Original author: David Ma

Original compilation: Luffy, Foresight News

existpart 1In , I categorize lending and borrowing protocols in Web3. As a quick refresher, a lending agreement is a set of rules that govern how a borrower temporarily borrows assets from a lender and promises to repay those assets. This agreement will define how interest will be charged to the borrower and how the mortgage will be structured to protect the lender. Part 1 of this series explored topics related to interest periods: demand vs. term, loan rollovers vs. perpetuals, etc., and categorized some agreements within that framework.

In this article, I will continue to discuss how interest rates are determined in various lending agreements.

interest rate

The interest rate is an additional fee that the borrower pays the lender. For ease of comparison, interest rates are often quoted in an annualized format, expressed as an annual percentage rate (APR) or yield (APY). The difference between the two is that APR assumes no compounding, while APY assumes compounding. For example, with an APR of 10%, compounding half-yearly would result in an APY of 10.25%.

The relationship between the two is expressed by the following formula:

APY = (1 + APR / k)^k — 1, where k is the number of times of compounding per year.

In Web3, most loans are continuously compounded (large k values) because most loans are demand loans. So they use APY quotes to tell lenders how much money they will make in a year, assuming interest rates stay the same. For term loans, its more common to quote APR.

By the way, if 2020-style crude liquidity mining returns, please be wary of APY predatory offers, as these opportunities will not last long and the results of compound interest will be difficult to achieve. Calculating it mentally using APR is much more reliable. For a fixed reward pool, doubling the TVL means the reward is halved.

Now, with the definition out of the way, we can discuss interest rate pricing.

Pricing

Pricing is the mechanism for calculating how much interest rate borrowers and lenders will pay each other. While not exhaustive, this article will cover some of these mechanisms:

• Order book pricing: most flexible and market-driven, but trade-offs for user experience

• Utilization-based pricing: This model finds product-market fit in DeFi, but is not 100% efficient and underperforms in extreme cases

• Auction: Good pricing and efficient lending, but requires users to plan ahead, secondary market fragmentation, and other minor frictions.

• Ajna utilization model: a modification of the classic utilization model, suitable for use in oracle-less protocols

• Tazz Perpetual Loan Financing Model: A new p2p ool ​​lending primitive that allows the market to price interest rates, making collateral fully modular.

• Manual Pricing: Governance-led pricing.

Order book pricing

The most common way to price assets is to let the market adjust itself through the order book. Let borrowers and lenders issue limit orders specifying the amount and interest rate each is willing to borrow or lend. When an order is matched, a transaction is made.

However, order books also have disadvantages:

• Unskilled users dont know how to price them. These users simply want to transact without paying huge costs.

• Placing a limit order is like a free option. The less liquid the market is and the slower the block time, the more valuable the option is. In other words, the more the theoretical true price moves without the order being executed, the greater the option value contained in those limit orders themselves.

• Good operation of the order book requires active management. You need to cancel outdated limit orders and you need to play bidding war games with other players.

• It requires a lot of trading.

This is why order books remain unpopular on-chain. On the contrary, AMM, inquiry and auction are more suitable for blockchain products.

On the lending side, the order book faces greater challenges:

• Order book trading creates peer-to-peer loan matching for which default risk is irreplaceable.

• Continuing term loans create positions that are not fully interchangeable with each other. In contrast, protocols such as Pendle and Notional choose to issue loans for a fixed period on a specific date. The available loan terms are 37 days, 159 days, etc., which is strange.

• Short-term loans create more deals. You can automate the rollover, but how do you price the next loan?

All of this leads to market fragmentation, or at least a complicated trading experience. That said, NFT lending platforms like Blur and Arcade.xyz still rely on an order book-like user experience. They have all come up with features that can alleviate a poor user experience.

Blur incorporates a form of perpetual lending to eliminate the hassle of the term dimension.

Both Blur and Arcade have collection offers where lenders treat the entire collection of NFTs as fungible, and any NFT in the collection can be used as collateral.

Ever wondered how to interpret Blurs collectible lending chart? I wrote one herePost。

Arcade’s P2P loan matching and collection offers

AMM is a subcategory of order books. If a protocol can bring enough people together in the lending market for fungible tokens, then AMM is a good choice. Interest rates have better mean reversion capabilities than tokens, so using AMM to obtain LP interest rates is safer than LP tokens. This is how Pendle, Notional and Tazz work.

To recap, while order books work well with simple assets, lending order books have too many dimensions to consider and require clever ways to reduce the complexity of the user experience.

