Abstract: We introduce a pricing model developed for hedged preconfirmations with a focus on preserving underwriter funds and generating steady yields. The mechanism is demonstrated to work via backtesting over the historical gas data period of 14 months. We find that even with a simple static percentage premium underwriter can be appropriately compensated for the risk of gas price swings. Future steps for improving this kind of pricing approach are briefly discussed at the end.
At Luban, we are maximizing the efficiency and utility of Ethereum blockspace. Among other products, we are building hedged preconfirmations to stabilize transaction costs for the end users and bring experience more familiar to them from Web 2. The platform lets users purchase a future settlement guarantee by paying upfront the inclusion preconfirmation cost. Initially this service will be limited to the next 64 blocks, but we are working on extending it to weekly and monthly periods, eventually building upon it a convenient subscription plan tailored to the individual needs of our B2B partners and their customers. Based rollups, wallets, oracles, or any RaaS application can gain predictability for their business or quality improvements to the UX of their users via offering lower volatility gas prices.
However, in an environment with highly fluctuating gas fees, taking a short position against them carries significant risk. When considering a single transaction in isolation this calls for a very high premium paid to the underwriter to compensate for the event of a gas spike. Those high costs then would have a hard time attracting buyers, and so there wouldn’t be any demand for such service at elevated prices.
This shows that the hedging of future blockspace costs poses a challenge. It needs careful balancing of the premium to fairly compensate the underwriter for the risk they take on, while at the same time being as cheap as possible to the buyer to serve the existing demand. However there is a slight asymmetry in the equation, as without sellers there won’t form any market to begin with, and buyers willing to pay any price, still won’t find a matching order. Therefore, pricing of such gas insurance always has to prioritize the insurer not blowing up and being satisfied for the risk adjusted yield earned., otherwise the liquidity in such market will quickly dry out.
We believe that the strongest focus in pricing insurance-like products has to lie in preserving the underwriter’s capital through minimizing drawdowns and providing competitive yields to be an attractive option with respect to other yield opportunities that are out there. Through this assumption a market can be bootstrapped and establish the supply-demand connection, and then pricing can be finely tuned to lower the costs for the buyers as much as it is possible without negatively impacting the sellers.
We approach solving this problem by presenting the pricing model that optimizes for stable long term profitability of the underwriter, such that on average, any potential losses incurred can be recovered via the accumulation of premia by continuous preconfirmation underwriting. This method ensures that there are always willing sellers of the hedged preconfirmation service and the willing buyer won’t be left without a counterparty when the need arises. Our primary goal is to create a reliable service available to businesses and end users that need to often spend gas in their operations.
Last year, Hasu has voiced his concerns about gas derivatives being unsolvable due to the high premiums required for such hedging or the low yields paid to underwriters. We believe our approach addresses this conundrum, offering both low premium payments on hedged gas subscriptions and attractive ETH-denominated yields to underwriters.
While methods such as Black-Scholes are widely recognized to form a basis of derivatives pricing, assumptions on which these equations are built are often not relevant to how the real markets behave. This is particularly pronounced in Ethereum blockspace markets where the prices are not following the process of geometric brownian motion. Rather, they look more like noise around a slowly shifting mean (with some seasonality elements), with significantly higher jumps overlaid on top due to events that cause a spike of demand for on-chain operations. This is far from what brownian motion looks like.
Base fee post EIP-1559 from “**EIP-1559 In Retrospect”**
Geometric Brownian Motion from “Understanding Quantitative Finance”
Taking this kind of movement as assumption implies that asset returns are normally distributed (that is, having a normal (Gaussian) distribution) over short time intervals, leading to a log-normal distribution of prices. What clearly follows is, that the Black-Scholes model is only suitable for a random process that naturally forms a Gaussian distribution, which is approximately true for many financial instruments like equities. However, even simply by inspection, we can see that the gas prices are not following such distribution. Further analysis can show that the gas distributions can’t be represented by a single function at all, and rather need to be formed by summing up several, differently shaped distribution functions where each is a result of different kind of on-chain behavior forming in different conditions.
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The Black-Scholes equation is used for pricing European options. Its formulation relies on modelling the dynamics of asset prices using stochastic calculus, and expressed as:
$$
⁍ $$
where:
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Brownian motion is a type of stochastic movement used in physics to model random movements of particles in a fluid. Using this equation for modelling asset prices assumes they are following such geometric brownian motion:
$$ ⁍ $$
where: