Similarities between Uniswap V3 LP and traditional permanent call and put options

Uniswap V3 brings 4,000 times more capital efficiency and more traditional options play.

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

While the stated goal of revamping the Uniswap v3 LP smart contract may improve capital efficiency and provide better control of liquidity positions, an underappreciated consequence of the new liquidity system is that Uniswap v3 liquidity positions are effectively represented as two familiar option types: cash-backed puts and covered calls.

This is the first article in a series that will explore the similarities between Uniswap v3 liquidity positions and more traditional derivatives.

Similarities between Uniswap V3 LP and traditional permanent call and put options

Uniswap LP tokens and options. Deploying a Dai-ETH Uniswap v3 LP position to one point above the current spot price is equivalent to writing a Dai-ETH covered call option.

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

Concentrated Liquidity: Liquidity providers (LPs) have the ability to concentrate their liquidity by “tying” liquidity to any price range. This improves the capital efficiency of the pool and allows LPs to approach their preferred reserve curve while still being effectively aggregated with the rest of the pool.

Similarities between Uniswap V3 LP and traditional permanent call and put options

Centralized liquidity. Uniswap V3 liquidity can be provided to a specific range. Fees are charged only when the asset price is within the deployed pips.

While the implementation of centralized liquidity requires a complete rewrite of the AMM LP protocol (including the move from ERC20- to NFT-based liquidity positions), Uniswap v3 gives LPs more control over their positions. In addition, LPs can deploy centralized liquidity positions to approach any liquidity distribution, including existing AMMs such as Balancer or Curve.

Interval orders and single point liquidity
While a liquidity position deployed between 0 and ∞ will reproduce the returns of an Uniswap v2 position, liquidity can be deployed between any two values. This results in a theoretical increase in capital efficiency of an astounding 4000x.

In addition, one application of pooled liquidity is the ability to create range orders.

Using Uniswap v3, one can approach a limit order by offering a single asset as liquidity in a specific range. As with traditional limit orders, range orders are set up with the expectation that they will be executed at some point in the future and that the target asset can be withdrawn after the spot price has crossed the full range of the order.
In the event of price fluctuations, deploying a “wide range” order may increase the fees charged, meaning that users may receive a discount when buying or selling assets.

Similarities between Uniswap V3 LP and traditional permanent call and put options

Left: Deploys liquidity above the current spot price, creating a range order that converts ETH to DAI as the price moves between the low and high. right. Deploying liquidity within a narrow single point range creates a “covered call-like” payoff, where ETH is sold as soon as the spot price crosses the strike price.

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

In a way, this is similar to a covered call option. the LP token exactly replicates the way an asset in a covered call option is sold only when the spot price is above the strike price at expiration. However, the LP token has no expiration date and the underlying asset is automatically converted through trading activity.

Note that due to the put-call parity, the return graph for the covered call is identical to the return graph for the cash-backed put. Therefore, depending on whether the strike price is above or below the current spot price at the time of liquidity deployment, the Uniswap v3 liquidity position behaves as a short cash-backed put or covered call.

Similarities between Uniswap V3 LP and traditional permanent call and put options

covered call options. Covered calls have limited profit potential, and they are most favorable in a neutral to bullish environment. Image credit: Julie Bang ©Investopedia

Expected Payout for Non-Expiring Perpetual Options
Option sellers typically receive a premium when they sell an option, and the price of that option can be derived from a Black-Scholes (BS) model. We won’t discuss all the details of the BS model in this article, but the gist of it is that the price of an option depends on the current spot price, the time to expiration, and a parameter called implied volatility, which reflects the expected future price change of the underlying asset.

Since the Uniswap v3 LP position has no implied volatility and no expiration date, we cannot directly apply a BS-like model to estimate the price or expected return of a single point LP position. However, we know that the accruals grow at a rate proportional to i) the volume of trades and ii) the size of the liquidity position compared to all liquidity offered. Thus, if a liquidity provider owns 1% of all liquidity deployed at the current price point, they will charge a fee of 1% of all trades within that price point.

In addition, each time the spot price crosses the liquidity scale, the fee charged will also equal a fixed 0.3% (or 1% or 0.05%, depending on the fee structure of the AMM). This is because the entirety of the liquidity position needs to be converted when the tick is crossed, so the 0.3% fee is charged on the total value of the LP position.

Thus, if liquidity is provided at a strike level very close to the current price, the liquidity provider may be able to charge the 0.3% fee multiple times as the spot price leaves and re-enters the strike level. On the other hand, if the price increases or decreases rapidly in an extreme market, the LP may only be able to charge 0.3% once.

ROI of ETH-Dai LP positions
To quantify the return on investment (ROI) of an LP token covered call position, let’s look at the hypothetical scenario in the chart below.

Here, the user locks 1 ETH in an LP position defined by the (2498.9, 2513.9) pip on June 8, when the price of ETH was 2400. the position is held for 11 days and is removed on June 17 when the price returns to 2400 Dai.

Similarities between Uniswap V3 LP and traditional permanent call and put options

LP covered call option. Single pip liquidity accrues a fixed fee of 0.03% each time the asset price visits the pip value. Here, the ETH spot price crossed 2,500 multiple times between June 8 and 17 and the LP earned an annual ROI of 150%. Charging a fee lowers the break-even point and increases the profit potential of the position.

During these 11 days, the price of ETH crossed 2,500 16 times. In this case, in addition to the fees charged when the price was between 2498.90 and 2513.90, the user would have received a return of 4.8% over the 11 days. Even if we consider only the 0.3% charged each time, this corresponds to an annual return on investment of 150%.

Of course, if the price drops more than 4.8% when liquidity is cancelled, LPs will suffer an impermanent loss. And if the price rises above 2513.90, the realized return will also be limited.

However, the position has the same return profile as a covered call, and these hypothetical loss profiles are understood to be a component of any covered call strategy. In other words, there is no additional risk associated with a covered call strategy compared to simply holding the underlying asset. At the same time, profits from limiting upside are rewarded by charging a fee/premium to lower the breakeven point of the position.

In order to accurately estimate the expected ROI of an LP position, we still need to know the theoretical number of times an asset will visit a particular price (i.e., “dwell time”). Dwell times and the number of re-entry events can be calculated using diffusion-based asset pricing models that do not use the same assumptions as those used to derive the Black-Scholes model for option pricing. We will present these models in a future article.

Future Work
This article highlights the similarities between Uniswap v3 LP positions and option derivatives, showing how single point liquidity positions can behave like covered call (or short) options.

Interestingly, since LP tokens never expire, a single point liquidity position will behave like a “perpetual” covered call option. While these are not the same as the Everlasting options proposed by Paradigm’s Dave White and Sam Bankman-Fried, the Uniswap v3 liquidity position does not need to be rebalanced daily and can be managed passively with minimal input from the user.

In a future article, we will discuss how the Uniswap V3 LP token replicates more complex short premium option strategies such as short calls, straddles, and wide straddles. We will also derive the expected investment returns for these strategies.

Stay tuned!

Posted by:CoinYuppie,Reprinted with attribution to:
Coinyuppie is an open information publishing platform, all information provided is not related to the views and positions of coinyuppie, and does not constitute any investment and financial advice. Users are expected to carefully screen and prevent risks.

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