Panoptic Series: (2) Panoptic, an oracle-free options protocol
1. Replication of Options through Uni V3 LP Position
1.1 Analysis of Uni V3 LP Position
In the previous post, we briefly confirmed that the Uni V3 LP position has a similar profit structure to a put option (or covered-call). This is based on the fact that if the price ratio of the token pair deviates from the initially set price range, the Uni V3 LP position is converted to a specific token within the token pair. So, how do the token amount and total value of the Uni V3 LP position actually change with price movements?
According to (Lambert, 2021a) and a series of articles by Guillaume Lambert, the CEO of the Panoptic protocol, the token amount within the pair in Uni V3’s whitepaper can be summarized as follows:
Here, the total position value V(P) = (token1) + P*(token0), and this can be arranged into the following equation using the scaling factor r = √(tH/tL) and the strike price K = √(tH*tL).
1.2 Replicating Covered-Call Position Using Uni V3 LP Position
Meanwhile, assuming S=Ke^(-rt) at ATM, meaning the market price of the underlying asset is equal to the current price of the option exercise, the call option price 𝐶(𝑆,𝑡) derived from the Black-Scholes equation is approximately K𝜎√(t/2𝜋). Suppose we assume that the pay-off of the covered call calculated based on this approximation formula equals the net liquidity value of Uni V3. In that case, the time to maturity t can be expressed as a function of the scaling factor r, and the scaling factor r is also a function of t, time to maturity.
This means that by adjusting the price range of the Uni V3 liquidity provision, i.e., the scaling factor r, we can “replicate” a particular covered call with a specific exercise price and time to maturity. In fact, a covered call that sells ETH-17MAR23–1800 call options on Deribit and holds the ETH spot can be replicated on Uni V3 by providing liquidity in the [1636, 1971] range with a scaling factor r of 1.097 (current price of $1,740). The following images show the replicated Uni V3 position value and the PnL of the ETH-17MAR23–1800 covered call calculated by the Deribit Position Builder.
The user can replicate an options position using Uni V3, thus avoiding liquidity issues in current DeFi option protocols and centralized exchanges such as Deribit. In DeFi option protocols based on AMM, a lack of liquidity often makes huge price impacts, and even impossible to take a position in strike prices far from the current price. Similarly, in Deribit, after a call option is written, there must be a counterparty to buy that option, and liquidity is also lacking for options with strike prices that are far from the current price. However, by replicating an options position using Uni V3, it is possible to construct a position that has a similar pay-off to the desired option by adjusting the scaling factor, r. Moreover, there is no need to search for a trading counterparty, and it is possible to maintain the position permanently.
2. Streaming Premium: Option Pricing without an Oracle
2.1 Everlasting options vs. Panoptic
In <1>, we looked at how Uni V3 LP positions are similar to an option’s profit structure and how it is possible to replicate specific options by adjusting the price range that provides liquidity. However, the Panoptic protocol has a unique selling point: it provides a pricing mechanism that does not require an oracle.
Panoptic protocol options are essentially perpetual options with no specific expiration date, and the usual Black-Scholes equation cannot determine a typical price. The feature that it is impossible to decide on a fair price for perpetual options makes it difficult for DeFi protocols to open a perpetual options market and contributes to reducing demand for perpetual options. This is in contrast to the fact that perpetual futures dominate the cryptocurrency futures market.
Perpetual futures maintain the mark price (futures trading price) close to the index price (underlying asset trading price) based on the funding fee structure. This enables users to maintain their futures positions lowly without rolling them over after expiration. Ultimately, the funding fee structure played a crucial role in making most retail investors prefer perpetual futures over futures contracts with specific expiration dates. In trading perpetual futures, long positions pay a funding fee proportional to (mark price — index price) to short positions. This structure increases demand for short positions when the difference between the mark price and index price widens, keeping the price of perpetual futures moving similarly to the underlying asset.
(White and Bankman-Fried, 2021) first introduced the concept of everlasting options by taking inspiration from the structure of perpetual futures, where the funding fee mechanism is used to maintain the option price at a level close to the underlying asset’s price.
While everlasting options simplify the pricing of perpetual options by having continuous maturities, they still heavily rely on Oracle solutions. This means that the option price may not perfectly correspond to the price changes of the underlying asset, and there is a high possibility of a discrepancy between the predicted and actual pay-off at settlement. To address the issues that may arise from Oracle problems in perpetual options and effectively calculate the price of perpetual options, the Panoptic Protocol has introduced the “Streaming Premium Mechanism” to calculate option premiums based on the total transaction fees generated from Uni V3 positions.
