BakUp: Automated, Flexible, and Capital-Efficient Insurance Protocol for Decentralized Finance

Programmable blockchains [1, 2, 3, 4, 5] have led to an era of decentralized finance, or DeFi, where centralized intermediaries are replaced by software code, also known as smart contracts, to provide financial services. This has spawned novel financial innovations such as automated execution, resulting in no market downtime, and permissionless access, increasing user inclusiveness and applications’ interoperability compared to its traditional (TradFi) counterpart. This paradigm shift has led to increased utilization of DeFi systems in recent years, with several billion dollars exchanging hands daily [6].

Despite its success, DeFi is not free from risks, thus impeding its rapid adoption [7, 8, 9]. These risks can generally be classified as technical or economic [10]. Technical risks arise from exploiting the vulnerabilities of smart contracts, such as programming bugs and/or unintentional functional specification inconsistencies that can lead to irreversible loss of funds held by a DeFi protocol. The second type of risks, stem from economic inefficiencies within a protocol. Technical and economic exploitation, along with external factors, often lead to unexpected behavior in DeFi metrics. This includes fluctuations in token prices and liquidity in automated market-making (AMM) pools, as well as extreme borrowing rates in lending protocols¹¹1https://finance.yahoo.com/news/defi-lenders-spooked-curve-exploit-193953614.html. Such deviations can rupture the functioning of dependent protocols [11] or result in losses for end users. For example, the liquid staking protocol Lido Finance [12] has a wrapped token for staked ETH (stETH), which is expected to maintain its price stability relative to ETH. However, if this characteristic fails due to the aforementioned reasons, stETH investors may incur unforeseen losses. This emphasizes the imperative need for robust DeFi risk management tools to safeguard users from such consequential risks.

One category of solutions to the above problem involves insurance, where the risk of users (policyholders) is transferred to underwriters. However, the very nature of DeFi demands an insurance platform that is (a) automated, ensuring instantaneous claim payout; (b) permissionless in access to achieve interoperability; (c) resilient against both technical and economic vulnerabilities, as it is the last resort for financial adversities; (d) flexible to underwrite a vast pool of policies; and (e) capital-efficient, i.e., any locked capital should be capable of earning yield.

An insurance platform completely implemented using smart contracts achieves the first two properties, viz., automation and permissionless access. However, the latter three merits, viz., resilience, flexibility, and capital-efficiency inherently compromise the objectives of each other. For instance, a high level of resilience in contract design implies high immutability, which in turn hinders the underwriting flexibility derived from adaptability or upgradability. Simultaneously, the resilience of the smart contract platform may not align well with capital efficiency, as yield generation often involves interactions with third-party protocols that are susceptible to vulnerabilities.

This paper proposes BakUp, a design for a modular, flexible, and capital-efficient smart contract platform that uses binary conditional tokens to provide insurance policies. BakUp allows users to independently align between resilience, flexibility, and capital efficiency by comprising three distinct modules: a core module for basic capital accounting to ensure no defaults, an oracle module for underwriting policies, and a yield module on the periphery of the above two for capital management. The core module is immutable, while the oracle module can be created permissionlessly with a custom developer-defined logic, which can range from conservative to highly customizable. Simultaneously, the peripheral yield module operates independently from the main protocol, making it optional for users to engage in yield-generation activities. Interestingly, this optional feature doesn’t pose any risk to the capital of users who choose not to participate, allowing users—both underwriters and policyholders—with varying risk preferences to interact simultaneously on the platform without imposing risks on others.

Here, we first present the design of the core module. Subsequently, we describe the oracle module and demonstrate a contract design capable of underwriting the de-pegging of stable assets using a combination of on-chain and off-chain price sources. Thereafter, we present the yield module’s design that integrates the DeFi Risk Transfer protocol [13] for secure yield generation, allowing users to mitigate their technical risks by paying an additional premium. This allows users to choose between unsecured yield (high-risk/reward), secure yield (medium-risk/reward), or no yield at all (low-risk/reward). The insurance policies, implemented as a binary conditional ERC20 token, can be traded on both decentralized (DEX) and centralized exchanges (CEX). As such, this paper also presents a DEX marketplace by analyzing the divergence loss of liquidity providers in three broad strategies for the passive liquidity provision of these tokens. Empirical results show that conservative strategies and parameterization can help mitigate the loss of liquidity providers by over $47\%$ compared to the naive strategy in the worst-case scenario.

