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Agent-Based Simulation of a Perpetual Futures Market (2501.09404v1)

Published 16 Jan 2025 in q-fin.TR

Abstract: I introduce an agent-based model of a Perpetual Futures market with heterogeneous agents trading via a central limit order book. Perpetual Futures (henceforth Perps) are financial derivatives introduced by the economist Robert Shiller, designed to peg their price to that of the underlying Spot market. This paper extends the limit order book model of Chiarella et al. (2002) by taking their agent and orderbook parameters, designed for a simple stock exchange, and applying it to the more complex environment of a Perp market with long and short traders who exhibit both positional and basis-trading behaviors. I find that despite the simplicity of the agent behavior, the simulation is able to reproduce the most salient feature of a Perp market, the pegging of the Perp price to the underlying Spot price. In contrast to fundamental simulations of stock markets which aim to reproduce empirically observed stylized facts such as the leptokurtosis and heteroscedasticity of returns, volatility clustering and others, in derivatives markets many of these features are provided exogenously by the underlying Spot price signal. This is especially true of Perps since the derivative is designed to mimic the price of the Spot market. Therefore, this paper will focus exclusively on analyzing how market and agent parameters such as order lifetime, trading horizon and spread affect the premiums at which Perps trade with respect to the underlying Spot market. I show that this simulation provides a simple and robust environment for exploring the dynamics of Perpetual Futures markets and their microstructure in this regard. Lastly, I explore the ability of the model to reproduce the effects of biasing long traders to trade positionally and short traders to basis-trade, which was the original intention behind the market design, and is a tendency observed empirically in real Perp markets.

Summary

  • The paper demonstrates that its advanced agent-based model accurately replicates the peg of perpetual futures prices to the underlying Spot market.
  • The paper employs Geometric Brownian Motion and Shewhart Charts to simulate market signals and assess the impact of varying agent and market parameters.
  • The paper distinguishes between positional and basis trading behaviors, showing that simple trader strategies can effectively capture complex market dynamics.

Agent-Based Simulation of a Perpetual Futures Market: An Advanced Analysis

The paper presented, Agent-Based Simulation of a Perpetual Futures Market, by Ramshreyas Rao, introduces a sophisticated agent-based model tailored for a Perpetual Futures market. This model builds on the canonical agent and order book framework established by Chiarella et al. (2002), advancing it to operate within the intricate dynamics of a Perpetual Futures environment featuring both long and short traders. Such traders demonstrate distinct positional and basis-trading behaviors, which this work encapsulates and examines thoroughly.

Key Contributions and Findings

The paper confirms the model's ability to reproduce core features of a Perpetual Futures market, specifically the pegging of Perpetual Futures prices to the underlying Spot market. This goes beyond the aim of conventional stock market simulations, which typically focus on replicating stylized facts like volatility clustering and return distributions. For Perpetual Futures, such features are largely inherited from their linkage to the Spot market, thus allowing the model's focus to remain on the intricate workings of futures premiums under different market conditions.

A pivotal aspect of the paper is the exploration of how varying market and agent parameters—such as order lifetime, trading horizon, and spread—affect these premiums. A notable finding is that simple and typical agent behavior effectively captures the dynamics of the futures market, aligning simulated empirical results with known market behaviors. The research also explores trader biases, distinguishing positional trading from basis trading, thereby elucidating the tendencies witnessed in real Perpetual Futures markets.

Technical Approach and Methodology

To create this advanced agent-based model, Rao employs foundational agents that include Chartist and Noise traders, drawing their lineage from established models. The agents utilize distinct forecasting methods, leveraging historical market signals to predict future outcomes. This methodological choice underscores the model's robustness, allowing it to simulate key market behaviors such as price pegging.

The paper employs Geometric Brownian Motion to simulate Spot price signals consistently across multiple runs, ensuring repeatability and variability across simulations. Parameters such as forecasting horizons and volatility are systematically varied, allowing detailed analysis of their impact on market behavior.

The use of Shewhart Charts represents a significant methodological advancement, enabling precise characterization of the Perpetual Futures market's peg to its underlying Spot price. These charts facilitate a clear representation and quantitative analysis of the peg's fidelity across various simulation parameters, including trader detachment due to positional exits and spread variations.

Implications and Future Directions

This research provides a platform for examining Perpetual Futures markets through a sophisticated yet tractable model, with implications extending across theoretical and practical realms of finance. Specifically, it offers significant insights into the microstructure of these markets, allowing better understanding and potential anticipation of market dynamics.

Practically, this model holds potential for application in optimizing trading strategies and enhancing market stability through informed parameter tuning. The model's robustness and alignment with empirical observations suggest it may serve as a foundation for future research into Perpetual Futures, particularly in cryptocurrency markets where these derivatives have become prominent.

As Perpetual Futures establish themselves as critical financial instruments in volatile markets, the ongoing refinement of agent-based modeling in this context promises to yield enhanced predictive accuracy and market insights. Future work could explore the impact of liquidity variances, agent wealth dynamics, and the incorporation of real-world Spot price signals to further calibrate and validate the model against live market conditions. Such endeavors would not only refine the model's precision but potentially transform our understanding and application of Perpetual Futures in broader economic contexts.

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