Hedging Impermanent Loss

More technical look into how we'll be hedging IL with traditional European style options

One intriguing application of Carmine Options AMM is hedging against impermanent loss (IL). If you're not familiar with IL, it's a form of potential loss liquidity providers (LPs) in swapping protocols (like Uniswap) can experience when the price of tokens they're providing moves significantly. The key point to remember is that this potential loss isn't linear; the more dramatic the price swing, the greater the possible loss.

Now, you're probably wondering, "How does this work with options?" Well, it's possible to create options that align perfectly with this IL curve. These can either be traditional options at specific strike prices or a specialized "IL option".

Starting from Q3, we're planning to address IL by buying traditional options. This approach is called overhedging, as it provides a extra cover at points between available strike prices. Eventually, we aim to offer special options that perfectly track the impermanent loss curve, but this page shows how it's possible to hedge it with traditional European options, such as the ones offered by Carmine today.

Addressing IL by buying traditional options on the AMM

We'll construct the hedge from traditional options such as this Put with a strike price at -10. To abstract away the current price, we express price as relative to current price. Meaning if current ETH price is 2000 USD, the put depicted below has a strike price of 1800.

We can buy multiple of these options and construct a more complicated hedge that way

Multiple put options and their resulting payoff

As you can see, we can build essentially any payoff structure by combining various options together.

Let's apply this to the Impermanent Loss curve shown earlier and combine everything.

Note that the sign for the sum of options is inverted

The original Impermanent Loss curve is now this:

Keep in mind that in this simplified example, we used only three options of each type (call and put). In reality, we'll obviously use all available options, making the hedge much more precise.

Also note that we decided to overhedge – we actually make money, because at points between the available strike prices, the payoff from options outweighs the IL.

For a more another explanation of our approach to hedging impermanent loss, feel free to check out our Medium post. Our goal at Carmine Options AMM is eventually to be the risk layer of DeFi.