This paper is organized as follows. Section II gives background knowledge, Section III presents the design and implementation of the various modules, Section IV gives a market analysis of the underlying tokens, including liquidity provision strategies, that are later evaluated in Section V. Section VI discusses related works, and Section VII concludes this work.

For the proper functioning of BakUp, it is essential to have an efficient marketplace where users can buy or sell policy and underwriting tokens in exchange for a common currency. Therefore, studying the incentive mechanism for various users to participate in the marketplace is crucial. This includes examining the risk-adjusted returns for the liquidity providers. In this paper, we focus on studying LP strategies for the trading pair $P_{i}/U_{i}$ on AMMs, although other pairs such as $P_{i}/C$ or $U_{i}/C$ can also exist. This is because the former pair is sufficient for buying or selling $P_{i}$ and $U_{i}$ in exchange for $C$ (as explained next). Another advantage is that the liquidity provision for this trading pair does not require currency tokens.

Let $p_{i}$ denote the spot price of $P_{i}$ relative to $U_{i}$. A user purchasing a small quantity $\delta$ of $P_{i}$ (such that slippage on AMM is negligible) can perform the following ordered actions in a single transaction:

• •

  Mint $\frac{\delta p_{i}}{1+p_{i}}$ units of $P_{i}$ and $U_{i}$ by depositing $\frac{\delta p_{i}}{1+p_{i}}(1+f)\cdot C$.

• •

  Swap $\frac{\delta p_{i}}{1+p_{i}}\cdot U_{i}$ for $\frac{\delta}{1+p_{i}}\cdot P_{i}$ on AMM.

The user now holds $\delta\cdot P_{i}$. Similar can be done when the user wants to sell $\delta\cdot P_{i}$:

• •

  Swap $\frac{\delta}{p_{i}+1}\cdot P_{i}$ for $\frac{\delta p_{i}}{1+p_{i}}\cdot U_{i}$ on AMM.

• •

  Burn equal $P_{i}$ and $U_{i}$ to receive $\frac{\delta p_{i}}{1+p_{i}}\cdot C$.

The procedure for buying and selling underwriting tokens is analogous to the above. As a result, the effective buying and selling prices of $P_{i}$ in terms of $C$ are $\frac{p_{i}}{1+p_{i}}(1+f)$ and $\frac{p_{i}}{1+p_{i}}$, respectively and for $U_{i}$, they are $\frac{1}{1+p_{i}}(1+f)$ and $\frac{1}{1+p_{i}}$, respectively. Therefore, the market’s risk assessment results in different values of policy and underwriting tokens, and it gets expressed as a single price $p_{i}$. The following describes various strategies for liquidity providers on concentrated liquidity AMMs, which we then evaluate in the subsequent section.

Similarly, if $p_{i}>\frac{1-\epsilon}{\epsilon}$, then the price of $U_{i}$ relative to $C$ satisfies:

As $U_{i}$ can also be redeemed for at least $\epsilon\cdot C$ upon contract expiration, another arbitrage opportunity arises. A trader can purchase them at a lower price of $p_{U_{i}}$ and subsequently redeem them for at least $\epsilon\cdot C$ at the contract expiration. Consequently, Inequality (7) holds.

Considering a concentrated liquidity pool for the pair $P_{i}/U_{i}$, the LPs thus need to deposit policy tokens in the price interval $[p_{i},\frac{1-\epsilon}{\epsilon}]$ (prices above the spot price) and underwriting tokens in the price interval $[\frac{\epsilon}{1-\epsilon},p_{i}]$ (prices below the spot price) with some distribution. Suppose an LP mints $1$ unit each of two tokens, and provisions them as liquidity with $p_{i}$ being the entry spot price. We consider three limiting passive strategies for liquidity provision:

1. 1.

