Introduction

Structuring base fee derivatives is not easy. To get the discussion started, we provide a very rough example of how base fee options could be constructed. Note that this is not meant to be used in practice as still a lot of research needs to be done on the security of these options. It is meant as a sequel on my post on the design space of structuring blockspace derivatives.

Characteristics

To allow users to hedge against base fees in the next block, we have designed call options with the base fee as the underlying. The option has a strike price K. The contracts are denoted in sizes of 1 gas unit. Let the maximum number of gas units supplied in option contracts be denoted as g'. Let the price of the option be denoted as P; it will be determined by market forces.

EIP-1559 Update Rule

The base fee in each block is dependent on the block size of the previous block. If the gas used is more than the target amount, the base fee increases, if it is less, the base fee decreases. To be more precise, it follows this formula:

Cost of Manipulation

The initial problem that a base fee option seller faces is that the base fee is manipulable. If profitable, a block builder could fill up the block with transactions or deliver a completely empty block. The cost of manipulation is independent of the number of option contracts the block builder has, but the payoff is. This means that manipulation is not incentivized if the amount of contracts supplied is appropriately limited.

We define the cost of manipulation: the amount of base fees a manipulater needs to pay to fill block i. Note that we disregard the case here were an empty block is delivered. This case is harder to study and the payoff is maximized by the premium buyers pay.

The profit, pi, a manipulator can make must be non-positive in order to not be incentivized to manipulate and hence secure the option contracts.

Here g' denotes the maximum secure supply of option contracts that can be issued denoted in gas units. This is actually the variable of interest.

The payoff here is the maximum possible payoff, because that is what a manipulator will attain. To obtain a worst-case scenario maximum secure supply, we use the lowest possible price of the option contract to lead us to the following:

Intuitively, we can supply four times as many gas units in option contracts as the amount of gas units a manipulator needs to pay. This is the case because the profit is at most the difference between the expected value of the base fee and the realized base fee, which is 25%, while the cost of manipulation is the entire base fee, 4 times as much. The problem, however, is that the gas demand is unknown when determining how many contracts to sell.

Maximum Supply

When selling the options, the amount sold and the price need to be established at roughly the same time. If the price of the options is high, the expected gas demand is high. A lot of natural gas demand means that the cost of manipulating this block is low, meaning only few contracts can be issued. Using the same logic, many contracts can be issued if the price is low.

Using the EIP-1559 update rule and the worst case maximum secure supply, we obtain that

with

Gas Demand and Price

The price of an option is the expected value of its payoff minus the strike price.

Therefore, estimating the price of the option is equivalent to estimating the gas demand in the block before maturity: block i.

Equivalently, we find that

Market Mechanism

The basefee at block i+1 is unknown at the time of selling the options (otherwise there would be no speculation market). Therefore, it is also unknown how many gas units can be sold in the call options. We can estimate this amount using the market price. By establishing the market price, and assuming the implied expected value, we can find the expected value of the base fee in the next block.

With the market-based expected base fee, we also find the expected amount of gas units that can be sold as follows.

Here it is assumed that expected base fee decreases with 12.5% in the next block, but that the gas demand is not actually 0, hence this is a very advantageous situation for a possible attacker.

If you assume option prices move in line with expected gas demand - hence taking the price of the option into account when calculating the profit from manipulation - the supply becomes the following.

The maximum secure supply is thus a lot larger assuming option prices do move along with the amount of gas necessary to manipulate a block.

Price Changes

Initially, let the amount of gas unit options sold be at most equal to the maximum secure supply in the worst case. A market price is then determined and a number of options are sold, this number will not increase later. If and when the market price changes, the maximum secure supply also changes, since the profit of manipulation changes either directly - options become more expensive - or by opportunity costs - users sell their options to other users on- or off-chain.

Here the expected price change along the EIP-1559 update rule is represented by

As the price of an option increases, the maximum secure supply also increases, hence changes in the price of an option, do not mean manipulation is incentivized.

Estimation Error

Market participants want to engage in base fee options because they believe the market-based expected value is not equal to the actual value. To model this, we introduce an estimator with an error term.

This error term better represents the user's expectation.

This error term, expressed in units of gas, leads to the following expected maximum secure supply.

A larger error terms implies that less contracts should be issued. It is not helpful to incorporate an error term into the model as users will adjust their strategies accordingly, making it only a nuisance. It could, however, be useful for individual liquidity providers to assess their risks.

If Expectation ≠ Reality

We have seen what the maximum secure supply is under different assumptions. Under the worst case that prices are set at the minimum but cost of manipulation is dependent on gas demand, the amount of option contracts is dependent on gas demand.

What if the price of the options is purely driven by speculation and not correlated to gas demand. In the case that a manipulator can profit from filling up a block, this means the base fee increases in the next block, leading to negative externalities for Ethereum users.

The only case that a person may be incentivized to manipulate, is when the maximum secure amount has been sold and held by one person or cartel and the expected base fee at the sale was lower than the realized base fee and the person or cartel can also build the block. We deem this case highly unlikely, but since it has large negative externalities, we make a fail-safe.

The cost of manipulation is given as.

This can only be observed in the (i + 1)th block. A manipulator is incentivized to wait as long as possible with filling up block i as the gas demand might still increase, coincidentally leading to a more honest price discovery. To prevent network manipulation, the fail-safe provided to the manipulator is as follows.

The smart contract that handles the option payoff, only does so at least two blocks after maturity, block i + 3. A manipulator has the chance to pay a cost to the smart contract at block i + 2 that is strictly smaller than the cost of manipulation, but that is determined similarly. If this cost is payed, it is burned, and all options are payed out the maximum payoff. The cost of the fail-safe could be as follows.

This means manipulators are incentivized to wait and not manipulate the real base fee and attain a higher payoff. Also implying that no just-in-time strategies for manipulation will appear. The fail-safe makes pricing the option more difficult, however, the pricing for this option is not standard, even if manipulation could never occur, as the payoff is bounded.

Censorship attacks and the Put-Call Parity

In this model a manipulator is assumed to only perform an attack on raising the base fee and thereby filling up the block. A manipulator could also leave the block empty and thereby lower the base fee. This attack is more difficult to model as the cost of it is unclear due to tips being very variable and possible MEV, meaning the opportunity cost of delivering an empty block cannot be determined accurately.

Conclusion

This article roughly shows some of the practical considerations one should take when designing next-block base fee options. It is in no way meant to be implemented directly! Base fee derivatives is a subject that requires a lot more research in order to not form a threat to the protocol.

In principal, the fail safe can be generalized to base fee derivatives over a longer period of time, however, it becomes increasingly costly for the seller as the cost of fail safe must be strictly lower than the cost of manipulation but the cost of manipulation can only be roughly lower bounded.

Another important note is that their may be more on- or off-chain sellers of base fee derivatives meaning that you do not determine the maximum issued supply. Although no one is incentivized to supply more than the maximum secure supply, it can happen when two or more parties issue derivatives individually.

If you have ideas on base fee derivatives or are interested in it, please do not hesitate to reach out.

Thanks to Barnabé Monnot for discussion and feedback.