ARBITRAGE STRATEGIES IN PERPETUAL FUTURES AND STOCK INDEX FUTURES
This thesis examines two aspects of arbitrage in financial markets. The first part analyzes arbitrage in perpetual futures, which track underlying prices through a funding swap mechanism. We show that the clamping function embedded in the mechanism—previously overlooked in the literature—creates inherent no-arbitrage bounds that persist even in the absence of transaction fees. Using two years of Binance data, we empirically confirm the validity of these model-free bounds. The second part studies arbitrage strategies in stock index futures under a reinforcement learning (RL) framework. We formulate the problem as an exploratory stochastic control problem with entropy-regularized rewards, transforming the optimal switching structure into a standard control setting. An interpretable learning algorithm is developed, and a policy improvement theorem is established. Simulations and empirical results demonstrate the effectiveness of the proposed RL approach, which is broadly applicable to optimal switching problems.
reinforcement learning, stock index futures, optimal switching, clamp function, funding swap, perpetual futures
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