How to Create Perpetual Options in Uniswap v3

1. Value of a short call option

A user that sells a call option at strike K must sell the underlying asset if the asset price S is higher than the strike price K at expiration. When the user does possess the asset, the position is called a covered call.

  • t = current time
  • T = expiration time
  • S = underlying price
  • K = strike price
  • σ = volatility
  • μ = drift = 0

2. Value of a Uniswap v3 Short Put Option

As discussed in my previous post, we can derive an expression for the Net Liquidity value of a Uniswap v3 LP position using the specs provided in the Uniswap whitepaper.

3. Comparing a covered call to a Uni v3 LP position

In my previous post, I postulated that the value of a covered call is very similar to the value of a Uniswap v3 position. How similar are they?

Uniswap v3 options with specific DTE and delta

In our post about understanding the value of Uniswap v3 liquidity positions, we derived the following expression for the delta of a position:

Example: creating a 7DTE, 30δ Uniswap v3 options

Let’s work out a few simple examples:

  • If the current ETH-Dai price is 3300 and you want to create a perpetual position that mimics a 7DTE 30δ covered call option, then you’d need to create a LP position with a lower tick equal to 2447 and an upper tick equal to 3808.
https://www.desmos.com/calculator/fsupjiyq2n
  • You want to create a perpetual position that mimics a 21DTE 50δ covered call between ETH and the UNI token? If the current price is 115 UNI/ETH, then you’d need to create a LP position with a lower tick equal to 81 and an upper tick equal to 175.
  • If you’re feeling complacent and you want to create a perpetual position that mimics a WBTC-USDC 365DTE 16δ covered call option and the current price is 59500, then you’d need to create a LP position with a lower tick equal to 4900 and an upper tick equal to 144200.
  • If you want to live on the edge and you want to create a ETH-Dai perpetual position that mimics a DTE equal to 1 minute, a delta equal to 50δ and the current price is 3500, then you’d need to create a LP position with a lower tick equal to 3492 and an upper tick equal to 3508.

Towards a new financial primitive?

In this post, I’ve described how Uniswap v3 positions are analogous to perpetual short options. Option writers can deploy short options positions between any two assets, for any ‘effective’ expiration time, at any delta, and without the need to deploy an intermediary protocol.

  • Fixed-DTE options: Uniswap v3 LP positions have the potential to be a new financial primitive. While a single-tick position is still identical to a regular option, extending the range can alter the option payoff for a better risk control and reduced (gamma) risk.
  • Rebalancing: Ideally, the position would need to be rebalanced if delta is too far from target. A 1DTE option would need to be rebalanced very frequently due to it having a large gamma, while a 200DTE option may only need to be rebalanced every week or so.
  • Gamma: By specifying a range, the user is also specifying a maximum gamma for their position. Gamma explodes as the option approaches expiration, so deploying a position with a fixed range and constant gamma greatly reduces gamma risk.
  • Returns and Volatility: By prescribing a specific user-defined delta of less than 1, the position holder will likely receive reduced returns while decreasing portfolio volatility.
  • What about Long options? To mint long Uni v3 options, the minter would first lock assets in a LP NFT token and sell it for less than the position’s intrinsic value (this is the same as buying an option for a net debit). BUT the user can claim back the underlying at the strike price at any time — ie. exercise the option.

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Guillaume Lambert

Guillaume Lambert

Asst professor in Applied Physics at Cornell. LambertLab.io PI and proud father. Interests: Biophysics, Math, Crypto, and Options (often all at the same time).