Option-based pricing of secured lending in P2P crypto markets
摘要
Secured lending in crypto markets, so-called crypto loans, enables borrowers to borrow cryptocurrencies by providing collateral in other cryptocurrencies. We investigate the payoff structure of crypto loans and derive a no-arbitrage term structure of borrowing rates, specifically designed for the crypto loans market, noted for its volatile collateral prices and the anonymity of its participants. Inspired by the literature on stock loans, we identify the position of borrowing in crypto loans as maintaining a long position in an American barrier option, with the crypto collateral serving as the underlying asset. Our analysis of the no-arbitrage borrowing rate term structure for crypto loans is grounded in option pricing theory. We identify several key features of the term structure: (i) it inherently exhibits contango; (ii) in scenarios where the collateral price process is continuous and a penalty associated with liquidation is absent, the fair borrowing rate equals the risk-free rate; (iii) it is sensitive to variations in contract parameters. Through the application of numerical methods, we calculate and visualise the term structure for an array of contract parameters.