrage for major pairs). I discuss extension to other cost functions and directions for future research.

Price benchmarks are used to incorporate market price trends into contracts, but their use can create opportunities for manipulation by parties involved in the contract. This paper examines this issue using a realistic and tractable model inspired by smart contracts on blockchains like Ethereum. In our model, manipulation costs depend on two factors: the magnitude of adjustments to individual prices (variable costs) and the number of prices adjusted (fixed costs). We find that a weighted mean is the optimal benchmark when fixed costs are negligible, while the median is optimal when variable costs are negligible. In cases where both fixed and variable costs are significant, the optimal benchmark can be implemented as a trimmed mean, with the degree of trimming increasing as fixed costs become more important relative to variable costs. Furthermore, we show that the optimal weights for a mean-based benchmark are proportional to the marginal manipulation costs, whereas the median remains optimal without weighting, even when fixed costs differ across prices.

Passive investing has gained immense popularity due to its low fees and the perceived simplicity of focusing on zero tracking error, rather than security selection. However, our analysis shows that the passive (zero tracking error) approach of waiting until the market close on the day of index reconstitution to purchase a stock (that was announced days earlier as an upcoming addition) results in costs amounting to hundreds of basis points compared to strategies that involve gradually acquiring a small portion of the required shares in advance with minimal additional tracking errors. In addition, we show that under all scenarios analyzed, a trader who builds a small inventory post-announcement and provides liquidity at the reconstitution event can consistently earn several hundreds of basis points in profit and often much more, assuming minimal risk.

The digitalization of financial markets has shifted trading from voice to electronic channels, with Multi-Dealer-to-Client (MD2C) platforms now enabling clients to request quotes (RfQs) for financial instruments like bonds from multiple dealers simultaneously. In this competitive landscape, dealers cannot see each other's prices, making a rigorous analysis of the negotiation process crucial to ensure their profitability. This article introduces a novel general framework for analyzing the RfQ process using probabilistic graphical models and causal inference. Within this framework, we explore different inferential questions that are relevant for dealers participating in MD2C platforms, such as the computation of optimal prices, estimating potential revenues and the identification of clients that might be interested in trading the dealer's axes. We then move into analyzing two different approaches for model specification: a generative model built on the work of (Fermanian, Gu\'eant & Pu, 2017); and discriminative models utilizing machine learning techniques. We evaluate these methodologies using predictive metrics designed to assess their effectiveness in the context of optimal pricing, highlighting the relative benefits of using models that take into account the internal mechanisms of the negotiation process.

This paper considers a continuous time Kyle-Back model which is a game problem between an insider and a market marker. The existing literature typically focuses on the existence of equilibrium by using the PDE approach, which requires certain Markovian structure and the equilibrium is in the bridge form. We shall provide a new approach which is used widely for stochastic controls and stochastic differential games. We characterize all equilibria through a coupled system of forward backward SDEs, where the forward one is the conditional law of the inside information and the backward one is the insider's optimal value. In particular, when the time duration is small, we show that the FBSDE is wellposed and thus the game has a unique equilibrium. This is the first uniqueness result in the literature, without restricting the equilibria to certain special structure. Moreover, this unique equilibrium may not be Markovian, indicating that the PDE approach cannot work in this case. We next study the set value of the game, which roughly speaking is the set of insider's values over all equilibria and thus is by nature unique. We show that, although the bridge type of equilibria in the literature does not satisfy the required integrability for our equilibria, its truncation serves as a desired approximate equilibrium and its value belongs to our set value. Finally, we characterize our set value through a level set of certain standard HJB equation.

We propose a profitable trading strategy for the cryptocurrency market based on grid trading. Starting with an analysis of the expected value of the traditional grid strategy, we show that under simple assumptions, its expected return is essentially zero. We then introduce a novel Dynamic Grid-based Trading (DGT) strategy that adapts to market conditions by dynamically resetting grid positions. Our backtesting results using minute-level data from Bitcoin and Ethereum between January 2021 and July 2024 demonstrate that the DGT strategy significantly outperforms both the traditional grid and buy-and-hold strategies in terms of internal rate of return and risk control.

We present a Markovian market model driven by a hidden Brownian efficient price. In particular, we extend the queue-reactive model, making its dynamics dependent on the efficient price. Our study focuses on two sub-models: a signal-driven price model where the mid-price jump rates depend on the efficient price and an observable signal, and the usual queue-reactive model dependent on the efficient price via the intensities of the order arrivals. This way, we are able to correlate the evolution of limit order books of different stocks. We prove the stability of the observed mid-price around the efficient price under natural assumptions. Precisely, we show that at the macroscopic scale, prices behave as diffusions. We also develop a maximum likelihood estimation procedure for the model, and test it numerically. Our model is them used to backest trading strategies in a liquidation context.

