How to hedge options with SQUEETH

Opyn is deploying an easy-to-use quadratic contract SQUEETH (squared ETH) that can be used to hedge options, CFMMs like Uniswap, and anything else that has a curved payoff. Here we’ll show an example hedging an ETH/USD call option.

It’s significant that SQUEETH can hedge any ETH/USD option because it means these options can be more cheaply and transparently manufactured. Option markets suffer from bad liquidity and high bid/offer spreads because the market is fragmented across many strikes and expiries. SQUEETH changes this by providing a single clearing house for option risk.

We can see how the hedge works with some charts. The first chart shows the value of a call option as a function of ETH price. The option value increases with ETH price and the slope increases from 0 to 1 (the slope is the “delta” of the option).

The second chart shows option pnl of the call option (blue) and a delta hedge (red). If ETH is at 4000 and we hedge with futures, the hedge will be approximately right for small changes, but increasingly wrong for larger changes in either direction.

Call option with 4000 strike

Call option deconstructed

To hedge this remaining risk (the yellow in the second chart) we use our quadratic contract. The logic of using a quadratic contract like SQUEETH to hedge is that the left-over risk after the delta hedge is quite close to quadratic.

Option hedge process

Here’s how to hedge an option with SQUEETH:

Step 1: Sell an amount of SQUEETH with the same gamma as the option

Step 2: Buy ETH futures to hedge the delta from the option and the SQUEETH

The resulting position will still have cubic and higher order terms, but the hedge holds remarkably well, as we show in the example.

Consider the following ETH/USD call option:

Strike: 4000

Time to expiry: 30 days

Implied volatility: 90%

Our aim is to hold a portfolio of SQUEETH and futures that offsets the change in the price of ETH.

Option greeks

The option delta and gamma can be calculated from the option price given the current ETH price, the strike, and the expiry.

(you can see the calculations and try different values in this sheet)

Squeeth value and greeks

Squeeth is ETH² adjusted for funding. For our purposes we can just see it as the ETH price (p) squared:

The greeks are:

Options with a delta and gamma hedge

To fully hedge the option we need:

• Sell 0.00019 SQUEETH to match the gamma from the option position.
• Buy 1.53 ETH futures to hedge the delta from SQUEETH
• Sell 0.55 ETH futures to hedge the delta from the option position

The table shows how the hedge works. The option pnl is hedged almost perfectly (to within about 1% accuracy) with the SQUEETH hedge.

Hedging a call option with SQUEETH

Some practical considerations for the hedge

A few things to keep in mind:

1. Funding — The final position will receive funding from short the short SQUEETH but pay funding (implicitly) through time decay on the option. The net effect of the funding should be similar if SQUEETH and options are pricing correctly. If not, this creates a profitable trade, either buying options and selling SQUEETH or the reverse.
2. Portfolio hedging — In practice it’s more likely that SQUEETH will be used as a hedge for a portfolio of options rather than a single option, in which case the hedge will be aggregated across the portfolio — we can add up the delta and gamma for each option and the associated SQUEETH positions. We imagine a market maker using SQUEETH effectively to change option portfolio risk in the aggregate (long a bunch of short dated gamma and paying theta, sell some SQUEETH to reduce the theta bill and cut the gamma, etc).
3. Constant gamma vs changing gamma —Options have changing gamma whereas SQUEETH has constant gamma. This makes it easy to determine how much SQUEETH you need at a point in time, but it means that the squeeth hedge for options will need to be rebalanced as the price changes.

Converting to oSQTH for trading

To get a tradable portfolio we need to convert from squeeth to oSQTH. If the current traded price of oSQTH is $1164.35 the ratio of oSQTH to squeeth is 4000²/1164.35 = 13741.57. The target oSQTH for the hedge is then 0.00019*13741.57 = 2.634.

The full trade to match the option with oSQTH is:

• Buy 1 4000 strike 1 month option
• Sell 2.634 oSQTH
• Buy 0.98 ETH futures

A hint at a general hedging framework

There is a more general pattern here to hedge any function payoff with a combination of a futures and a quadratic hedge — the first two terms of the Taylor series for the value of a pricing function V:

If we need the higher order terms we need instruments ETH³, ETH⁴, etc. But typically the first two terms get us most of the way there, and this is why we chose SQUEETH as the first deployment.

Acknowledgements: Zubin Koticha, Andrew Leone, Wade Prospere