Mitigating Decentralized Finance Liquidations with Reversible Call Options

Research report

TLDR

Fixed spread liquidations (FSLs) are heavily used in crypto (AAVE, COMP, etc) – this paper introduces a novel derivative, a reverse call option (RCO), for FSLs to mitigate liquidations and their effects. RCOs allow sellers to terminate the contract prior to its maturity date, thereby mitigating liquidations and changing pricing structures.

Proposes a new kind of derivative – reverse call options (RCOs). Its distinguishing feature is that the seller of a European call option can pay a premium to the buyer to terminate the option before its maturity. RCOs for FSLs align incentives for external parties, known as supporters, to deposit collateral in positions to maintain their solvency.
RCOs are applied practically via the implementation of a protocol, MIQADO, which incentivizes supporter behavior via RCOs. Back-testing on AAVE v1, AAVE v2, and Compound show that the implementation of a basic MIQADO protocol utilizing RCOs based on an out-of-the-box Black-Scholes model mitigated the liquidation of 89.82% of collateral.

Highly applicable. In the future, we should build a rudimentary MIQADO protocol internally and simulate it on our historical policy portfolios. Full RCO implementation in Concrete's context is non-trivial, but a basic implementation for back-testing/simulation purposes is possible.
These authors are top tier when it comes to academic DeFi liquidation research – this is the latest piece in a series of FSL related work they’ve published. They are particularly useful as their work is generally more practical than most academically-sourced academic work.

FSLs are used across DeFi – allows a liquidator to repay a fraction of the borrower’s debt and acquire collateral at a discount. This system is simple, but leads to cascading liquidations since selling collateral leads to collateral price depreciation leads to more liquidations leads to selling collateral etc.
Pricing for the RCOs is generated by Black-Scholes model. The premium factor, theta, is also determined by the Black-Scholes model – it is the percentage of the loan value the supporter is optimally expected to deposit. The lending protocol sets their own premium factor, and the supporter compares the real and theoretical values to determine profitability.
Simulation engine is predicted on all liquidations, on a rolling window basis, from Compound, AAVE, and Maker liquidations from 2020-2022. The simulation hinged on the assumption that a MIQADO protocol overlaid all of these lending protocols. As such, these models simulated two behavior types.
Data for the simulation engine was pulled directly on-chain and simulated with different call option thresholds on the same data. No out-of-sample data was simulated.

The fact that this paper utilizes a completely basic version of Black-Scholes to generate the optimal premium factor value and still has good results merits closer examination. Especially so given that the authors do not articulate what measure of volatility they use, which is, in their own words, pivotal to the success of any MIQADO-type protocol.
Practical implementation of a MIQADO protocol with RCOs requires the parametrization of the premium factor and time to maturity which is a non-trivial empirical process. The paper does not explicitly detail how to attack this problem.
Aside from the implementation of a full MIQADO protocol, RCOs are interesting in and of themselves. It makes sense for Concrete to be the seller of such policies but such a system would require significant re-designs.

Interested to know how TVL percentage is measured in the introduction – “With over 15B USD of total value locked (TVL), DeFi’s lending and borrowing services account for 30% of DeFi’s locked up assets.”
Short liquidations, where the liquidators sell the collateral immediately after, account for ~38% of all FSL liquidations. The paper notes that the maximum collateral price depreciation caused by a series of short liquidations is 26.9% – unclear what collateral type this is.
This paper focuses exclusively on over-collateralized lending systems.

The lending pool is represented as where P is defined by 2 parameters — Dt, the debt owed by the borrower (denominated in stables) and Ct, the collateral (think of this as the number of tokens because it is not denominated in stables definitionally).
Health factor is what determines liquidations. HF_t(P)=C_t*p_t*D_t where pt is the price of the collateral in terms of stables and is essentially a slippage/buffer term. When it is less than 1, the loan is available for liquidation.
In line with the health factor formulation, the collateralization ratio is calculated as CR_t(P)=C_t*p_t*D_t.
The general form of a protocol that uses an FSL mechanism is given by PROTFSL=⟨L,θ,kCF,S⟩
k_CF represents the close factor – the percentage of the debt position that liquidators are allowed to repay in a single FSL event. This is a constant.
S represents the spread on collateral value that the protocol offers liquidators for their services. For example, AAVE offers between 5% and 15% for liquidators – 5% for ETH specifically.
Accordingly, maximum liquidator profit on a single FSL event is (Dt*kCF)*S.

MIQADO is a particular instance of the generalized form of an FSL protocol (as described above). MIQADO’s novelty lies in its implementation of RCOs which incentivizes external parties to “support” positions by depositing collateral and maintaining its solvency.
The sole functional difference between RCOs and vanilla European options is that RCOs allow for the seller to terminate the contract early. Resulting differences include changes to pricing – sellers must pay for the extra control they have after all. This is manifested via the termination premium.
The premium factor is a key mechanistic element - it is the primary determining factor for risk tolerance from a borrower/protocol PoV and profit from a supporter/liquidator PoV.
The lender sets a constant premium factor for the protocol and an optimal premium factor is calculated by supporters. The spread between these values determines profitability of supporting actions.

The authors of this paper have been toying with FSL ideas for a while. The first paper in this series is also in the Blueprint library.
Paper co-authored by Tarun Chitra articulating some of the liquidation risks described in this paper in much more detail with regard to Compound. Little outdated but still a good read.

Last updated 1 year ago