Why Is Financial Engineering Important in Bridging? Episode 2

Kevin Chan
Published in
6 min readOct 18, 2022


Interest Rate Model vs. Bonding Curve (AMM)


In tradfi, the best market makers are consistent in their pricing and are always able to facilitate a client’s needs. Market makers are responsible for making sure there is both buy and sell liquidity on the market. Good market makers keep their principal portfolio balanced in such that any new client trade is possible and prices are predictable and consistent. Bad market makers can get offside with their positions and pass on worse, or punitive, pricing to subsequent clients who are not helping their imbalanced position.


Across Protocol strives to be the equivalent of a good market maker in the cross chain bridging space. Across does not change its pricing based on the direction of bridge transfers. Users can always expect consistent prices regardless of the direction of their transfer (and regardless of other users’ transfers). The pricing is only impacted when the system-wide capacity utilization is constrained. The net result is a cross chain bridge that is less costly to operate resulting in a better user experience for users and LPs.

In the previous episode, we showed how one liquidity pool with automated rebalancing provides higher capital efficiency relative to fragmented liquidity pools in other bridge designs. Higher capital efficiency results in lower fees to users and higher returns for liquidity providers.

In this episode, we explore how the choice of a fee model impacts the bridge user’s experience and economics. We compare the difference between a bonding curve for AMM protocols, used by most bridging solutions, versus an interest rate model for borrowing and lending protocols used by Across Protocol.

How an AMM Bridge Matches Orders

Most cross chain bridges use an automated market maker (AMM) to balance supply and demand and charge fees to bridge users. These bridges typically involve swapping a synthetic intermediary bridge token (for example hTokens for Hop and nTokens for Synapse) on an AMM against the canonical asset of that destination. In an ideal scenario where bridge users are consistently doing small, offsetting transfers between destinations, these “AMM bridge” pools are relatively balanced and result in little slippage.

However, if transfers in and out of a destination become lopsided, the AMM bridge will need to rely on arbitrageurs to rebalance these pools vs. pools on other destinations.

When this happens, the price between the intermediary bridge token and canonical tokens becomes attractive for someone to initiate a transaction to rebalance the pools. Here is an illustration of what the pricing imbalance could look like, with the price bouncing around parity.

AMM illustration. The red lines represent the deadweight loss of the AMM design.

You can see how prevailing flows in one direction result in a pricing imbalance. When that imbalance becomes high enough, a keeper or arbitrage bot can make a small profit. If someone is going against prevailing flows before an arb hits, they have positive slippage, and if someone is going with prevailing flows, they pay a slippage penalty.

As illustrated above, an AMM bridge creates an inconsistent user experience and a tax on the system where users pay higher fees due to slippage and LPs suffer impermanent loss to arbitrageurs. What’s further disappointing is that some bridge protocols as a whole actually have the liquidity to better service these users; however, given their design, the assets are scattered in smaller fragmented AMM pools on various chains and cannot be fully utilized resulting in higher slippage for the user. An additional cost to an AMM bridge is the threat of Relayer Extractable Value (REV or effectively MEV type activity performed by relayers) where users could get “front-run” on large transfers. As of now, most of these bridges have permissioned relayers, but it will become a concern as they scale and decentralize. Across was cognizant of these disadvantages and spent some time coming up with a different approach that would remove the arb tax and make sure that 1 ETH = 1 ETH.

Why use an interest rate model for bridging?

In any cross chain bridge, when a liquidity provider facilitates a bridge transfer they are actually engaged in lending and not token swapping. When a user wants to bridge a token to a destination, they want the canonical version of that token at the destination — they should not care about the supply and demand of an AMM-style bridge protocol’s synthetic intermediary token (which is currently used in many bridging solutions). The actual risk exchanged between the bridge user and the LP is a borrow and lend transaction — not a token swap.

For example, to move ETH from Optimism to Mainnet, the canonical bridge would take 7 days. A user wants that to happen immediately whereas an LP has idle assets he’s willing to provide to facilitate this. When the bridge transfer happens the user is effectively borrowing ETH from the LP for 7 days. The cost to the bridge user is the opportunity cost of ETH to the LP and this can be represented as an interest rate.

Across uses the above framework in designing the economics of the bridge and implements the interest rate models of Aave and Compound. The total utilization of an asset across the entire protocol is the driver that determines fees. This results in steady, consistent fees that only increase at high utilization rates. This mechanism also helps attract more LP capital to enter the pool when needed as the higher utilization rate increases the expected APY. Overall, it provides a better user experience that more accurately prices the risk exposure exchange between the bridge user and LP.

Putting It All Together

The combination of a one liquidity pool design along with an interest rate fee model provides high capital efficiency and a good user experience. Across keeps the majority of its LP assets on mainnet, where it is most secure, and the protocol operates bots to rebalance between destinations using the canonical bridge. However, most AMM bridges have multiple fragmented liquidity pools that require arbitrageurs external from the protocol to perform this rebalancing, thus taxing bridge users and harming LPs. Across’ interest rate fee model is driven by the overall utilization of assets in its single liquidity pool which provides more consistent pricing. In contrast, prices paid by users of an AMM bridge are driven by the current supply and demand at a single destination’s smaller liquidity pool. Across Protocol borrowed financial engineering concepts to better match risk exposures and maximize capital efficiency. The net result is a cross chain bridge that is architectured differently and provides lower fees and a better user experience.

If you have any thoughts or observations about the financial engineering of Across, please engage us by tweeting to @AcrossProtocol or replying in the comments.



Kevin Chan

Treasurer at UMA