Optimal Liquidation of Perpetual Contracts

Battle Count: 85

Highly relevant to quantitative trading, particularly for cryptocurrency perpetual contract markets where daily turnovers are in billions of USD. The paper provides actionable closed-form trading strategies for liquidation, quantifies the interaction between funding rates and optimal execution, and offers practical approximations for non-linear payoff structures (everlasting options). The Almgren-Chriss perturbation framework and the inventory-funding rate relationship (Proposition 3) are directly implementable in trading systems.

The identity payoff strategy (Theorem 2) is closed-form and straightforward to implement given the ODE solutions for ξ(t) and π(t), which require numerical integration. The asymptotic approximations (Theorems 6, 8, 9) involve computing expectations of ψ(S_u) conditional on S_t=s, which for general ψ requires numerical methods (e.g., Monte Carlo or PDE solvers). The short-time approximation (Proposition 9) is particularly simple: substitute ψ(s) for s in the identity-payoff strategy. Overall, moderate complexity due to the need for numerical ODE integration and conditional expectation computations.

The paper provides fully closed-form solutions for the identity payoff case and explicit asymptotic formulas for the general case. All simulation parameter values are stated in figure captions. However, no code repository or numerical implementation details (e.g., discretization schemes for simulations) are provided. The ODE system (11) is noted as not solvable in closed form by symbolic algebra systems, requiring numerical integration.