Analysis of Uniswap V3 liquidity positions: What are the similarities with traditional options?

In May, Uniswap released the third version of its Automated Market Making (AMM) protocol. A major improvement of Uniswap v3 is that liquidity providers (LPs) can deploy liquidity to a specific price range, instead of all prices from 0 to ∞ in Uniswap v1 and v2.

Although the stated goal of transforming Uniswap v3 LP smart contracts may improve capital efficiency and provide better liquidity position control, an under-recognized consequence of the new liquidity system is that Uniswap v3’s liquidity positions effectively perform There are two familiar types of options: cash-backed put options and covered call options.

This is the first article in this series and will explore the similarities between Uniswap v3 liquid positions and more traditional derivatives.

2b84450e114f5f2fbdded5e7d787a1b5_ksvg7MK.png-articleUniswap LP tokens and options. Deploying the Dai-ETH Uniswap v3 LP position to a position higher than the current spot price is equivalent to writing a Dai-ETH covered call option.

Uniswap V3 liquidity

Uniswap v3’s liquidity provides the ability to deploy liquidity to any price range (from the Uniswap v3 white paper).

Centralized liquidity: Liquidity providers (LPs) have the ability to centralize their liquidity by “binding” liquidity in any price range. This improves the capital efficiency of the capital pool and allows LPs to approach their preferred reserve curve while still effectively converging with the rest of the capital pool.

8f2cec21d232541e8aa173f8d0895428_JR8xHK0.png-articleConcentrated liquidity. Uniswap V3’s liquidity can be provided to a specific range. Only when the asset price is within the deployed point, will the fee be charged.

Although the implementation of centralized liquidity requires a complete rewrite of the AMM LP agreement (including the transfer from ERC20-to NFT-based liquidity positions), Uniswap v3 allows LPs to have more control over their positions. In addition, LP can deploy a centralized liquidity position, close to any distribution of liquidity, including existing AMM, like Balancer or Curve (for more details see Dan Robinson’s article ).

Interval orders and single point liquidity

Although liquidity positions deployed between 0 and ∞ will reproduce the returns of Uniswap v2 positions, liquidity can be deployed between any two values. This makes capital efficiency, in theory, have been dramatically 4000-fold increase .

In addition, one application of centralized liquidity is the ability to create range orders:

Using Uniswap v3, people can approach limit orders by providing a single asset as liquidity within a specific range. Like traditional limit orders, the setting of interval orders also hopes to be executed at a certain point in the future. After the spot price crosses the full range of the order, the target asset can be withdrawn.

In the event of price fluctuations, the deployment of “broadband” orders may increase the fees charged, which means that users may receive discounts when buying or selling assets.

f11ed524ea405fd0a24bdaa2d17a83c5_EHXOWCx.png-articleLeft: Deploy liquidity above the current spot price, create a range order, and convert ETH to DAI when the price moves between low and high points. Right: Deploy liquidity in a narrow single point range to create a “covered call option” payment, that is, sell ETH immediately when the spot price exceeds the strike price.

If we look at the other end of the graph and consider the value of a Dai-ETH LP position deployed to a single point, we find that when the position is just below that point, it will be 100% ETH, and just above that point When it is 100% Dai.

In a way, this is similar to a covered call option. The LP token fully replicates the method of selling assets in covered call options only when the spot price is higher than the exercise price at the time of expiration. However, LP tokens have no expiry date, and the underlying assets are automatically converted through trading activities.

Please note that due to the bearish-bullish parity, the covered call return graph is exactly the same as the cash backed bearish return graph. Therefore, depending on whether the exercise price is higher or lower than the current spot price at the time of liquidity deployment, Uniswap v3 liquidity positions are represented as bearish short cash guarantees or bullish covered reserves.

