01’s Binary Options AMM

6 min readAug 23, 2021

Market Makers

If you read our intro, you’ll know that 01 is building a decentralized binary options market. Traders can buy options for whether or not they believe Bitcoin’s price will be above or below the strike price. You might be wondering who chooses the price of each option. That’s where an Automated Market Maker, AMM for short, comes in. AMMs come in many flavours, the most notable ones include Uniswap’s constant product market maker, or Augur’s LS-LMSR. Those all sound a bit complicated, so let’s rewind a little and talk about traditional market making.

Traditional market makers are people (or software). They sell the assets, and they decide the prices of each based on their views of the market. Options can yield returns for traders, so as the seller of the option, the market makers themselves pay the traders’ winnings. An AMM, on the other hand, decides, on its own (hence the automated), asset prices based on market demand. The LS-LMSR, for example, makes sure prices per option always sum to (just above) 1, and prices assets (more or less) based on the proportion of each asset bought in the market. An AMM gets its money from Liquidity Providers, or LPs, who deposit money in the pool to “make the market” and determine the initial market prices.

What’s wrong with this?

The real problem arises if all the traders are correct about the outcome of the market.

In this case, the LPs pay out of pocket.

Ideally, the cost of shares bought on the losing side covers the winners’ payout, but this isn’t always the case. For example, if all the traders buy on the same side, and all win, that would spell doom for liquidity providers.

This problem could solve itself through LP fees which the traders have to pay, but this only happens when the market price of the winning option passes a certain threshold. All trades that happen before remain unfavourable to LPs.

The 01 AMM

At the basis of 01 Protocol’s AMM lies an LS-LMSR, which we just discussed.

As outlined above, AMM’s are flawed in that they only reflect the views of the takers, and not that of the makers — the prices are determined by what traders are buying.

A traditional market maker bases prices on their views, so where are the views of the makers in the AMM?

This is what we solve in our AMM.

The Secret Sauce

The Binary Options market is meant to reward traders for making smart but not obvious predictions.

Predicting that the price of Bitcoin will be up from the strike price in 5 minutes when it’s already up by 10% is not a risky trade.

To counteract this effect, 01 adjusts the price of each option based on the current bitcoin fluctuation with respect to the strike price.

If the price of Bitcoin is up, then the AMM will increase the price of longs while decreasing the price of shorts to incentivize less obvious and higher risk trades.

While, in theory, traders buy as a function of the current Bitcoin fluctuation, the price is slow to move when there has already been a large volume of trades.

Incidentally, if the price of BTC changes suddenly, passing from way above the strike price to way below the strike price traders can take a lot from LPs by simply buying out cheap options in the new obvious (low risk) position.

This goes against the purpose outlined above, so we increase the price of this option by some amount to counteract the sudden price fluctuation.

Said otherwise, 01’s market maker reacts instantly to large fluctuations in Bitcoin’s price, as a real market maker in a traditional market would.

This protects LPs by ensuring that their deposits won’t vanish as a result of anomalies in Bitcoin price.

This plot shows LPs returns over time for a short 30 minute market where volatility can wreck havoc on LP returns. The average realized gain for LPs are shown, geometrically averaged over N=1000 runs. Even if the worst closing price outcome for LPs always occurs, they will only see small losses. Notice that gains decrease significantly near the end of market close. This isn’t surprising, since the outcome is pretty much determined by that time and most trades will be unfavourable to LPs. Conversely, the worst-case scenario improves near the end of the market since people will be paying higher fees at that point. According to our simulations, LPs see an average (geometric) return of 0.05%. This applies for active markets where both sides are traded, and the provided liquidity is close to the trade volume. It is possible that markets will not be active or one sided which might decrease the overall return.

Additionally, to protect LP funds, we implement gradual injection of liquidity as a function of volume into the pool as opposed to fixed liquidity for every pool. This ensures that, for low trade volumes, LPs will not be overexposed to large amounts of risk. Again, if there is too much liquidity at the start of the market, the LS-LMSR will make prices hard to move making risk-free options inexpensive but risky options expensive which is undesirable. All this while decreasing slippage for traders — liquidity injection pads the liquidity pool to lower price movements.

Why all the fuss?

Technically, LP returns can be increased using the LS-LMSR by tuning certain parameters. This can alter the LS-LMSR to make it more sensitive to inventory. That is, trades affect the price of the asset more easily. This means that the price will quickly react if traders buy the same option. This minimizes arbitrages, and is favourable for LPs. The problem with this approach is that it exposes traders to large slippage rates: if someone makes a large order, then prices will change drastically. This is shown explicitly in the following plot: our market maker can yield the same returns for LPs while decreasing slippage for traders.

Average slippage over LP gains with and without price adjustment

Note that slippage is inflated in our simulations to explore baseline scenarios. In reality, slippage is expected to be smaller than reported here. What’s important is that in all the methods we tested, the price adjustment method always improved slippage rates for traders while maintaining LP profits.

Comparison to BSM

The Black-Scholes Model (BSM) is an options pricing model which is widely used in traditional finance. How does our price adjustment differ from the BSM? Firstly, the BSM relies on many parameters which characterize the asset in question. This involves volatility, which measures the instability of the price of the asset. Due to the unpredictability in price and volume of short duration cryptocurrency markets, we decided our approach was more efficient.

Moreover, the BSM does not take into consideration market inventory, i.e. the amounts of each option sold. Naturally, the prices should depend on demand and not solely on asset dynamics. This omission has seen LPs lose money over time in other options protocols. In our case, we have an AMM which takes inventory into account (the views of the traders), while also adapting to the dynamics of the asset in question. We believe this makes our approach more robust.

Let’s Recap

The 01 AMM is a modified LS-LMSR where prices also reflect the views of the maker.
The same LP returns can be achieved while reducing slippage rates for traders.
The 01 Binary Option AMM makes few assumptions about the underlying asset to edge profits in robust fashion.
The AMM takes into consideration both the views of takers and makers to price options.

If you have any comments, feedback, questions, or want to point out any mistakes we may have made, we’d love to hear it!