Asteria Propose Promising Solution against Impermanent Loss

Impermanent Loss (IL), compared to its glorious twin brother Automated Market Making (AMM), is equally “famous” but in the exact opposite way. It is not an exaggeration that Liquidity Providers (LP) are the most essential group in the entire DeFi ecosystem, which IL is hurting ceaselessly.

Different DeFi explorers are aiming to eliminate this Achilles' Heel for good. Uniswap V3 is trying with customized range limitations of liquidity to provide based on grid trading practices. Some protocols provide issuance-like functionality while Asteria, as the rising star of decentralized option protocol, is approaching this by hedging with options.

The first definition of Impermanent Loss is not simple and understanding it is one of the main goals of this article, so do not be concerned if it does not make sense straight away.

What is Impermanent Loss?

(DeFi experts can skip to Section 2 directly if you are quite familiar with IL)

Impermanent Loss (IL) – This is a temporary loss that the liquidity provider is exposed to when the asset price changes. Perhaps counterintuitively the LP is exposed to a loss in bidirectional price movements. That is that even if the asset goes up the LP will lose. The loss is only realised if the LP withdraws their assets however. It is typically defined as compared to just holding that asset. I’ll come back to explaining this and the graph below.

Automated Market Maker – This mechanism was originally designed in the 90s to avoid troubles associated with human manipulation of manual books. Ironically they are being reintroduced in DeFi to avoid troubles associated with centralized, hierarchical finance.

XYK Model – ‘X*Y=K’ is the most common model for automated market makers. Ensuring a constant K is maintained between the relationship of X (x token) and Y (y token).

Liquidity Provider (LP) – The entity that provides liquidity to the pool in exchange for fees and other benefits.

As explained in the definition Impermanent Loss is the potential loss of a Liquidity Provider – it is only realized if the liquidity provider withdraws the assets. What might come as a surprise is that the liquidity provider suffers in both directions. In price appreciation this is because traders step in for arbitrage opportunities between the LP pool’s price and the price on another exchange or pool (representing the price appreciation). This has been discussed elsewhere in articles covering DeFi’s “Impermanent Loss”:

Table 1

Table 1 shows the bidirectional loss that would be realized if the LP were to remove the assets from the pool. Obviously we are dealing with cryptocurrencies which have associated volatilities. Therefore, such exposure is expected and this presents a problem for DeFi to get liquidity providers. Prospective liquidity providers can observe this state of play and opt to instead just hold the asset as this would allow them to accrue better profit and loss scenarios.

As a quick example, we will run some numbers.

If the holder can consider two scenarios of holding or providing liquidity they will see that it is better that they had held the asset. (This is where Asteria’s solution of options comes into play)

Table 2

	Price (USDT)	Supplied or held	Value ($)
DAI	$1	10,000	10,000
ETH	$500	20	10,000

Table 2 shows what assets the holder has at T1. They can decide to either hold them or put them into a liquidity pool. The liquidity provider has $20,000 worth of assets initially (T1). This is a 50/50 liquidity pool, there are other possibilities but we will focus just on this one for simplicity.

Now ethereum’s price appreciates by 20% - elsewhere, say another exchange – so it goes up 100 USDT. It now costs 600 USDT (T2). After T2 there would be two scenarios.

Scenario 1: If they had decided to hold the assets they would have $22,000 worth of assets:

Table 3

	Price (USDT)	Held	Value ($)
Dai	$1	10,000	10,000
Ethereum	$600	20	12,000

Scenario 2: If they had decided to give liquidity and supply the assets they would have a potential loss if they withdrew the assets:

Table 4

	Price (USDT)	Supplied	Value ($)
Dai	$1	10954.5*	10954.5*
Ethereum	$600	18.3*	10954.5*

This is because an arbitration process would occur between the pool and the outside. The total amount of assets they had in scenario 2 would be 21908.9*. The impermanent loss is defined by the difference between the total USD value of Table 3’s assets and the total USD value of Table 4’s assets.

So the IL is: (10,000 + 12,000) – (10954.5 + 10954.5) = 91.1

It’s crucial to remember that it is impermanent such that the LP does not withdraw the assets. It is permanent loss if the LP withdraws the assets after T2 – when the price has moved (and for example arbitration has occurred).