   Uniform: This strategy consists of depositing $1\cdot P_{i}$ in the price interval $[p_{i},\frac{1-\epsilon}{\epsilon}]$, and $1\cdot U_{i}$ in the price interval $[\frac{\epsilon}{1-\epsilon},p_{i}]$ with the two intervals having a constant liquidity. This is depicted in Figure 6(a).

2. 2.

   Concentrated around $p_{i}$: This strategy involves depositing, with a constant liquidity, $1\cdot P_{i}$ in $[p_{i},p_{r}]$, and $1\cdot U_{i}$ in $[p_{l},p_{i}]$ for some $p_{l},p_{r}$. Such a strategy is expected to earn a higher trading fee than the uniform strategy since liquidity is concentrated around the spot price. This is depicted in Figure 6(b).

3. 3.

   Concentrated at the edges: This strategy consists of depositing, with a constant liquidity, $1\cdot P_{i}$ in $[p_{r},\frac{1-\epsilon}{\epsilon}]$, and $1\cdot U_{i}$ in $[\frac{\epsilon}{1-\epsilon},p_{l}]$ for some $p_{l},p_{r}$. Such a strategy is expected to earn lower trading fees than the uniform strategy since liquidity is concentrated away from the spot price. This is depicted in Figure 6(c).

The next Section evaluates the divergence loss of the LPs under the above strategies and examines ways to mitigate risk.

Divergence Loss is defined as the opportunity cost for an LP to provide token reserves as liquidity compared to just holding them. In this section, we assess the divergence loss experienced by liquidity providers across the three strategies: uniform, concentrated around the entry price, and concentrated at the price interval edges (Figure 6). Our evaluation addresses the following two questions: $(1)$ Which parameters significantly impact the divergence loss of liquidity providers and to what extent? $(2)$ What are some optimal techniques to mitigate the risk of divergence loss for liquidity providers?

We adhere to an evaluation methodology where we assume that an LP mints $1$ unit of $P_{i}$ and $U_{i}$ and creates a liquidity position with an entry price $p_{i}=\textbf{p}$. If there is no liquidity provision, the value of these tokens at the conclusion of the contract is always $1$ unit of $C$ (enforced by Invariant (2)). To evaluate the divergence loss, we calculate the total value of the tokens held by the LP at the conclusion of the contract and represent it as a fraction of $1\cdot C$. We use four equally-spaced values for $\epsilon:$ $\{0.01,0.07,0.13,0.19\}$ and do not consider any further higher values since $\epsilon\ll 1$. For plotting, we take the natural logarithm of the x-axis, for the price interval $[\frac{\epsilon}{1-\epsilon},\frac{1-\epsilon}{\epsilon}]$, and then min-max normalize it to the range $[0,1]$. Here is a summary of divergence loss in the three strategies:

1. 1.

   Uniform: If there is no catastrophe, i.e., the underlying assertion does not hold, $p_{i}=\frac{\epsilon}{1-\epsilon}$ at event expiration and the LP ends up with only $P_{i}$. Their $1\cdot U_{i}$ is exchanged for an average price of $\sqrt{\frac{\epsilon\textbf{p}}{1-\epsilon}}$, which is the geometric mean of the extreme prices $\{\frac{\epsilon}{1-\epsilon},\textbf{p}\}$ as derived in Section II-B. Therefore, the LP ends up with $1+\sqrt{\frac{1-\epsilon}{\epsilon\textbf{p}}}$ units of $P_{i}$ each worth $\epsilon\cdot C$, thus a total value of $\epsilon+\sqrt{\frac{\epsilon(1-\epsilon)}{\textbf{p}}}$ units of $C$.