We study an optimal execution strategy for purchasing a large block of shares over a fixed time horizon. The execution problem is subject to a general price impact that gradually dissipates due to market resilience. This resilience is modeled through a potentially arbitrary limit-order book shape. To account for liquidity dynamics, we introduce a stochastic volume effect governing the recovery of the deviation process, which represents the difference between the impacted and unaffected price. Additionally, we incorporate stochastic liquidity variations through a regime-switching Markov chain to capture abrupt shifts in market conditions. We study this singular control problem, where the trader optimally determines the timing and rate of purchases to minimize execution costs. The associated value function to this optimization problem is shown to satisfy a system of variational Hamilton-Jacobi-Bellman inequalities. Moreover, we establish that it is the unique viscosity solution to this HJB system and study the analytical properties of the free boundary separating the execution and continuation regions. To illustrate our results, we present numerical examples under different limit-order book configurations, highlighting the interplay between price impact, resilience dynamics, and stochastic liquidity regimes in shaping the optimal execution strategy.

This paper investigates the optimal hedging strategies of an informed broker interacting with multiple traders in a financial market. We develop a theoretical framework in which the broker, possessing exclusive information about the drift of the asset's price, engages with traders whose trading activities impact the market price. Using a mean-field game approach, we derive the equilibrium strategies for both the broker and the traders, illustrating the intricate dynamics of their interactions. The broker's optimal strategy involves a Stackelberg equilibrium, where the broker leads and the traders follow. Our analysis also addresses the mean field limit of finite-player models and shows the convergence to the mean-field solution as the number of traders becomes large.

This document analyzes price discovery in cryptocurrency markets by comparing centralized and decentralized exchanges, as well as spot and futures markets. The study focuses first on Ethereum (ETH) and then applies a similar approach to Bitcoin (BTC). Chapter 1 outlines the theoretical framework, emphasizing the structural differences between centralized exchanges and decentralized finance mechanisms, especially Automated Market Makers (AMMs). It also explains how to construct an order book from a liquidity pool in a decentralized setting for comparison with centralized exchanges. Chapter 2 describes the methodological tools used: Hasbrouck's Information Share, Gonzalo and Granger's Permanent-Transitory decomposition, and the Hayashi-Yoshida estimator. These are applied to explore lead-lag dynamics, cointegration, and price discovery across market types. Chapter 3 presents the empirical analysis. For ETH, it compares price dynamics on Binance and Uniswap v2 over a one-year period, focusing on five key events in 2024. For BTC, it analyzes the relationship between spot and futures prices on the CME. The study estimates lead-lag effects and cointegration in both cases. Results show that centralized markets typically lead in ETH price discovery. In futures markets, while they tend to lead overall, high-volatility periods produce mixed outcomes. The findings have key implications for traders and institutions regarding liquidity, arbitrage, and market efficiency. Various metrics are used to benchmark the performance of modified AMMs and to understand the interaction between decentralized and centralized structures.

In this work, we aim to reconcile several apparently contradictory observations in market microstructure: is the famous "square-root law" of metaorder impact, which decays with time, compatible with the random-walk nature of prices and the linear impact of order imbalances? Can one entirely explain the volatility of prices as resulting from the flow of uninformed metaorders that mechanically impact them? We introduce a new theoretical framework to describe metaorders with different signs, sizes and durations, which all impact prices as a square-root of volume but with a subsequent time decay. We show that, as in the original propagator model, price diffusion is ensured by the long memory of cross-correlations between metaorders. In order to account for the effect of strongly fluctuating volumes q of individual trades, we further introduce two q-dependent exponents, which allow us to describe how the moments of generalized volume imbalance and the correlation between price changes and generalized order flow imbalance scale with T. We predict in particular that the corresponding power-laws depend in a non-monotonic fashion on a parameter a, which allows one to put the same weight on all child orders or to overweight large ones, a behaviour that is clearly borne out by empirical data. We also predict that the correlation between price changes and volume imbalances should display a maximum as a function of a, which again matches observations. Such noteworthy agreement between theory and data suggests that our framework correctly captures the basic mechanism at the heart of price formation, namely the average impact of metaorders. We argue that our results support the "Order-Driven" theory of excess volatility, and are at odds with the idea that a "Fundamental" component accounts for a large share of the volatility of financial markets.

Cryptocurrency price dynamics are driven largely by microstructural supply demand imbalances in the limit order book (LOB), yet the highly noisy nature of LOB data complicates the signal extraction process. Prior research has demonstrated that deep-learning architectures can yield promising predictive performance on pre-processed equity and futures LOB data, but they often treat model complexity as an unqualified virtue. In this paper, we aim to examine whether adding extra hidden layers or parameters to "blackbox ish" neural networks genuinely enhances short term price forecasting, or if gains are primarily attributable to data preprocessing and feature engineering. We benchmark a spectrum of models from interpretable baselines, logistic regression, XGBoost to deep architectures (DeepLOB, Conv1D+LSTM) on BTC/USDT LOB snapshots sampled at 100 ms to multi second intervals using publicly available Bybit data. We introduce two data filtering pipelines (Kalman, Savitzky Golay) and evaluate both binary (up/down) and ternary (up/flat/down) labeling schemes. Our analysis compares models on out of sample accuracy, latency, and robustness to noise. Results reveal that, with data preprocessing and hyperparameter tuning, simpler models can match and even exceed the performance of more complex networks, offering faster inference and greater interpretability.

