Foundations of Fiat-Denominated Loans Collateralized by Cryptocurrencies

TL;DR

The paper tackles the challenge of enabling fiat-denominated loans collateralized by cryptocurrencies with minimal trusted custody. It develops three protocols—Pi1 (fixed-rate), Pi2 (oracle-based collateral adjustment), and Pi3 (oracleless with bounded arbiter control)—and analyzes their strategic properties using subgame-perfect equilibrium in extensive-form games. Pi1 and Pi2 are shown to sustain honest behavior as SPE under their respective setups, while Pi3 demonstrates meaningful stability and reduced arbiter control under specific assumptions and online participation. Collectively, the work advances secure, mixed CeFi–DeFi lending by balancing trust in an arbiter with automated on-chain enforcement, and it outlines practical tradeoffs and extensions, including Bitcoin compatibility and potential privacy enhancements. The results have practical implications for designing crypto-backed lending infrastructures that avoid full custody and accommodate volatile exchange rates, contributing to safer integration of fiat and crypto finance.

Abstract

The rising importance of cryptocurrencies as financial assets pushed their applicability from an object of speculation closer to standard financial instruments such as loans. In this work, we initiate the study of secure protocols that enable fiat-denominated loans collateralized by cryptocurrencies such as Bitcoin. We provide limited-custodial protocols for such loans relying only on trusted arbitration and provide their game-theoretical analysis. We also highlight various interesting directions for future research.

Figures (5)

• Figure 1: Timeline of important events in the basic protocol.
• Figure 2: Game tree induced by $\Pi_1$ showing the actions the borrower and lender can take at each step of the protocol. Vertices labelled $L$ are lender vertices and vertices labelled $B$ are borrower vertices. The first element of the utility vector (in fiat) at each leaf node corresponds to the utility of the lender, and the second element the utility of the borrower. The dotted and dashed path depicts the honest strategy.
• Figure 3: Game tree induced by the protocol with price oracle when the terminal exchange rate $p_t<p_0$ showing the actions the borrower and lender can take at each step of the protocol. The first element of the utility vector (in fiat) at each leaf node is corresponds to the utility of the lender, and the second element the utility of the borrower. The dotted and dashed path depicts the honest strategy.
• Figure 4: Transaction depicting the release of collateral in $\Pi_1$.
• Figure 5: Game tree induced by the protocol without oracle showing the actions the borrower and lender can take at each step of the protocol. In the liquidation game, the vertex $E$ represents a move from nature and $\ell$ denotes liquidation. The dotted rectangle around the lender vertices in the liquidation game denote that they belong in the same information set. For ease of presentation, we use $\beta$ to denote $(\frac{y}{2}-\epsilon)p_i-1$. LRG at the leaf nodes in the liquidation game the expected payoff from the loan repayment game phase.

Theorems & Definitions (21)

• theorem 1
• remark 1
• proof
• proof
• theorem 2
• definition 1
• definition 2
• proof
• proof
• proof