Cryptocurrency lending pools are services that allow lenders to pool together assets in one cryptocurrency and loan it out to borrowers who provide collateral worth more (than the loan) in a separate cryptocurrency. Borrowers can repay their loans to reclaim their collateral unless their loan was liquidated, which happens when the value of the collateral dips significantly. Interest rates for these pools are currently set via supply and demand heuristics, which have several downsides, including inefficiency, inflexibility, and being vulnerable to manipulation. Here, we reduce lending pools to options, and then use ideas from options pricing to search for fair interest rates for lending pools. In a simplified model where the loans have a fixed duration and can only be repaid at the end of the term, we obtain analytical pricing results. We then consider a more realistic model, where loans can be repaid dynamically and without expiry. Our main theoretical contribution is to show that fair interest rates do not exist in this setting. We then show that impossibility results generalize even to models of lending pools which have no obvious reduction to options. To address these negative results, we introduce a model of lending pools with fixed fees, and model the ability of borrowers to top-up their loans to reduce the risk of liquidation. As a proof of concept, we use simulations to show how our model's predicted interest rates compare to interest rates in practice.

翻译：加密货币借贷池是一种服务，允许贷方将单一加密货币的资产汇集起来，借给提供超额抵押（抵押品价值高于贷款额）且抵押品为另一种加密货币的借款人。除非贷款被清算（当抵押品价值大幅下跌时发生），借款人可以偿还贷款以取回抵押品。目前这些借贷池的利率通过供需启发式方法设定，存在效率低下、灵活性不足、易受操纵等缺陷。本文将借贷池简化为期权模型，并运用期权定价理论探索借贷池的公平利率。在贷款期限固定且仅能在期末偿还的简化模型中，我们获得了解析定价结果。随后我们考虑更现实的动态还款且无固定期限的模型。我们的主要理论贡献是证明在此设定下公平利率不存在。进一步研究表明，这种不可能性结果甚至可推广至无法直接简化为期权的借贷池模型。针对这些负面结论，我们提出引入固定费用的借贷池模型，并模拟借款人通过追加抵押降低清算风险的能力。作为概念验证，我们通过仿真实验展示了该模型预测利率与实际利率的对比情况。