Utilization-based pricing

Utilization of a given lending pool is the ratio of total assets lent to total assets available for loan.

Utilization-based pricing defines interest rates as some increasing function of utilization.

Aave, the first and largest on-chain lending platform, takes this approach. It remains the most popular way to price interest rates on liquid and fungible assets.

Note that Aave did not start with this design. The 2018 white paper by EthLend (the name of Aave before the rebrand) outlined the p2p periodic order book, with the utilization-based model introduced in their 2020 white paper. This radical rethinking of financial primitives (Uniswap AMM is another example) is one of the joys of DeFi.

Aave’s borrowing interest rate

Since this is not explained in the white paper, my guess as to the motivation behind this approach is very simple. Consider an economic model – when interest rates are high, fewer people are willing to borrow money and more people are willing to lend. The best rate is one where the number of people willing to borrow money exactly matches the number of lenders, and the utilization rate is 100%.

When interest rates are too low, more people are willing to borrow than there are lenders. Utilization will reach 100%, but it doesnt tell us where in the model we are currently. Additionally, the lender cannot exit the loan.

When interest rates are too high, a large supply of loans goes unused. The APY spread (1-utilization) increases as interest rates increase. This is before the platform charges fees.

Because unobservable lending curves vary with market conditions, the challenge is to keep interest rates close to optimal while retaining some buffer for lenders to exit.

Aave’s “interest rate mode” mentioned above is a bit of a misnomer. Math geeks like to call this a PID controller, but its only partially automated. First, Aave selects a target utilization (e.g. 90%) and an entanglement curve. If utilization regularly exceeds 90%, Aaves governance will steepen the interest rate curve in an attempt to push utilization down. If utilization is too low, the opposite is true.

Sometimes, the market encounters special situations where the PID controller reacts too slowly. For example, during the Ethereum merger in September 2022, pre-merger ETH will be forked into PoS ETH and PoW ETH. PoW ETH is considered by the market to be worth approximately 2% of PoS ETH. Market participants see this and want to keep as much pre-merger ETH in their wallets as possible. One way is to put the stablecoin as collateral and borrow ETH. As long as the cumulative interest over the life of the loan is less than 2%, its a profitable deal. Earning 2% in less than 1 week means paying over 100% APR. Aaves interest rate is capped at 100%. Needless to say, in the days leading up to the merger, Aave, Compound, Euler, Inverse, and every PID controller lending protocol all hit their ETH utilization limits. If I remember correctly, Inverse had no rate cap and the APR ended up being 1000%.

One final thing to note about utilization-based pricing is that it fits naturally with a peer-to-peer structure, hence demand loans. Therefore, we often see these attributes combined naturally.

All in all, the benefit lies in the user experience under normal market conditions: borrow anytime, leave anytime. But when utilization reaches 100% (as during the Ethereum merger), lenders are left with no recourse. Other disadvantages are the capital inefficiency of the 10% loan buffer and the inability to provide term loans.

auction

Auctions are a time-tested method of issuing new debt (primary market issuance). U.S. Treasuries, the most liquid government securities in the world, use auctions to price new debt. In a lending agreement, borrowers and lenders submit secret bids to regularly held auctions, find market clearing rates, and issue new debt to clearing rate participants.

Term Finance is a relatively new protocol inspired by this mechanism. their auctionImplementation detailsWorth reading.

Auctions can efficiently match lenders and borrowers. Unlike an order book, which requires locked capital to place orders awaiting execution, or a loan pool based on a utilization model that provides a buffer for lender withdrawals, no capital sits idle. The only unproductive period is when the asset is locked during the auction.

Auctions also produce high-quality pricing because market participants converge on a Schelling point to aggregate their information.

On the downside, auctions require some pre-planning and are not as user-friendly. Its a good bet for U.S. Treasuries, but the term loan market isnt heavily involved in the cryptocurrency space. Another challenge is the fragmentation of the market, with cryptocurrencies having many similar but non-fungible assets. This will be a harder product to launch, but I hope that one day Term Finance will be able to issue Ethereum T-bills with the full support of Ethereum.

Ajnas Utilization Model

Ajna is one of the few lending protocols that does not rely on oracles. A complete explanation of how Ajna achieves this goal is beyond the scope of this article. Rather, the way its rates are designed deserves discussion.

