Research II

Backtesting historical NFT prices to find the best TWAP period. Based on the responsiveness (measure of freshness) and stabilization (measure of max drawdown protection).

Overview

The main goal of our Oracle is to provide stable and fresh price data for the Parallel money market.

In this research article we'll be determining the optimal TWAP period that meets the criteria for Parallel.

An optimal period should provides both a stable price (reduce jitter and anomalies) and a reactive price (match realtime marketplace data and track changes in price trends).

Since these two metrics are directly competing there is not an explicit "best" value, but there is some preferred trade off of reactiveness and stabilization that should satisfy our requirements.

Target Question

What TWAP period will best maximize our reactiveness and stability?

Breakdown of metrics

Reactiveness
Stabilization

Reactiveness ****

Reactiveness is related to how closely we track the price. A 100% reactive price would track realtime floor price 1:1. However 100% reactive is undesirable because we want to avoid extreme changes and price manipulation.

Reactiveness = \sum_{i=1}^{D}(x_i-y_i)^2

Stabilization

Stabilization is related to how much short fall protection is provided to a collateral provider. A completely stable price would have 100% short fall protection, meaning that the TWAP period would avoid all historical liquidations for users who borrowed 100% of their borrow limit for a period of time.

Stabilization = \sum_{i = 1}^n [\frac{x_{t}}{max(x_{[t - p]})} < \frac{LTV}{LiqThres} ]/n

Exploring the indicators

We can start by exploring the historical data of a couple projects, and plot the TWAP values to help shape an intuitive understanding of the implications of TWAP period width.

Projects

Azuki
Bored Ape
Cryptopunks
Doodle

Responsiveness

We can visualize the reactiveness of a TWAP window by plotting the TWAP in comparison to the realtime price. Since a short window will only look at recent prices, the width of the window directly correlates to how much we want to smooth (reduce reactiveness) our prices.

In the following examples the lines are

Color

TWAP Period

Orange

6 hours

Green

24 hours

Red

72 hours

Stabilization

We can visualize the impact of larger TWAP window on the max drawdown. Looking at the chart below we can see the blue line that represents the max drawdown for a 30 day window.

The blue line describes the currently twap value divided by the max value within the window. Which simulates the scenario of a user providing and NFT at the top of the recent market and supplying collateral for at least 30 days.

In the following examples the lines are

Color

TWAP Period

Orange

6 hours

Green

24 hours

Red

72 hours

Above we can see in both the Azuki backtest (top) and the bored apes (bottom) that widening the TWAP period results in a lifted line, and more short fall protection. We can also see that by utilizing wider a TWAP we can be more robust to short term market trends.

Optimizing

We can search for an optimal set of values by iterating our metrics over a handful of NFT projects and different TWAP period widths.

For the case of this research we will not be exhaustive and we will only explore a subset of possible solutions.

However our research is ongoing, and not only limited to TWAP, so we can revisit these numbers in later research.

TWAP windows

1 hour
3 hours
6 hours
12 hours
18 hours
24 hours
30 hours
36 hours
42 hours
48 hours

Key indicators

Relative Increase of shortfall protection
Relative responsiveness

Responsiveness results

The values shown represent the negative mean squared error between our TWAP values and the realtime price for all historical data points. This results in an error of 0 when there is no TWAP applied since we are 1:1 with the real time price. Results get larger as the error increases, meaning the values are less in sync with the realtime price.

We can see how as we widen the TWAP period we lower our responsiveness.

Minutes

azuki

boredapeyachtclub

cryptopunks

doodles-official

Average

0.00

-0.08

-0.42

-0.12

-0.01

-0.16

180

-0.16

-0.92

-0.36

-0.04

-0.37

360

-0.28

-1.60

-0.70

-0.08

-0.66

720

-0.50

-2.99

-1.32

-0.15

-1.24

1080

-0.76

-4.36

-1.92

-0.22

-1.82

1440

-1.05

-5.73

-2.52

-0.30

-2.40

1800

-1.38

-7.18

-3.13

-0.39

-3.02

2160

-1.70

-8.66

-3.76

-0.47

-3.65

2520

-2.05

-10.10

-4.41

-0.55

-4.28

2880

-2.41

-11.44

-5.07

-0.63

-4.89

Stabilization results

The values shown represent the percent of minutes that a user would be liquidated if they took out 100% collateral at the highest price in the last 30 days. A value of 0 represent a collection that would have never resulted in a liquidation.

We can see how as we widen the TWAP period we reduce the maximum drawdown, and in some cases reduce the value to 0 when the original short fall likelihood is already very low.

minutes

azuki

boredapeyachtclub

cryptopunks

doodles-official

Average

0.24

0.00

0.06

0.17

0.00

0.04

180

0.16

0.00

0.04

360

0.16

0.00

0.04

720

0.16

0.00

0.04

1080

0.15

0.00

0.04

1440

0.15

0.00

0.04

1800

0.14

0.00

0.04

2160

0.13

0.00

0.03

2520

0.13

0.00

0.03

2880

0.13

0.00

0.03

Summary

Finally we can summarize our findings by simply calculating the mean value across the projects. This should give us an average impact on our metric for each time period we're interested in.

minutes

responsiveness

stabilization

0.000000

0.061120

-0.161703

0.041279

180

-0.371128

0.041174

360

-0.663773

0.040791

720

-1.240942

0.039170

1080

-1.815482

0.038040

⭐️ 1440

-2.400869

0.036583

1800

-3.019885

0.035586

2160

-3.649925

0.032839

2520

-4.279159

0.031971

2880

-4.885476

0.031445

Using the table above we can quantify the tradeoff when we widen our TWAP period. We can see that without any period we are extremely responsive (a score of 0) and we have an average rate of 6% liquidation likelihood as a maximum drawdown for 30 day holders.

By widening our period to a value greater than 720 minutes or 12 hours, we can see that we gain almost 2.5% more shortfall safety in our stabilization metric.

At 720 minutes we still have some room for improvement, we can reduce our liquidation likelihood to 3.65% if we extend our period to 1440 minutes or 24 hours. 1440 minute window does reduce our average responsiveness, but this is still within an acceptable range.

Conclusions

We should set our TWAP period to a value close to 24 hours or 1440 minutes. This period should provide us with enough reaction to closely follow the realtime market and also provide enough added stability so NFT providers can be confident they will not be liquidated in a flash drawdown.

We're dedicated to improving our pricing mechanism over time and provide more research about the best way to price NFTs. This insight will help us continue to improve our Oracle and bring the best service and experience to all Para Space users.

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Last updated 7 months ago