Providing liquidity on a decentralized exchange earns fees, but exposes the provider to impermanent loss when prices move. IILX turns that exposure into a number — forward-looking, extracted directly from options, and updated in real time.
On a decentralized exchange, prices are quoted by an AMM rather than an order book. When the market moves, arbitrageurs trade against the pool until its price catches up. That rebalancing is not free: it leaves the liquidity provider holding more of whatever fell and less of whatever rose.
The result is impermanent loss — the gap between what a liquidity position is worth and what the same assets would have been worth if you had simply held them. Impermanent loss increases with the size of the price move. Liquidity provision is therefore a compensated short position in volatility: fee income accrues while markets are calm, and the cost materializes when they are not.
Concentrated liquidity lets you deploy capital over a chosen price interval rather than the entire price range, which turns impermanent-loss exposure into an explicit design choice:
You can always calculate a realized impermanent loss from realized prices. That is little help when deciding what to do today. IILX measures the risk before it materializes, and updates with the market's forward-looking view as it is priced into derivatives.
Impermanent loss has a remarkably simple description. For a full-range position it is one eighth of the variance of the relative price between the two assets. The entire risk of providing liquidity therefore reduces to a single quantity — variance — and variance is precisely what option markets price.
That is the same logic as the VIX. The VIX does not forecast how volatile the S&P 500 will be; it replicates volatility from a strip of index options and reports what the market charges for it. IILX applies the identical construction to liquidity provision: impermanent loss is replicated by a portfolio of options and valued at the prices those options trade at.
Concentrated liquidity changes only the scope. The same replication is restricted to the price range you choose, which is why the index is published for a family of range widths alongside the full-range benchmark.
The cost of providing liquidity can be extracted from the options market. That is what IILX does.
How the option market prices impermanent loss, over a chosen horizon and range width.
What impermanent loss actually turned out to be, measured from realized prices.
Implied minus realized: whether providers were paid more than the risk ended up costing.
The current option surface for the underlying asset.
Markets quote a handful of expiries; the index needs a clean 7- or 30-day view, so the surface is fitted and interpolated to it.
Each option in the replicating basket is valued at the volatility the market is quoting for it.
Repeated across range widths from ±10% to ±90%, plus the full-range case — giving a surface rather than a single number.
The formulas behind each step, the realized-loss definitions, and the numerical details are written up separately: read the full methodology →
A forward-looking measure is only worth having if it beats looking backward. Tested on hourly BTC and ETH data since January 2023, it does.
IILX explains about twice as much of the impermanent loss that subsequently materialized as a realized measure does.
Sorting days by IILX, pools earned that much more in fees over the following week in the highest bucket than in the lowest.
IILX exceeded what actually materialized in roughly three quarters of seven-day windows — the compensation for bearing the risk.
High IILX brings more fee income, and more impermanent loss. Net of the two, the advantage disappears — which is exactly why the headline APR of a pool cannot tell you whether the fee is worth the risk.
| White paper | IILX — The Derive Implied Impermanent Loss Index. L. Schönleber, A. Papanicolaou, S. Dawson. Documents how the index is constructed and how to interpret it. PDF → |
| Underlying | The Implied Impermanent Loss in Decentralized Liquidity Provision. A. Papanicolaou, L. Schönleber, T. Li. Derives the option-implied valuation of impermanent loss and the risk premium that goes with it. SSRN → |
| Underlying | Implied Impermanent Loss for Concentrated Liquidity. L. Alberici, A. Papanicolaou, L. Schönleber. Extends the measures to positions concentrated in a finite price range. |
Questions about the methodology, an application we have not thought of, or a pool you would like covered — get in touch.