Dynamic Collateral Control for Permissionless Spot Perpetual Basis Trading

Paper: arXiv 2605.05089

Authors: Anatoly Krestenko, Mikhail Butov, Rostislav Berezovskiy, Danila Bolotin

Abstract

We study permissionless spot–perpetual basis trading in decentralized finance as a collateral control problem. The strategy holds spot inventory, hedges directional exposure with a short perpetual, and allocates capital between spot inventory and derivative margin under on-chain liquidity and execution frictions. The paper delivers three results. First, it solves a static control problem for the collateral share and shows that the risk-constrained formulation provides a more robust operating benchmark relative to the economic optimum. In comparative calibration, the required collateral rises monotonically under volatility stress. The collateral is the lowest for BTC and increases significantly for long tail assets such as LINK and DOGE. Second, the paper derives an asymmetric dynamic extension in which the lower boundary of intervention is solvency driven, and the upper boundary is determined by a trade-off between carry-loss and the cost of rebalancing. Monte Carlo simulation shows that the lower boundary remains structurally relevant, whereas meaningful interior upper triggers survive mainly in the regimes with high carry and low costs. Third, the paper validates an execution-aware implementation with live routed execution and historical backtests. The execution layer shows that the realized wedges are significant, but become worse in the case of selling the basis. This justifies a minimum effective rebalancing size and a positive execution buffer. The historical validation shows that in the case of a fixed control rule the realized performance is predominantly explained by the funding environment.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a rigorous mathematical derivation of a dynamic control problem using asymmetrically bounded triggers, matched with professional-grade empirical validation including live routed execution and historical backtests across multiple assets.

Research Flowchart

  flowchart TD
    A[Research Goal: Optimize Collateral Control for DeFi Basis Trading] --> B[Methodology: Static/Dynamic Control & Execution Modeling]
    B --> C[Inputs: On-chain Liquidity, Volatility, & Historical Funding Data]
    C --> D[Computational Process: Monte Carlo Simulations & Live Execution Backtesting]
    D --> E[Outcome 1: Risk-Constrained Benchmark vs Economic Optimum]
    D --> F[Outcome 2: Asymmetric Boundary Triggers based on Carry/Rebalancing Cost]
    D --> G[Outcome 3: Execution Buffer & Rebalancing Size Validated]

Cited References (40)

1. Handbook of Brownian Motion: Facts and Formulae (2015)
2. Applied Stochastic Control of Jump Diffusions (2007)
3. Perpetual Futures Pricing — → 2310.11771
4. Fundamentals of Perpetual Futures — → 2212.06888
5. Perpetual Future Contracts in Centralized and Decentralized Exchanges: Mechanism and Traders’ Behavior (2024) — link
6. Uniswap v3 Core (2021)
7. The Dominance of Uniswap v3 Liquidity (2022)
8. Liquidations (2025) — link

4 of 40 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.