1cd7b376ba6159fc93abf49c1d242605_PuTCjfJ.png-articleCovered call options. Covered call options have limited profit potential, and they are most beneficial in a neutral to bullish environment. Image source: Julie Bang ©Investopedia

Expected rate of return for non-expiring perpetual options

Option sellers usually receive a premium when they sell options, and the price of the option can be derived through the Black-Scholes (BS) model. We will not discuss all the details of the BS model in this article, but the main point is that the price of an option depends on the current spot price, expiration time, and a parameter called implied volatility. Implied volatility reflects The expected future price change of the underlying asset.

Since Uniswap v3 LP positions have no implied volatility and no expiry date, we cannot directly apply models similar to BS to estimate the price or expected return of single-point LP positions. However, we know that the growth rate of accrued fees is directly proportional to the following factors: i) transaction volume and ii) the size of the liquidity position compared to all the liquidity provided. Therefore, if a liquidity provider owns 1% of all liquidity deployed at the current price point, they will charge 1% of all transactions within that price point.

In addition, each time the spot price crosses the liquidity scale, the fee charged will also be equal to a fixed 0.3% (or 1% or 0.05%, depending on AMM’s fee structure). This is because all liquid positions need to be converted when they cross the tick mark, so the 0.3% fee is charged based on the total value of the LP position.

Therefore, if liquidity is provided at an exercise price very close to the current price, when the spot price leaves and re-enters the exercise price, the liquidity provider may be able to charge 0.3% multiple times. On the other hand, if prices increase or decrease rapidly in extreme markets, LP may only be able to charge a fee of 0.3% once.

Return on investment of ETH-Dai LP positions

In order to quantify the return on investment (ROI) of the LP token covered call position, let’s take a look at the hypothetical scenario in the figure below.

Here, the user locked 1 ETH in the LP position defined by (2498.9, 2513.9) points on June 8, when the price of ETH was 2400. The position remained for 11 days and was removed when the price returned to 2400 Dai on June 17.

52ced04044ca5cb5a32ac435c2632faf_eskOesk.png-articleLP covered call option. A single point of liquidity will accumulate a fixed fee of 0.03% each time the asset price accesses the point value. Here, the spot price of ETH crossed 2500 several times between June 8th and 17th, and LP obtained an annual return on investment of 150%. Charging fees reduces the break-even point and increases the profit potential of the position.

In these 11 days, the price of ETH has crossed 2500 points 16 times. In this case, in addition to the fees charged when the price is between 2498.90 and 2513.90, the user will receive a 4.8% return within 11 days. Even if we only consider the 0.3% charged each time, it is equivalent to an annual return on investment of 150%.

Of course, if the price drops by more than 4.8% when liquidity is cancelled, LP will suffer impermanence losses. And if the price rises more than 2513.90, the realized benefits will also be limited.

However, the position’s return profile is the same as the covered call, and these hypothetical loss scenarios are understood to be an integral part of any covered call strategy. In other words, compared to simply holding the underlying assets, the covered call strategy has no additional risks. At the same time, limiting rising profits will be rewarded by charging fees/premiums to lower the break-even point of the position.

In order to accurately estimate the expected return on investment of the LP position, we still need to know the theoretical number of times an asset visits a specific price (ie, the “dwell time”). The dwell time and the number of re-entry events can be calculated using diffusion-based asset pricing models. These models use assumptions that are different from those of the Black-Scholes model used to derive option pricing. We will introduce these models in a future article.

Future work

This article highlights the similarities between Uniswap v3 LP positions and option derivatives, and shows how single-point liquid positions behave like covered call (or short) options.

Interestingly, since the LP token will never expire, the single-point liquidity position will behave like a “perpetual” covered call option. Although these are different from the Everlasting options proposed by Paradigm’s Dave White and Sam Bankman-Fried, Uniswap v3 liquidity positions do not need to be rebalanced every day, and can be managed passively, with little user input.

In a future article, we will discuss how Uniswap V3 LP tokens replicate more complex short premium options strategies, such as short call, straddle options, and wide span options. We will also derive the expected return on investment of these strategies.

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