   When there is a catastrophe, the LP ends up with only $U_{i}$. As above, their $1\cdot P_{i}$ is exchanged for an average price of $\sqrt{\frac{(1-\epsilon)\textbf{p}}{\epsilon}}$, giving them a total of $1+\sqrt{\frac{(1-\epsilon)\textbf{p}}{\epsilon}}$ units of $U_{i}$. Since $U_{i}$ is worth $\epsilon\cdot C$, they receive a value of $\epsilon+\sqrt{\textbf{p}\epsilon(1-\epsilon)}$ units of $C$.

   The above two cases are shown in Figure 7(a) & 7(d), respectively. We can observe that when the normalized entry price is closer to $0$$(1)$, the divergence loss is higher for the catastrophic(non-catastrophic) scenario. Also, for a given p, the divergence loss is lower at higher values of $\epsilon$. The worst loss (at p=$\frac{\epsilon}{1-\epsilon}$ or $\frac{1-\epsilon}{\epsilon}$) can be reduced from $0.98$ to $0.62$ by varying $\epsilon$ from $0.01$ to $0.19$.

2. 2.

   Concentrated around p: In the case with no catastrophe, the final price $\frac{\epsilon}{1-\epsilon}$ is less than $p_{l}$. Therefore, the LP’s $1\cdot U_{i}$ is exchanged for an average price of $\sqrt{p_{l}\textbf{p}}$, which is the geometric mean of the extreme prices $\{p_{l},\textbf{p}\}$. As before, this gives a total value of $\epsilon+\frac{\epsilon}{\sqrt{p_{l}\textbf{p}}}$ units of $C$. If there is a catastrophe, the LP’s $1\cdot P_{i}$ is exchanged for an average price of $\sqrt{\textbf{p}p_{r}}$. This gives a total value of $\epsilon+\epsilon\sqrt{\textbf{p}p_{r}}$ units of $C$.

   These two cases are shown in Figure 7(b) & 7(e). For a given p and $\epsilon$, we choose a range of values for the widths $\textbf{p}-p_{l},$ and $p_{r}-\textbf{p}$. This range represents $10-50\%$ of p for $\textbf{p}-p_{l}$, and $10-50\%$ of $1-\textbf{p}$ for $p_{r}-\textbf{p}$ and is represented by the shaded region in the figure. The median value of the widths, given by $\textbf{p}-p_{l}=0.3\textbf{p}$, and $p_{r}-\textbf{p}=0.3(1-\textbf{p})$, is represented by the solid line. For a given p and $\epsilon$, the divergence loss in this strategy is higher compared to the uniform strategy, particularly between $1\text{-}19.4\%$ at the interval edges (p=$\frac{\epsilon}{1-\epsilon}$ or $\frac{1-\epsilon}{\epsilon}$) for different values of $\epsilon$, and median values for $p_{l}$ and $p_{r}$. This is the cost LPs need to pay to achieve capital concentration (hence a higher fee revenue) in this strategy. However, the LPs can reduce their loss by choosing $p_{l},$ $p_{r}$ farther from p. The divergence loss, as in the previous case, reduces for higher values of $\epsilon$ with the worst loss reducing from $0.99$ to $0.74$ by choosing $\epsilon$ from $0.01$ to $0.19$.

3. 3.

