Curve-depeg

Predictive modelling of depegging on Cuve.fi.

Curve and the virtual price

The price of token at the stableswap Curve.fi is calculated by the the equation below.

$$ A = \frac{A_{contract}}{2} $$

$$ D = \frac{1}{3 \cdot \sqrt[3]{2}} \frac{(432 A y_1 x_1^{2} + 432 A x_1 y_1^{2} + \sqrt{6912 (4 A - 1)^{3} x_1^3 y_1^3 + (432 A x_1^2 y_1 + 432 A x_1 y_1^2)^{2}})^{\frac{1}{3}} - 4 \sqrt[3]{2} (4 A - 1) x_1 y_1} {\sqrt[3]{432 A y_1 x_1^{2} + 432 A x_1 y_1^{2} + \sqrt{6912 (4 A - 1)^{3} x_1^3 y_1^3 + (432 A x_1^2 y_1 + 432 A x_1 y_1^2)^{2}}}}$$

$$ s = \frac{D}{2}$$

$$ y(x) = -\frac{x}{2} - \frac{s}{4A} + s + \frac{\sqrt{(2Ax^2 + sx - 4Asx)^2 + 8Axs^s}}{4Ax}$$

The equation describes a curve whose shape depends on the amount of token $(x_1$ and $y_1)$ in the pool and a parameter, $A$. An example of such a curve is shown in the figure below. The example is of a hypothetical pool with $4 \cdot 10^6$ of $tok_1$, $16 \cdot 10^6$ of $tok_2$ and $A = 16$.

The virtual price is given by the negative of the tangent to the point $(x_1, y_1)$ on the curve. In the figure the tangent is shown by dashed lines.

Changing the number of tokens and/or $A$ changes the shape of the curve which in turn, influences the price. The figure below shows examples of this.

The more extreme the ratio of the two tokens become the more the price deviates from $1$. This can be counteracted by increasing $A$, which leads to a greater range of ratios with a price close to $1$, but sharper drop-offs at the end of this range. This is shown over a greater range of token ratios and values for $A$ in the figure below.

In the figure above, the red line indicates the border between peg $(0.95 \geq price_{x_1} \leq 1)$ and depeg $(price_{x_1}< 0.95)$.

Predicting depeg

We want to predict depegs $(price_{x_1} < 0.95$ or $price_{x_1} > 1.05)$ 24 hours in advance.

Data

We have data from five Curve.fi pools where depeg occurred (USDN-3CRV, MIM-UST, sETH-ETH, pUSd-3Crv, UST-3Pool). From each pool we have the number of tokens over variable number of days, from 77 (pUSd-3Crv) to 626 (USDN-3CRV) days. We computed the virtual price from the pool data. We defined a depeg as a 1% deviation from a price of $1$, perfect peg. Thresholding the price data gave us binary time series that we trained learners to predict future depegs (24 hours).

Modelling

Learners were fitted three times on four of the five pools, each time with a different hold-out pool. We averaged the results across the three different runs and selected the learner and window length resulting in the highest $F_1$ score.

We compared six different learners and 19 window lengths between 1 and 70 days.

Learners

Logistic Regression
Naive Bayes Classifier
Support Vector Classifier
Decision Tree Classifier
Random Forest Classifier
Gradient Boosting Classifier

Results

We got the best results with a Gradient Boosting Classifier and a window length of three days.

The results are surprisingly good and could be used to manage pools.

Use

Paths are relative to the working directory.

Search for the best predictive model:

from model import search_cls
best, results = search_cls()

Fit, predict and plot:

from model import fit_predict
fit_predict()

Sravanthgithub/Curve-depeg