Vol-range AMM

Learn what the volatility-range AMM is and how it works for traders and LPs

To fully understand how volatility-range AMMs work, let’s start with the basics of general AMMs and work our way up.

Order-book Model vs. AMM

Automated Market Makers (AMMs) are a type of decentralized exchange (DEX) protocol that uses an algorithm to automatically set the price of an asset. Instead of relying on an order book, as is common with traditional exchanges, AMMs use algorithms to set and adjust prices based on supply and demand.

The key differences between the AMM and order book model are the following:

• Market makers (called Liquidity Providers, or LPs) provide liquidity in a defined price range instead of placing discrete limit orders.

• Limit orders from LPs are “reversed” when fulfilled, meaning if an LP sold asset A, he is now buying asset A (at a lower price). This reversal is automated by a smart contract.

• On an AMM, there is always a price (if LPs keep their liquidity on the market). The spread is typically a percentage of the price, for example, 0.6% of the current asset price.

• There are no maker/taker fees like on an order book. Traders pay half the spread plus slippage, and that’s how LPs earn (buying low, selling high).

• Automation allows LPs to provide liquidity once and earn trading fees for a longer time, without any action needed on their side.

Price-range AMM

Traditional AMMs, like the original Uniswap model, require liquidity providers (LPs) to provide liquidity across the entire price curve, from $0 to infinity. Concentrated liquidity enables LPs to add liquidity within specified price ranges, concentrating their capital where it's most utilized. This makes them more flexible, but also more challenging to manage. By defining a specific price range for trading liquidity, an LP gains more leverage, but also incurs greater risk.

In simpler terms, concentrated liquidity enhances capital efficiency for LPs by allowing them to allocate capital within a price range where trading predominantly occurs. For instance, an LP might select a price range from $1400 to $1800 for an asset that has been trading within that range over the past 3 months.

Dilemma: Low Capital Efficiency vs. Complexity

Given that options are leveraged instruments, the price of an option can fluctuate much more than its underlying instrument. For instance, a 5% change in the underlying price might result in a 50% change in the option's price. Leveraged instruments often clash with price-range AMMs because the leverage that an LP benefits from largely depends on the asset trading within a specific (and often narrow) range.

If an LP wants to maintain an active position, they must opt for a broader range, which subsequently reduces capital efficiency.

Conversely, by choosing a narrower range, the LP can achieve higher capital efficiency. However, this comes with the caveat of needing to actively manage their positions and associated risks. The question arises: just how intricate can risk management become?

Let's consider an example where an option is trading at $100. For an at-the-money option, an LP might choose to provide liquidity within the $80 - $120 range. Half the time, such an option could expire worthless. In this scenario, when the option's price declines to $80, the LP would have acquired all the options within that range. Now, the LP holds the options, having spend all cash to buy them. What's the next move? If the LP opts to open another LP position, he would need to hedge the options and provide additional cash. This process might need to be repeated several times throughout the option's lifespan if the LP wishes to maintain high leverage.

In essence, the LP is faced with a choice: either accept lower capital efficiency or deal with the complexities of risk management.

Volatility-range AMM

The solution we've implemented at Gamma Options is the "Volatility-range AMM". Our AMM allows LPs to offer liquidity to the options market in a manner that more naturally aligns with fluctuations in option dollar prices.

Instead of adding liquidity based on a USD price range, an LP selects an implied volatility (expressed in percentage) range within which their position remains active. Given that volatility typically doesn't vary as much as option's USD price, this setup is ideal for LPs. The volatility range addresses the previously mentioned dilemma, allowing LPs to achieve high capital efficiency while also simplifying risk management.

For traders, the experience is consistent with other AMMs. They receive USD price quotes from the AMM at the time of the trade.

However, LPs have a distinct experience compared to providing liquidity to price-range AMMs, primarily because they are adding liquidity in a volatility range.

Volatility Range

Given that LPs provide liquidity based on a volatility range, the AMM actively keeps track of current volatility (vol price). Utilizing the Black-Scholes formula, the AMM can subsequently quote prices in USD based on the current volatility. The conversion from volatility to USD price is executed on-chain and adapts dynamically for each trade. The volatility remains constant unless affected by a trade.

Let's examine an example: Suppose the current implied volatility is 40%, and the LP anticipates no volatility fluctuations. He adds liquidity within the [30%, 50%] range. Here's how his position breaks down:

• Buying options within the [30%, 40%] subrange.

• Selling options within the [40%, 50%] subrange.

Should a trader purchase options, the current volatility might adjust. Subsequently, the position might appear as:

• Buying options within the [30%, 41%] subrange.

• Selling options within the [41%, 50%] subrange.

It's evident that the current volatility shifted once a trader acquired options from the AMM. As for the option's USD price? At the moment of transaction, the AMM would have presented a USD price for the trader based on an average volatility (approximately 40.5%), taking into account factors like the underlying asset, strike price, expiration, and risk-free rate, all derived from the Black-Scholes model.

Tracking volatility price rather than USD price presents several considerations for LPs.

Underlying Price Fluctuations

Firstly, the USD price of an option can fluctuate on a vol-range AMM even if there's no change in volatility. For instance, if the underlying asset appreciates, the USD price of a call option might also increase. The option's USD price isn't strictly tied to volatility, as elements like the underlying asset and the risk-free rate significantly influence it.

Isolated Margin

Secondly, LPs may need to deposit more cash than initially required, to make sure they always have enough cash to cover their buy side. This is because the USD price of an option can rise without a corresponding increase in volatility. Consider our previous example where the LP is purchasing within the [30%, 40%] subrange. The AMM can determine the necessary cash amount to cover this at the position opening time. However, what ensues if the option's USD price surges by 50%? In such a scenario, the LP wouldn't have sufficient funds to buy options within that subrange. Consequently, the LP must allocate additional cash to cover his position up to a certain USD price.

It's imperative for all LP positions to be fully covered. So, what happens if an LP lacks the necessary cash to buy options within their subrange? Their LP position is forcibly closed with a penalty.

To learn more about Isolated margining, see LP Position Margining.

To avoid such forced closures, LPs must monitor and manage their liquidity. They have the flexibility to deposit or withdraw cash from their position whenever to avoid getting penalized.

Leverage

LPs can enhance capital efficiency by allocating assets into a narrower range, benefiting from the fact that volatility typically remains more stable than option $USD price. This offers inherent leverage from the AMM.

Additionally, LPs have another leverage source. They can borrow from the Margin pool to cover their sell-side subrange. Specifically, they might borrow ETH for call options or USD for put options, subsequently issuing and adding them to selected range.

The cumulative leverage an LP can utilize is a product of both AMM and Margin leverages.

Fees

LPs accumulate trading fees when their position remains active, meaning when the current volatility is within their selected range. Typically, option markets exhibit wider price spreads compared to spot markets. On Gamma Options markets, these spreads adjust based on underlying and strike prices. Notably, deep out-of-money options command larger spreads, while in-the-money options have tighter ones.