Agents' Behavior and Interest Rate Model Optimization in DeFi Lending

37 Pages Posted: 23 Apr 2024 Last revised: 26 Apr 2024

See all articles by Charles Bertucci

Charles Bertucci

Ecole Polytechnique, Palaiseau - CMAP CNRS-UMR 7641 and Ecole Polytechnique

Louis Bertucci

Institut Louis Bachelier

Mathis Gontier Delaunay

Morpho Labs

Olivier Gueant

Université Paris I Panthéon-Sorbonne

Matthieu Lesbre

Morpho Labs

Date Written: April 22, 2024

Abstract

Contrasting sharply with traditional money, bond and bond futures markets, where interest rates emerge organically from participant interactions, DeFi lending platforms employ rule-based interest rates that are algorithmically set. Thus, the selection of an effective interest rate model is paramount for the success of a lending protocol. This paper delves into the modeling of agents' behaviors on lending platforms, proposing a theoretical framework for formulating optimal interest rate models. We show that, under perfect information, an optimal control model with a state constraint generates an optimal interest rate policy that has a shape similar to that of popular markets. Furthermore, we formally analyze interest rate policies based on PID controllers, which work efficiently based on fewer assumptions. Using public data of popular markets on the Ethereum blockchain, we analyze agent's behavior, build a realistic simulation environment and highlight the main tradeoffs in the design of interest rates for decentralized lending platforms.

Keywords: Decentralized Finance, decentralized lending protocols, interest rate models, stochastic optimal control, PID controller

JEL Classification: C50, C61, D47, G23

Suggested Citation

Bertucci, Charles and Bertucci, Louis and Gontier Delaunay, Mathis and Gueant, Olivier and Lesbre, Matthieu, Agents' Behavior and Interest Rate Model Optimization in DeFi Lending (April 22, 2024). Available at SSRN: https://ssrn.com/abstract=4802776 or http://dx.doi.org/10.2139/ssrn.4802776

Charles Bertucci

Ecole Polytechnique, Palaiseau - CMAP CNRS-UMR 7641 and Ecole Polytechnique ( email )

Route de Saclay
Palaiseau, 91128
France

Louis Bertucci (Contact Author)

Institut Louis Bachelier ( email )

Palais Brongniart
28 Place de la Bourse
Paris, 75002
France

Olivier Gueant

Université Paris I Panthéon-Sorbonne ( email )

17, rue de la Sorbonne
Paris, IL 75005
France

Matthieu Lesbre

Morpho Labs ( email )

Paris
France

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