Pricing and hedging of decentralised lending contracts

ArXiv ID: 2409.04233 “View on arXiv”

Authors: Unknown

Abstract

We study the loan contracts offered by decentralised loan protocols (DLPs) through the lens of financial derivatives. DLPs, which effectively are clearinghouses, facilitate transactions between option buyers (i.e. borrowers) and option sellers (i.e. lenders). The loan-to-value at which the contract is initiated determines the option premium borrowers pay for entering the contract, and this can be deduced from the non-arbitrage pricing theory. We show that when there are no market frictions, and there is no spread between lending and borrowing rates, it is optimal to never enter the lending contract. Next, by accounting for the spread between rates and transactional costs, we develop a deep neural network-based algorithm for learning trading strategies on the external markets that allow us to replicate the payoff of the lending contracts that are not necessarily optimally exercised. This allows hedge the risk lenders carry by issuing options sold to the borrowers, which can complement (or even replace) the liquidations mechanism used to protect lenders’ capital. Our approach can also be used to exploit (statistical) arbitrage opportunities that may arise when DLP allow users to enter lending contracts with loan-to-value, which is not appropriately calibrated to market conditions or/and when different markets price risk differently. We present thorough simulation experiments using historical data and simulations to validate our approach.

Keywords: Decentralised Finance (DeFi), Option Pricing, Deep Neural Networks, Hedging Strategies, Lending Protocols

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced financial mathematics, including non-arbitrage pricing theory, nonlinear PDEs for options with rate spreads, and barrier option frameworks, indicating high mathematical complexity. It also demonstrates high empirical rigor through the development of a deep neural network-based hedging algorithm, validation via historical data and simulations, and discussion of real-world application to decentralized lending protocols.

  flowchart TD
    A["Research Goal<br>Price & Hedge Decentralised Lending Contracts"] --> B{"Key Methodology"}
    B --> C["Derivative Pricing Theory<br>Loan = Option, LTV = Premium"]
    B --> D["No-Friction Model<br>Derive Null Optimal Exercise"]
    B --> E["Deep Neural Network<br>Learn Hedging Strategy"]
    C & D --> F["Computational Process<br>Simulation & Data Replication"]
    E --> F
    F --> G{"Key Outcomes"}
    G --> H["Hedge Lender Risk<br>Beyond Liquidations"]
    G --> I["Identify Arbitrage<br>Mispriced LTVs"]
```mermaid
flowchart TD
    A["Research Goal: Pricing & Hedging<br>Decentralised Lending Contracts"]
    A --> B["Methodology: Derivative Framework"]
    B --> C["Model Loan as Option<br>LTV determines Premium"]
    B --> D["No-Friction Analysis<br>Null Optimal Exercise"]
    C & D --> E["Deep Neural Network<br>Learning Hedging Strategies"]
    E --> F["Computational Process<br>Simulation & Historical Data"]
    F --> G{"Outcomes"}
    G --> H["Hedge Lender Risk<br>(Beyond Liquidations)"]
    G --> I["Arbitrage Detection<br>Mispriced LTVs"]