Gamma transform

This is an implementation of the gamma transform concept by Guillame Lambert [1].

A simple optimization problem to find the amount of Uniswap V3 single tick liquidity positions that perfectly hedge the gamma of a long squeeth position.

Squeeth an ETH perpetual by Opyn [2].

This work is part of the research conducted while designing the Haptic protocol and is made available for educational purposes.

Why this?

From [1]

Why would someone want to hedge a long squeeth? I’m not entirely sure. While holding a squeeth means that one would need to pay a fixed funding rate, a net positive income may result from shorting ETH (if ETH is shorted on a perp futures exchange) and deploying a Uni v3 LP position (by collecting Uni v3 LP fees).

Requirements

• R

Installation

• Install R from here (Ubuntu)
• Clone this repository

Usage

• Open a terminal and navigate to the repository
• Check that the file has executable permissions or grant them with chmod +x solve.r
• Run ./solve.r

References

[1] https://lambert-guillaume.medium.com/gamma-transforms-how-to-hedge-squeeth-using-uni-v3-da785cb8b378

[2] https://medium.com/opyn/squeeth-primer-a-guide-to-understanding-opyns-implementation-of-squeeth-a0f5e8b95684