Lenders first select a valuation of collateral (e.g. ETH) against which they are willing to lend the token (e.g. USDC). Borrowers are matched from the highest valuation downward. Borrowers with the riskiest loans (highest loan-to-collateral ratio) set a highest threshold price (HTP), and lenders with lower valuations will not receive interest.

https://www.ajna.finance/pdf/Ajna_ELI5.pdf

Lenders don’t want to set the valuation too high because they could lose money in the event of a default. Lenders also don’t want to set the valuation too low because they won’t get any interest.

The interest rate is determined by the utilization function, but the calculation here only considers lenders that set collateral valuations above the HTP. Rates start at 10% and are multiplied or divided by 1.1 every 12 hours, depending on how utilization compares to Target Utilization.

The main advantage is that despite the peer-to-pool design, the mechanism does not require any oracles to function. Lenders, on the other hand, need to constantly monitor their valuations. Like other utilization-based interest rate pricing mechanisms, APR is affected by unutilized borrowings.

Although borrowers and lenders can leave (demand) at any time, Ajnas minimum loan period is 1 week. Since Ajna hasnt been in the market long enough, its too early to know the full pros and cons of this mechanism.

True permissionless and immutable protocols are rare because they are difficult to enforce correctly. But when they do happen, they become the building blocks of composability. I really hope Ajna can become the Uniswap of the lending industry.

Tazz’s permanent loan financing model

Tazz is an upcoming lending protocol that introduces new interest rate pricing primitives. Again, a complete description of this mechanism is beyond the scope of this article.

Similar to Aave, Tazz debt starts as a zero-interest perpetual loan. Debt tokens (AToken in Aave terminology) can be traded on any DEX. In addition to protocol bankruptcy, Aaves Atoken and actual token transaction prices are almost always close to 1:1, while Tazzs debt token (ZToken) is priced by the market. The price of ZToken determines the interest rate on which notional debt accumulates (i.e. funds). If nominal debt continues to increase, collateral parameters will trigger liquidation.

Ongoing funding disbursements are proportional to k (1 – ZToken’s TWAP relative to the token price). The lower k, the longer the debt maturity and the more susceptible it is to interest rate risk.

Note that in this mechanism, staking is fully modular with the rest of the protocol. You can set up asset pools with no collateral, NFT collateral, LP tokens, illiquid tokens, locked tokens, oracle-based collateral pricing, or one-time pricing. It doesnt matter because the market can price the interest rate required to take the risk.

Notably, this makes:

• Peer-to-peer lending

• 100% loan utilization, so spreads are low

• Combined liquidity

• Any collateral type

One potential drawback is that it requires monitoring pool prices (but less than Ajna). If unrealistic prices persist for too long, this can result in unrealistic interest rates. ZToken’s liquid market will prevent both borrowers and lenders from having to monitor things too closely.

Manual/governance pricing

In light of GHOs unmooring, this pattern is worth mentioning. There are a number of Collateralized Debt Position (CDP) stablecoins. Makers DAI has the largest scale, followed by Liquiditys LUSD, Lybras eUSD, Prismas mkUSD, etc.

Although CDPs dont look like loans, they are not. Borrowers use ETH (Maker v1), LST (Prisma, Lybra) or other assets as collateral. The borrower mints a CDP and the protocol oracle calculates the dollar value at a 1:1 ratio. CDP can be sold on the open market, whereby the borrower borrows another asset and the lender receives the CDP. The loan is permanent and the value may not be fixed at $1. Borrowers pay an interest rate to the protocol, and lenders may receive another interest rate from the protocol (such as the Dai Savings Rate). Sometimes, there is a protection fund called a stability module to avoid CDP decoupling.

The disadvantage of manual pricing is that it is subject to governance processes, lengthy debates, low participation in community governance, etc., and therefore slow to react. The benefit is that human processes are harder to manipulate than code where edge cases can occur.

GHO has fallen since its inception

Aaves GHO is a CDP with manual interest rates. The current borrowing rate on GHO is 3% (lower than 5% on Treasury bills and Dai), and their lending (savings) rate on Aave is 0%. Therefore, there are too many people willing to borrow money and too few people willing to lend, causing the price of GHO to fall.

The debate on the Aave governance forum has been going on for months. The essence of the debate boils down to whether to peg the exchange rate or keep a stable interest rate (and therefore a variable one). GHO cannot have it both ways until it gains more market dominance.

in conclusion

In this article, we look at the various ways interest rates are priced in loan agreements. There are of course many more methods, but the goal of this series is to establish a taxonomy. So far, we have considered interest duration and interest pricing as the two main perspectives through which protocols can be analyzed and classified. In the next article I will discuss mortgages.