Maturity modulation

Background and goal

• The maturity of a neuron is not a tradable asset, it is an attribute of a neuron. The decentralized governance of the Internet Computer can change the treatment of maturity at any time.
• If a user wants to generate income from maturity, he/she needs to burn maturity to create new ICP via spawning a neuron which is a non-deterministic process.
• The maturity modulation function introduces uncertainty in the creation of ICP from maturity. This article explains how the maturity modulation function works.

Spawning maturity via the maturity modulation function

• The user triggers spawn maturity. A new neuron will be immediately spawned; however, this newly spawned neuron will have no ICP at start, only maturity.
• Spawned neurons will have a dissolve delay of 7 days and will be set to dissolving at the time of spawning.
• After 7 days when the neuron is dissolved, the amount of ICP, modulated by the function introduced below, will be minted from the neuron's maturity and be available to the user.

Description of the maturity modulation function

• At the day of modulation, for each of the last 29 days determine the 30-day moving average ICP price, which is displayed on the Internet Computer dashboard. Label these a₁ through a₂₉, where a₁ denotes the average rate on the previous day, a₂ denotes the rate two days ago and so on. The 30-day moving average prices are used because they exhibit less variance than day-to-day prices.
• Compute the relative 7-day return for each of the last four weeks. Thus,
  • w₁ = (a₁ - a₈) / a₈,
  • w₂ = (a₈ - a₁₅) / a₁₅,
  • w₃ = (a₁₅ - a₂₂) / a₂₂,
  • w₄ = (a₂₂ - a₂₉) / a₂₉.
• The values w₁, w₂, w₃and w₄ are bounded from -0.05 to 0.05 by clipping values to the limits of this range, i.e., capping by 0.05 and flooring by -0.05.
• Take the average w = (clipped(w₁) + clipped(w₂) + clipped(w₃) + clipped(w₄)) / 4.
• The resulting value w is a number between -5% and 5% that determines modulation.
• The maturity amount x is converted to x * (1+w) units of ICP.
• The maturity modulation function is updated once a day.

Example

• On Feb 1, 2022, the modulation function is 0.73% which is the average of the relative weekly returns w₁ = -4.59%, w₂ =-0.63%, w₃=5.00%, w₄ = 3.13%.
• If a user disburses on that day (day of transfer) 100 maturity, then this will result in 100.73 ICP.