Optimal Hedging with Margin Constraints and Default Aversion and its Application to Bitcoin Perpetual Futures

Abstract

We consider the hedging problem where a futures position can be automatically liquidated by the exchange without notice. We derive a semi-closed form for an optimal hedging strategy with dual objectives -- to minimise both the variance of the hedged portfolio and the probability of liquidations due to insufficient collateral. The optimal solution depends on the statistical characteristics of the spot and futures extreme returns and parameters that characterise the hedger by loss aversion, choice of leverage and collateral management. An empirical analysis of bitcoin shows that the optimal strategy combines superior hedge effectiveness with a reduction in the probability of liquidation. We compare the performance of seven major direct and inverse hedging instruments traded on five different exchanges, based on minute-level data. We also link this performance to novel speculative trading metrics, which differ markedly between venues.