#ResearchBites from the @Panoptic_xyz team.
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One of the core assumptions behind financial models is that prices follow a geometric brownian motion (GBM) --eg. Black-Scholes.
Does the price of the most traded asset in Uniswap v3 also follow a GBM?
Let's find out! 👇
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One of the core assumptions behind financial models is that prices follow a geometric brownian motion (GBM) --eg. Black-Scholes.
Does the price of the most traded asset in Uniswap v3 also follow a GBM?
Let's find out! 👇
We will analyze the 5, 30, and 100bps ETH-USDC UniV3 pools.
The 5bps pool gets 90% of all volume and, zooming in on the price action, appear to have a smaller "per trade impact" than the 30 and 100bps pools
What is the size distribution of the price jumps for each pool?
The 5bps pool gets 90% of all volume and, zooming in on the price action, appear to have a smaller "per trade impact" than the 30 and 100bps pools
What is the size distribution of the price jumps for each pool?
If the price were a GBM, then the size of the price jumps would be normally distributed.
Instead, the price jumps are narrowly peaks around size~0.
They also have a kurtosis that's much larger than a normal distribution's (high kurtosis = long-tail event are more likely).
Instead, the price jumps are narrowly peaks around size~0.
They also have a kurtosis that's much larger than a normal distribution's (high kurtosis = long-tail event are more likely).
Indeed, the distributions can't be fit to a gaussian. An exponential distribution also fails to cover the distribution's "long-tail".
Surprisingly, the size of each price jump fits very closely to a power law distribution.
(CT: tag someone who may know why it's a power law)
Surprisingly, the size of each price jump fits very closely to a power law distribution.
(CT: tag someone who may know why it's a power law)
Key insights:
- The 5bps pool gets 90% of all USDC volume
- The 5bps pool likely follows the CEX price more closely due to its 0.05% arbitrage fee
- The distribution of price jumps does not follow a normal distribution
- The price jumps follow a power law distribution (!)
- The 5bps pool gets 90% of all USDC volume
- The 5bps pool likely follows the CEX price more closely due to its 0.05% arbitrage fee
- The distribution of price jumps does not follow a normal distribution
- The price jumps follow a power law distribution (!)
Questions/Caveats:
- Can a GBM have a power law random process?
- What is the impact of a large kurtosis on price action?
- These distribution may be colored by uneven time steps
- A lot of the volume is arbitrage and not reflect "organic" order flow
- Can a GBM have a power law random process?
- What is the impact of a large kurtosis on price action?
- These distribution may be colored by uneven time steps
- A lot of the volume is arbitrage and not reflect "organic" order flow
We may tackles these questions in a future.
In the meantime, please follow @Panoptic_xyz for your daily dose of #ResearchBites and other important updates!
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This content is for educational purposes only and should not be relied upon as financial advice.
In the meantime, please follow @Panoptic_xyz for your daily dose of #ResearchBites and other important updates!
============
This content is for educational purposes only and should not be relied upon as financial advice.
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