   Concentrated at the edges: As before, in the case with no catastrophe, the LP’s $1\cdot U_{i}$ is exchanged for an average price of $\sqrt{\frac{\epsilon p_{l}}{1-\epsilon}}$. This gives a total value of $\epsilon+\sqrt{\frac{\epsilon(1-\epsilon)}{p_{l}}}$ units of $C$. If there is a catastrophe, the LP’s $1\cdot P_{i}$ is exchanged for an average price of $\sqrt{\frac{p_{r}(1-\epsilon)}{\epsilon}}$. This gives a total value of $\epsilon+\sqrt{p_{r}\epsilon(1-\epsilon)}$ units of $C$. These cases are shown in Figure 7(c) & 7(f) respectively. For a given p and $\epsilon$, we chose a range of values for the widths $\textbf{p}-p_{l},$ and $p_{r}-\textbf{p}$ as before. One can observe that the divergence loss in this strategy is the least of the three strategies. Compared to the uniform strategy, it is lower by $3.1\text{-}16.1\%$ at the interval edges (p=$\frac{\epsilon}{1-\epsilon}$ or $\frac{1-\epsilon}{\epsilon}$), and median values for $p_{l}$ and $p_{r}$. The loss increases when $p_{l},$ $p_{r}$ are farther from the edges. The lower divergence loss comes from a lower expected fee revenue since the position remains inactive when the price is outside its range. Lastly, the divergence loss reduces further with higher values of $\epsilon$, with the worst loss reducing from $0.95$ to $0.51$ by choosing $\epsilon$ from $0.01$ to $0.19$. This reduction is more than $47\%$ when compared to uniform LP strategy with $\epsilon=0.01$.

Of the two tokens (policy and underwriting) that an LP initially holds, they always end up with the token of lesser value. If $\epsilon$ is set to $0$, the LP ends with tokens worth zero and incurs a divergence loss of $1$. As this is unfavourable to LPs, it underscores the necessity of enforcing $\epsilon>0$.

The three LP strategies present a trade-off between divergence loss and increased fee revenue, resulting from enhanced capital concentration near the entry price. Additionally, an entry price closer to $0$ entails lower risk in a non-catastrophic outcome but higher risk in a catastrophic outcome, while the opposite is true for an entry price closer to $1$. Opting for a larger value of $\epsilon$ is another way to mitigate divergence loss risk, bringing it to as low as $0.51$ in the worst-case. However, since the policy tokens pays at least $\epsilon\cdot C$ regardless of the final state, one consequence of larger $\epsilon$ is a higher token price relative to $C$. This results in a lower coverage-to-premium ratio ($(1-\epsilon)/p_{P_{i}}$), even for low-probability adversities, and thus, one must consider this trade-off.

To summarize, BakUp gives its users–policyholders, underwriters, and liquidity providers–the tools to individually manage their risks and rewards. This is achieved through a modular approach. The invariant-based and immutable design ensures the robustness of the core module, the customizability of the oracle module enforces the flexibility of the insured policy, and most significantly, the optional and peripheral yield module empowers users to trade-off capital efficiency with external risk without compromising the security of the other users.

Other protocols, including ours, are based on Peer-to-Peer decentralized insurance [27] where individuals pool their insurance premiums and use these funds to mitigate individual damages. Some of them including Risk Harbour [28], Opium Protocol [29], cozy.finance [30], and Etherisc [31] facilitate automated underwriting done via smart contract while others like Unslashed Finance [32], Nsure [33], and Cover [34] have a voting-based claim assessment. Moreover, some of them including [29, 30] allow permissionless listing. In contrast to BakUp, none of the above protocols give their users the optional ability to manage yield on their capital. Instead, either the protocol offers no yield, or the yield management is performed by governance or delegated to a third party [35]. Some designs, including Risk Harbour V1 [36], propose using receipt tokens from yield platforms (e.g., cTokens on Compound) as disbursement currency. Such an approach permanently links the risk of the yield platform with the protocol’s underwriting module. On the other hand, BakUp disjoints the core, oracle, and yield modules and allows users to manage yield on their staked capital while having a permissionless policy creation.

A robust risk management system for the emerging area of DeFi requires a primitive platform with minimal external dependencies. This is successfully achieved in the BakUp protocol presented in this paper through a modular approach. At the same time, simulations suggest various mitigation strategies to minimize the risk for liquidity providers, contributing to the establishment of an efficient AMM marketplace. Possible future work in this direction includes (a) extending the conditional tokens from binary to $n$-ary with $n$ states to reduce the number of ERC20 tokens per adversity; (b) enabling the creation of a single underwriting and multiple corresponding policy tokens to model a collection of adversities as a single event. Such an approach is expected to reduce the total capital requirement from underwriters, thus improving capital efficiency.