Optimal Liquidation of Perpetual Contracts with Funding and Inventory Risk

Summary

This document studies how an agent should liquidate a position in a perpetual contract while balancing transaction costs, inventory risk, and funding payments. It formulates liquidation as a stochastic control problem and derives a closed-form optimal trading strategy when the contract’s payoff is the identity function of the underlying price.

For nonlinear payoff functions, the document offers approximate strategies for cases with a small funding-rate parameter or a short liquidation interval. It also establishes that the short-interval approximation can be expressed using the closed-form strategy from the identity-payoff case. The abstract describes theoretical derivations, but gives no market data, numerical comparisons, or implementation details, so it does not establish how the strategy performs in live trading or under specific exchange funding conventions.

Key ideas

• Liquidation is framed as a stochastic control problem with transaction costs, inventory risk, and funding payments.
• A closed-form optimal strategy is derived for an identity payoff function.
• For nonlinear payoffs, approximations apply when the funding parameter or liquidation interval is small.
• The short-interval nonlinear-payoff approximation is expressed through the identity-payoff strategy.

Tags

# Optimal Liquidation of Perpetual Contracts


# Optimal Liquidation of Perpetual Contracts









An agent holds a position in a perpetual contract with payoff function $ψ$ and attempts to liquidate the position while managing transaction costs, inventory risk, and funding rate payments. By solving the agent's stochastic control problem we obtain a closed-form expression for the optimal trading strategy when the payoff function is given by $ψ(s) = s$. When the payoff function is non-linear we provide approximations to the optimal strategy which apply when the funding rate parameter is small or when the length of the trading interval is small. We further prove that when $ψ$ is non-linear, the short time approximation can be written in terms of the closed-form trading strategy corresponding to the case of the identity payoff function.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.