2.2 Relationship between Time to Maturity and Option Pricing
The Streaming Premium Mechanism calculates the premium of a perpetual option based on the total transaction fees generated from Uni V3 positions rather than feeding the underlying asset’s price through Oracle. To derive this mechanism, the Panoptic Protocol presented the following flow:
1) Rewriting the option price into a function of θ (sensitivity of option price to maturity) integrated over t(time). Then statistically verify whether this approach can explain Black-Scholes-based option prices meaningfully.
2) Assuming the price of an option as the sum of premiums (θ∆t) exercised every ∆t. When ∆t is set to 0.1 DTE, it is verified that the theta function approximates the 1-tick liquidity position of Uni V3.
First, the Panoptic Protocol analyzed how well the time to maturity of an option explains the theoretical option price derived from Black-Scholes based on a Geometric Brownian Motion Monte Carlo simulation. According to the Whitepaper results, integrating θ over a random walk path S(t) of time to maturity generally reflects Black-Scholes option prices well. When calculating the option price by integrating θ over S(t), it converged to Black-Scholes option prices on average. However, this experiment revealed that the option price is heavily influenced by the price path over time, not just the underlying asset price itself. In approximately 33% of the results, the option price converged to zero because the underlying asset price never reached the strike price. In comparison, in 16% of the results, the underlying asset price arrived at the strike price multiple times, resulting in option prices that were 200% of the Black-Scholes-based option price.
2.3 Similarity between Theta Function and Uni V3 Liquidity
The experiment mentioned above found that integrating θ, the sensitivity of option prices with respect to time, over time effectively reflects the option price. Panoptic calculates the perpetual option premium based on the sum of premiums θ∆t generated by exercising the option every ∆t. What is the optimal value of ∆t for calculating the price of a perpetual option?
Panoptic discovered that setting ∆t to 0.1 DTE approximates the θ function to Uni V3’s 1-tick liquidity position, which resembles a Dirac delta function. The value of θ is now the height of the delta function times the elapsed time in the interval. The area under the delta function is (k²σ²)/2, and its width is k·tS (tickSpacing tS), so the height of the delta function is kσ²/2tS. This can be further expressed as the accumulated fee in the interval, (k²σ²/2tS) · tS. Comparing this to the actual fee generated per unit time in the Uni V3 pool (i.e., feeRate · (Volume · Time)/tickLiquidity), we can derive the fact that the implied volatility or σ of the perpetual option is 2 · feeRate · √(Volume/tickLiquidity).
Because the Streaming Premium model calculates premiums based on transaction fees generated in specific liquidity ranges, selling options do not create premiums with the execution. Instead, premiums are received at the time of position closure, similar to yield farming using leverage within a specific price range. In the case of buying options, like American options, users can exercise options at any desired time. During the settlement, the protocol uses the pool’s price ratio in Uni V3 directly, reducing pay-off errors caused by oracle issues.
3. The Next-Generation Protocol: More Freedom to the DeFi Options Market
Users can immediately trade options through the Panoptic protocol and even create synthetic positions by combining various perpetual options. This means the protocol can provide users with different structured products at the protocol level.
Several DeFi protocols have released DOVs (DeFi Option Vaults), but most only provide covered-call options or simple put option (protective puts) strategies. In addition, DeFi option protocols such as Hegic provide structured products that combine various maturities and strike prices beyond simple option products but have limitations in quickly processing many contract products. Furthermore, most protocols only offer options for limited tokens (ETH, BTC, etc.), which do not meet the diverse hedging demand of users.
Using Panoptic’s perpetual option issuance structure, users can trade various structured products based on Uni V3’s huge liquidity while reducing liquidity constraints. Unlike traditional DeFi structured products that require rolling positions weekly, there are no additional costs involved in rolling positions for ‘perpetual structured positions’ that utilize Uni V3. Also, since users can generate option positions for all token pairs that satisfy specific liquidity criteria in Uni V3, they can hedge their positions for tokens that were previously only possible to trade in futures or impossible to hedge at all.
While the Panoptic protocol is still in pre-launch, it can clearly contribute to providing users with greater freedom while trading in the DeFi options market. Team verse2 evaluates that next-generation option protocols such as Panoptic can help retail investors trade structured products previously inaccessible in traditional finance and reduce inefficiencies in DeFi options, increasing institutional investor inflows and overall growth in the DeFi options market.
This article is <Panoptic Series: (2) Panoptic, an oracle-free options protocol> provided by verse2. Please see the list below if you want to read the entire Series. We recommend that you read the articles sequentially.
1. Panoptic Series : (1) Panoptic, a perpetual options protocol on Uni V3
2. Panoptic Series : (2) Panoptic, an oracle-free options protocol
verse2 is a team that specializes in the development of Web3 products, and an incubator for potential Web3 projects. The team consists of skilled experts who have deep knowledge and experience in the field of Cryptofinance.
