Mitigating Decentralized Finance Liquidations with Reversible Call Options

Abstract

Liquidations in Decentralized Finance (DeFi) are both a blessing and a curse—whereas liquidations prevent lenders from capital loss, they simultaneously lead to liquidation spirals and system-wide failures. Since most lending and borrowing protocols assume liquidations are indispensable, there is an increased interest in alternative constructions that prevent immediate systemic-failure under uncertain circumstances.

In this work, we introduce reversible call options, a novel financial primitive that enables the seller of a call option to terminate it before maturity. We apply reversible call options to lending in DeFi and devise Miqado, a protocol for lending platforms to replace the liquidation mechanisms. To the best of our knowledge, Miqado is the first protocol that actively mitigates liquidations to reduce the risk of liquidation spirals. Instead of selling collateral, Miqado incentivizes external entities, so-called supporters, to top-up a borrowing position and grant the borrower additional time to rescue the debt. Our simulation shows that Miqado reduces the amount of liquidated collateral by 89.82% in a worst-case scenario.

Appendices

A Black-Scholes Model

We apply the Black-Scholes model [3] to price call options under optimal assumptions, such as the non-existence of dividend payouts. The option premium is calculated for European call options on a per-share basis. The payoff for $\mathcal {C}_S$ introduced in Fig. 2 is trivial to grasp but it does not yield any insights on the pricing of the option. With the BS model for a European call option determines the option price as

$$\begin{aligned} c = S_0e^{-r_f\cdot T} N(d_1) - Ke^{-r\cdot T} N(d_2) \end{aligned}$$

(9)

where

$$\begin{aligned} d_1 = \frac{\ln (S_0K)+(r-r_f+\sigma ^22) \cdot T}{\sigma \cdot \sqrt{T}} \end{aligned}$$

(10)

and

$$\begin{aligned} d_2 = d_1 - \sigma \cdot \sqrt{T}. \end{aligned}$$

(11)

$S_0$ is the spot exchange rate, $r_f$ is the foreign interest rate, $r$ is the domestic interest rate and $\sigma$ is the volatility of the underlying asset. For a detailed introduction to the Black-Scholes pricing model for European call options, we refer the interested reader to [8].

We remark that the B-S model does not take into account the decrease in risk and lowered average payoff due to termination by $\mathcal {C}_S$. We defer a more precise pricing model for reversible call options that to future work.

B Tables

Table 1. Accumulative collateral restraint by Miqado over a time-frame of 41 months.

Table 2. Payoffs for Miqado supporters at maturity assuming that borrowers would not rescue. We present the probability that a supporter (i) exercises the call option and profits, (ii) exercises the call option but loses, (iii) defaults. We also simulate the average profit for supporters. our simulations are based on the real market prices.