June 2022#Options

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**Summary**

- Liquidity providers on DEXes like Uniswap suffer from impermanent loss (IL), caused by the relative changes in asset prices;
- IL risks can be offset through buying and selling crypto options, as shown by a simulation run by the BDC Consulting analysts;
- Option strategies have other advantages for projects, including higher pool ROIs and attracting more liquidity providers.

*Impermanent loss is the biggest pain of AMM liquidity providers, but it can be overcome through careful hedging. An analysis by BDC Consulting looks at how an options strategy can compensate for IL and deliver a positive PnL – and how DeFi projects can integrate such products to attract more customers. *

Liquidity providers on decentralized exchanges like Uniswap earn a percentage of the trading fees generated by a pool, plus potential yield farming rewards. The problem is that often, the value of the assets that a provider withdraws from a liquidity pool turns out to be less than they could get by simply holding the same tokens in a wallet. This is known as impermanent loss (IL), and it happens due to the specific algorithm that AMMs use to calculate prices.

Uniswap, SushSwap, and others use the so-called x*y=k liquidity curve model, where for any pool composed of the X and Y tokens, their product always remains the same (k). As users buy tokens X, they deposit more Y in the pool, and the price of X relative to Y grows.

By the time a liquidity provider decides to withdraw their assets, the prices will have changed, and the composition and value of their pool share will not be the same. It can turn out that basic buy-and-hold in a wallet would be more profitable than investing in an AMM pool.

Impermanent loss is so called because, if the prices of X and Y were to go back to the initial values, the ‘loss’ would disappear. But in reality, the negative effect is quite permanent for many investors.

Uniswap v3 doesn’t provide a direct solution for IL, but it aims to increase capital through so-called __concentrated liquidity__. Liquidity providers can choose the price range in which their assets should be allocated to make sure that all of the capital is working and earning fees. The increase in fee revenue should offset the IL.

The real current liquidity of one’s pool position (i.e. the real amounts of X and Y that one holds) can be calculated according to the formula

where Pa and Pb represent the lower and upper limits of a price range the investor has chosen to concentrate the liquidity in, and L is the so-called virtual liquidity.

On the chart below, all possible liquidity positions at the constant price k form the line y=kx. The steeper the slope of the line, the higher the price. Liquidity determines the distance between a point on the line and the zero point, where the X and Y axes meet.

For any change in the price ratio k, IL can be calculated using the following formula:

When represented mathematically, the system is quite elegant, and there are even special __studies__ devoted to the math of Uniswap. Unfortunately, in practice concentrated liquidity isn’t a magic cure: __a recent study found__ that 49.5% of Uniswap v3 liquidity providers still earn less than they would if they stuck to HODLing. Another study by Bancor even suggests that __concentrated liquidity increases the risk of IL__.

Crypto traders often hedge their risks using perpetual futures contracts: for example, one may take a swing long trade and a scalp short one. However, for AMM liquidity providers, options provide a better hedge. This is because impermanent loss happens both when the price of one asset grows and when it drops – and options, which carry no risk of liquidation and come in both call and put flavors, can offset the risks more effectively. The only risk that the liquidity provider runs in this case is losing the premium.

In order to test the options hedging strategy, the analysts at BDC Consulting ran the following simulation:

1) The bottom limit of the price range for the ETH/USDC on Uniswap was set at 50% of the current price of 3741 USDC per ETH, resulting in 1735.5 USDC.

2) The analysts then simulated selling a put option on the __Deribit exchange__, which accounts for most of the traded BTC and ETH options volume. The chosen option’s strike price was the closest to the bottom limit of the chosen price range among all the put options with the expiration date of at least 15 days.

3) The simulation, which featured 70 options contracts expiring on June 24 with the strike price of $2,200, yielded a positive PnL of 0.7386 ETH. This, according to the researchers, should be enough to compensate for the IL.

Regular AMM investors often shy away from hedging strategies, thinking that they are too complex. Instead, they hope that the prices and trading volumes will keep going up somehow and they will end up in the green – but then face the unpleasant reality of impermanent loss.

Indeed, successful hedging involves a learning curve. A liquidity provider has to understand how IL depends on the size of price movements and how to calculate it; and then figure out the mechanics of options. However, the result is more than worth it: with a combination of put and call options one can effectively flatten the IL curve, where the impermanent loss is close to zero even when the price moves by as much as 30%.

For a team building or running a DeFi protocol, options can deliver even more value than to regular investor:

- Increasing the profitability of a liquidity pool;
- Lower risks when adding liquidity for risky, volatile instruments; this applies to both pool creators and major liquidity providers and market makers;
- Possibility to pay higher yield farming APYs while keeping the protocol sustainable, thus attracting more liquidity providers.

Decentralized options remain a complex and little-explored subject, but it’s perfectly possible to integrate regular options products into new or existing DeFi platform. The crucial step is to design a sustainable model, including pool APYs and hedging tools.

*The expert team at BDC Consulting has been working on such hedging product models for various clients from the DeFi industry. If you’d like to explore how to add option-based structured products to your liquidity pools to minimize volatility costs and increase the APYs, contact BDC Consulting today – it will be our pleasure to share our experience and ideas.*

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