Oracle

Pennysia introduces the Cube-Root TWAP (cbrtTWAP), an innovative variant of time-weighted average price (TWAP) oracle mechanism that strikes an optimal balance between arithmetic and geometric means.

The Challenge

Traditional oracle approaches face trade-offs:

• Arithmetic mean: Captures short-term price fluctuations with high precision but vulnerable to sudden spikes
• Geometric mean: Smooths out noise logarithmically yet doesn't reflect real-time movements accurately

As highlighted in research by Delphi Digital, choosing between these approaches involves significant trade-offs.

Our Solution

By combining both approaches and applying a cube-root transformation, cbrtTWAP produces adaptive, manipulation-resistant price points that are:

• Responsive enough to capture immediate market changes
• Stable enough to follow broader market trends
• Resistant to manipulation attempts

Mathematical Implementation

Step 1: Cube Root Transformation

We apply the cube root transformation to each price observation:

$$\sqrt[3]{P_t}$$

Where $P_t$ is the price at time $t$.

Step 2: Time-Weighted Average of Cube Root Prices

Calculate the time-weighted average of the transformed prices:

$${\sqrt[3]{P}}_{t_0,t_1}=\frac{{\text{cumulativeCbrtPrice}}_{t_1}-{\text{cumulativeCbrtPrice}}_{t_0}}{t_1-t_0}$$

This gives us the average cube root price over the interval $[t_0,t_1]$.

Step 3: Final cbrtTWAP Result

Apply the inverse transformation (cubing) to get the final oracle price:

$${\text{cbrtTWAP}}_{t_0,t_1}={\left({\sqrt[3]{P}}_{t_0,t_1}\right)}^3$$

This final result combines the responsiveness of arithmetic means with the stability of geometric means.