How Does Asteria Use Option to Tackle IL?

Asteria has introduced a solution to hedge against IL based on the Carr-Madan Formula. The basic concept is that for any return structure f(ξT) with respect to ξT that expires at time T, it can be realized by constructing a European Option portfolio with ξT as the target and expiration date T, under the condition of f(ξT) is second-order derivable, which is essentially a static investment strategy:

Asteria creates the portfolio of call options and put options with different strike prices and expirations to generate the following income:

exactly the opposite of IL.

Assuming ξ0=1

We get the curve of f, f’and f’’

By decomposing the IL, we can see that the automated spot market maker is equivalent to "free", providing the market with a set of call options and put option combinations with different strike prices (that is, the source of IL is the same as using Limit orders traded on centralized exchanges).

Backtesting Practices

Step 1: Volatility Estimations

Team Asteria calculates the annualized average volatility σ of a certain interval using the following method:

Where y_t="log" S_t-"log" S_(t-Δ) as the short-term logarithmic return rate of the underlying (S_t). They choose to use the volatility when the option is purchased to manage the risk of the entire portfolio and back tested with different interval lengths in the past, such as the volatility of one hour, one day, one week, half a year, and one year, to form a prediction of the volatility of different interval lengths in the future.

Step 2: Option Portfolio Pricing

Asteria applies the classic Black-Scholes-Merton option pricing model. Since cryptocurrency does not generate dividends, the price of European-style call options is the same as that of American-style call options, so Asteria uses American-style call options to construct the investment portfolio (The VIX calculation of CBOE index also refers to a similar method).

We take the option expiration T as 7 days and the annualized volatility σ as 2, by using 40 options with different strike prices, and substituting it into the Carr-Madan Formula to obtain one almost perfect portfolio for hedging IL：

As showed above, the cost of full hedging IL is only 0.7%, or the cost to hedge 10000 USDT staked is 70 USDT.

Step 3: Hedging and Payoff Testing

Based on the above testing data, Team Asteria designed an option based product named Impermanent Loss Hedger (ILH):

The user would only need to make three simple selections:

• Hedging Period: Daily/Weekly
• Hedging Mode: Bidirectional/Only Downside Protection/Only Upside Protection
• Hedging Level: High/Medium/Low

  
  

The key to the success for Asteria of this product is the capability to hedge, on behalf of option market makers/sellers, to gain the profit to pay off at the end of each cycle. So Team Asteria simulates the hedging (assume every 10 mins), for product on High Level & Bidirectional ILH and on both periods of Daily/Weekly, to identify the safety level to provide the basic payoff for product buyers and the liquidity pool’s return rate. The results are quite promising:

Each group represented by 4 graphs,

• Graph 1 showing the payoff at each expiration(weekly or daily)
• Graph 2 is histogram after hedging, the x-axis is the daily income in USDT, and the y-axis is the number of statistics
• Graph 3 illustrates the payoff results. Blue points represent the payoff promised (to compensate the IL). Yellow points represent the actual return of option hedging. x-axis is the rate changes between two tokens.
• Graph 4 is the scatter chart of the income promised to LP with a 45-degree straight line and the income after hedging. The X-axis and Y-axis are USDT, and the blue straight-line scatter chart with a 45-degree angle is the income promised to LP. The yellow scatter chart shows the hedged return corresponding to the return promised to the LP. For example, in a certain period, if the promised payoff is 50 and the hedging payoff is 75, the blue dot of the promised payoff will be marked at the coordinates (50,50), and the hedging payoff will be marked at the coordinates (50,75) as yellow dot.

  
  

Year 2019 Weekly Result

Year 2020 Weekly Result

Year 2021 Weekly Result
Year 2019 Daily Result

Year 2020 Daily Result

Year 2021 Daily Result

Conclusion

Asteria is building a practical cure for the IL headache. What to expect is not only a straightforward ILH product user interface would be launched, but API & templates of IL hedger are also available for LP themselves to customize the process or any third-parties to utilize for other product developments, both of which are awaited!