Optimal execution in financial markets refers to the process of strategically transacting a large volume of assets over a period to achieve the best possible outcome by balancing the trade-off between market impact costs and timing or volatility risks. Traditional optimal execution strategies, such as static Almgren-Chriss models, often prove suboptimal in dynamic financial markets. This paper propose flowOE, a novel imitation learning framework based on flow matching models, to address these limitations. FlowOE learns from a diverse set of expert traditional strategies and adaptively selects the most suitable expert behavior for prevailing market conditions. A key innovation is the incorporation of a refining loss function during the imitation process, enabling flowOE not only to mimic but also to improve upon the learned expert actions. To the best of our knowledge, this work is the first to apply flow matching models in a stochastic optimal execution problem. Empirical evaluations across various market conditions demonstrate that flowOE significantly outperforms both the specifically calibrated expert models and other traditional benchmarks, achieving higher profits with reduced risk. These results underscore the practical applicability and potential of flowOE to enhance adaptive optimal execution.

The paper explores the use of Deep Reinforcement Learning (DRL) in stock market trading, focusing on two algorithms: Double Deep Q-Network (DDQN) and Proximal Policy Optimization (PPO) and compares them with Buy and Hold benchmark. It evaluates these algorithms across three currency pairs, the S&P 500 index and Bitcoin, on the daily data in the period of 2019-2023. The results demonstrate DRL's effectiveness in trading and its ability to manage risk by strategically avoiding trades in unfavorable conditions, providing a substantial edge over classical approaches, based on supervised learning in terms of risk-adjusted returns.

Automated Market Makers (AMMs) are emerging as a popular decentralised trading platform. In this work, we determine the optimal dynamic fees in a constant function market maker. We find approximate closed-form solutions to the control problem and study the optimal fee structure. We find that there are two distinct fee regimes: one in which the AMM imposes higher fees to deter arbitrageurs, and another where fees are lowered to increase volatility and attract noise traders. Our results also show that dynamic fees that are linear in inventory and are sensitive to changes in the external price are a good approximation of the optimal fee structure and thus constitute suitable candidates when designing fees for AMMs.

This research systematically develops and evaluates various hybrid modeling approaches by combining traditional econometric models (ARIMA and ARFIMA models) with machine learning and deep learning techniques (SVM, XGBoost, and LSTM models) to forecast financial time series. The empirical analysis is based on two distinct financial assets: the S&P 500 index and Bitcoin. By incorporating over two decades of daily data for the S&P 500 and almost ten years of Bitcoin data, the study provides a comprehensive evaluation of forecasting methodologies across different market conditions and periods of financial distress. Models' training and hyperparameter tuning procedure is performed using a novel three-fold dynamic cross-validation method. The applicability of applied models is evaluated using both forecast error metrics and trading performance indicators. The obtained findings indicate that the proper construction process of hybrid models plays a crucial role in developing profitable trading strategies, outperforming their individual components and the benchmark Buy&Hold strategy. The most effective hybrid model architecture was achieved by combining the econometric ARIMA model with either SVM or LSTM, under the assumption of a non-additive relationship between the linear and nonlinear components.

We compare traditional approach of computing logarithmic returns with the fractional differencing method and its tempered extension as methods of data preparation before their usage in advanced machine learning models. Differencing parameters are estimated using multiple techniques. The empirical investigation is conducted on data from four major stock indices covering the most recent 10-year period. The set of explanatory variables is additionally extended with technical indicators. The effectiveness of the differencing methods is evaluated using both forecast error metrics and risk-adjusted return trading performance metrics. The findings suggest that fractional differentiation methods provide a suitable data transformation technique, improving the predictive model forecasting performance. Furthermore, the generated predictions appeared to be effective in constructing profitable trading strategies for both individual assets and a portfolio of stock indices. These results underline the importance of appropriate data transformation techniques in financial time series forecasting, supporting the application of memory-preserving techniques.

We conduct modeling of the price dynamics following order flow imbalance in market microstructure and apply the model to the analysis of Chinese CSI 300 Index Futures. There are three findings. The first is that the order flow imbalance is analogous to a shock to the market. Unlike the common practice of using Hawkes processes, we model the impact of order flow imbalance as an Ornstein-Uhlenbeck process with memory and mean-reverting characteristics driven by a jump-type L\'evy process. Motivated by the empirically stable correlation between order flow imbalance and contemporaneous price changes, we propose a modified asset price model where the drift term of canonical geometric Brownian motion is replaced by an Ornstein-Uhlenbeck process. We establish stochastic differential equations and derive the logarithmic return process along with its mean and variance processes under initial boundary conditions, and evolution of cost-effectiveness ratio with order flow imbalance as the trading trigger point, termed as the quasi-Sharpe ratio or response ratio. Secondly, our results demonstrate horizon-dependent heterogeneity in how conventional metrics interact with order flow imbalance. This underscores the critical role of forecast horizon selection for strategies. Thirdly, we identify regime-dependent dynamics in the memory and forecasting power of order flow imbalance. This taxonomy provides both a screening protocol for existing indicators and an ex-ante evaluation paradigm for novel metrics.