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Pricing and hedging of decentralised lending contracts

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  • Lukasz Szpruch
  • Marc Sabat'e Vidales
  • Tanut Treetanthiploet
  • Yufei Zhang

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.

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  • Lukasz Szpruch & Marc Sabat'e Vidales & Tanut Treetanthiploet & Yufei Zhang, 2024. "Pricing and hedging of decentralised lending contracts," Papers 2409.04233, arXiv.org.
    • Handle: RePEc:arx:papers:2409.04233
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    References listed on IDEAS

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    1. Kaihua Qin & Jens Ernstberger & Liyi Zhou & Philipp Jovanovic & Arthur Gervais, 2023. "Mitigating Decentralized Finance Liquidations with Reversible Call Options," Papers 2303.15162, arXiv.org, revised Mar 2023.
    2. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    3. Matheus R. Grasselli & Cesar Gómez, 2013. "Stock Loans in Incomplete Markets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 20(2), pages 118-136, April.
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