ATD (Automated Token Distributor)

Overview

The Automated Token Distributor (ATD) is a core component of VALOR's token distribution strategy. This document explains the ATD’s budget distribution mechanisms.

The below models can be updated due to the balance update

1. Budget Distribution

ATD’s budget distribution framework employs a probabilistic approach based on a standard normal distribution to allocate resources effectively across various tokens and market segments.

Key Definitions and Variables

Normal Distribution (PDF): A probability distribution function used to allocate budgets fairly, with a mean of 0 and a standard deviation of 1.
Budget Allocation Ratios: Ratios are derived from the PDF to determine the portion of the total budget allocated to each token.
Total Budget: It is set at 110% of the inflow over 24 hours. It is rounded down to 9 decimal places, and the remainder is discarded.

Process Explanation

Total Budget Calculation:
1. Case 1 (Accumulated Inflow < Accumulated Outflow):
  - The total budget is set at 110% of the inflow over the past 24 hours plus any carried-over budget
    $B_{total} = \left\lfloor (1.1 \times Inflow) \times 10^9 \right\rfloor / 10^9$
    Here, $Inflow$ is the inflow over the past 24 hours.
2. Case 2 (Accumulated Inflow > Accumulated Outflow):
  - The total budget is set at sum of each sSPL supply and ideal price.
    $B_{total} = \sum S \times P_{idl}$
  - Maximum budget = (Accumulated Inflow - Accumulated Outflow) * 1.1
Random Factor Generation:
- Generate a random number within the range of [-0.5, 0.5] from a normal distribution with a mean of 0 and a standard deviation of 1. This controls the variability in budget allocation.
- Calculate the probability density $p(x_i)$ for each random factor $x_i$ . This density influences how the budget is divided. The probability density function is:
  $p(x_i) = \frac{1}{\sqrt{2\pi}} e^{-\frac{x_i^2}{2}}$
Budget Allocation:
- Convert these densities into budget allocation ratios:
  $R_i = \frac{p(x_i)}{\sum_{j=1}^{9} p(x_j)}$
- Allocate the total budget to various tokens using these ratios:
  $B_i = \left\lfloor R_i \times B_{total} \times 10^9 \right\rfloor / 10^9$

2. Price Setting

The ATD's price-setting mechanism dynamically adjusts token prices around an ideal price to reflect market values.

Key Definitions and Variables

Ideal Price ( $P_{idl}$ ): The target price for the tokens.
Reference Price ( $P_{ref}$ ): The market price of the token in Black Market.
Next Price ( $P_{nxt}$ ): The price of the token after adjustment.
Standard Deviation ( $\sigma$ ): Controls the spread of price values around $P_{idl}$ .

These variables will be initialized on the procurement creation

Standard Deviation Calculation

The standard deviation $\sigma$ is calculated as:

\sigma = \sqrt{\frac{P_{idl}^2}{2 \ln(10)}}

This calculation determines the range of price fluctuations around the ideal price $P_{idl}$ , adjusting for market volatility.

Price Determination Model

Random Price Determination Model

This model dynamically calculates the next token price using a probability distribution function centered on $P_{idl}$ .

Detailed Process

Define Price Range:
- Establish the effective price range for the next pricing cycle:
  $\text{Effective Price Range} = [P_{ref} \times 0.9, P_{ref} \times 1.4]$
Generate PDF:
- Create a normal distribution centered on $P_{idl}$ with the calculated $\sigma$ .
Calculate Area Under Curve:
- Determine the total probability area under the PDF within the defined range:
  $A = \int_{P_{ref} \times 0.9}^{P_{ref} \times 1.4} f(x) \, dx$
Generate Random Factor and Set Next Price:
- Select a random value within the range [0, A], and determine the corresponding price using the inverse cumulative distribution function (CDF):
  $P_{nxt} = f^{-1}(r)$
- Here, $f^{-1}$ is the inverse function of the CDF, accurately determining the price corresponding to the random value $r$ .
Final Quantity Adjustment:
- Calculate the maximum quantity that can be purchased with the allocated budget:
  $Q_i = \left\lfloor \frac{B_i}{P_{nxt}} \right\rfloor$
- Round down to ensure accurate quantity calculation. (If $Q_i < 1$ , set $Q_i$ to 1)
- Adjust the final price using the actual quantity purchased:
  $P_{final} = \left\lfloor \frac{B_i}{Q_i} \times 10^3 \right\rfloor / 10^3$
- The final price $P_{final}$ is rounded down to 3 decimal places.
$B_i^\text{new} = B_i - (Q_i \times P_{final})$