A Guide for Choosing Optimal Uniswap V3 LP Positions, Part 1

  1. What should the center price be?
  2. What should be the value of the upper and lower ticks?
  3. What is the likelihood that the price of a given asset will remain within a specified price range after a certain time?
  4. How long to keep a position on?
  5. What’s a realistic profit target?

Expected move of a crypto asset price

Geometric Brownian Motion. 500 simulations of the price of an asset using the Geometric Brownian Process. We should expect the majority of the traces to remain within the expected move (dashed lines)
ETH Expected Move. Historical ETH price, with the expected move after July 25th (result from 100 simulations). The expected move starting at a price S0 should be ±S0*σ*√T with 68% probability.

Probability of ending up inside a defined range

Geometric Brownian Motion and Boundary Crossing. What is the probability that a Geometric Brownian Motion will stay within a range defined by a lower and upper tick?
Wiener Process and Moving Boundary Crossing. Brownian motion is centered around zero and has a variance equal to 1. The boundary is now moving with the price.
Probability of ending In-The-Money. Choosing a Uniswap LP position defined by range 20% above and 20% below a strike results in a probability of ending In-The-Money that depends on the duration T. In this figure, μ= 1%/year and σ= 100%/year.
Probability of ending in-the-money for various duration in days and range factors r. The range factors of 1.001, 1.006 and 1.02 correspond to a 1-tick wide liquidity for the 0.05%, 0.3%, and 1% fee tiers.

Towards an optimal Uni v3 LP position?



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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).