Market Impact

Optimal Portfolio Execution in a Regime-switching Market with Non-linear Impact Costs: Combining Dynamic Program and Neural Network ArXiv ID: 2306.08809 “View on arXiv” Authors: Unknown Abstract Optimal execution of a portfolio have been a challenging problem for institutional investors. Traders face the trade-off between average trading price and uncertainty, and traditional methods suffer from the curse of dimensionality. Here, we propose a four-step numerical framework for the optimal portfolio execution problem where multiple market regimes exist, with the underlying regime switching based on a Markov process. The market impact costs are modelled with a temporary part and a permanent part, where the former affects only the current trade while the latter persists. Our approach accepts impact cost functions in generic forms. First, we calculate the approximated orthogonal portfolios based on estimated impact cost functions; second, we employ dynamic program to learn the optimal selling schedule of each approximated orthogonal portfolio; third, weights of a neural network are pre-trained with the strategy suggested by previous step; last, we train the neural network to optimize on the original trading model. In our experiment of a 10-asset liquidation example with quadratic impact costs, the proposed combined method provides promising selling strategy for both CRRA (constant relative risk aversion) and mean-variance objectives. The running time is linear in the number of risky assets in the portfolio as well as in the number of trading periods. Possible improvements in running time are discussed for potential large-scale usages. ...

When is cross impact relevant? ArXiv ID: 2305.16915 “View on arXiv” Authors: Unknown Abstract Trading pressure from one asset can move the price of another, a phenomenon referred to as cross impact. Using tick-by-tick data spanning 5 years for 500 assets listed in the United States, we identify the features that make cross-impact relevant to explain the variance of price returns. We show that price formation occurs endogenously within highly liquid assets. Then, trades in these assets influence the prices of less liquid correlated products, with an impact velocity constrained by their minimum trading frequency. We investigate the implications of such a multidimensional price formation mechanism on interest rate markets. We find that the 10-year bond future serves as the primary liquidity reservoir, influencing the prices of cash bonds and futures contracts within the interest rate curve. Such behaviour challenges the validity of the theory in Financial Economics that regards long-term rates as agents anticipations of future short term rates. ...

PRIME: A Price-Reverting Impact Model of a cryptocurrency Exchange ArXiv ID: 2305.07559 “View on arXiv” Authors: Unknown Abstract In a financial exchange, market impact is a measure of the price change of an asset following a transaction. This is an important element of market microstructure, which determines the behaviour of the market following a trade. In this paper, we first provide a discussion on the market impact observed in the BTC/USD Futures market, then we present a novel multi-agent market simulation that can follow an underlying price series, whilst maintaining the ability to reproduce the market impact observed in the market in an explainable manner. This simulation of the financial exchange allows the model to interact realistically with market participants, helping its users better estimate market slippage as well as the knock-on consequences of their market actions. In turn, it allows various stakeholders such as industrial practitioners, governments and regulators to test their market hypotheses, without deploying capital or destabilising the system. ...

Machine Learning for Trading ArXiv ID: ssrn-3015609 “View on arXiv” Authors: Unknown Abstract In multi-period trading with realistic market impact, determining the dynamic trading strategy that optimizes expected utility of final wealth is a hard problem Keywords: Market Impact, Optimal Execution, Dynamic Trading, Utility Maximization, Algorithmic Trading, Equities / Quantitative Trading Complexity vs Empirical Score Math Complexity: 8.5/10 Empirical Rigor: 3.0/10 Quadrant: Lab Rats Why: The paper uses advanced multi-period optimal control theory, utility theory, and Hamilton-Jacobi-Bellman equations, indicating high mathematical complexity, but focuses on theoretical proof-of-concept in a simulated market with no real-world data, backtests, or implementation details, resulting in low empirical rigor. flowchart TD Start(["Research Goal"]) --> Method["Dynamic Trading Strategy<br/>Optimization with Market Impact"] Start --> Input["Realistic Market Data<br/>& Historical Prices"] Method --> Process["Computational Process:<br/>Multi-Period Optimization<br/>Maximizing Expected Utility"] Input --> Process Process --> Outcome1["Novel Optimal<br/>Execution Algorithms"] Process --> Outcome2["Quantified Market<br/>Impact Costs"] Process --> Outcome3["Dynamic Strategy<br/>Constraints Analysis"] Outcome1 --> End(["Key Findings"]) Outcome2 --> End Outcome3 --> End