Retroactive Airdrop Model for XGA

ℹ️🌐 Governance
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Retroactive Airdrop Model for Token Holders and Uniswap V3 Liquidity Providers

Proposal Title: Implement a Retroactive Airdrop Rewarding Token Ownership and Uniswap V3 Liquidity Provision

Summary:

This proposal outlines a model for a retroactive airdrop to reward users who have either held a FOLD token or provided liquidity to our protocol’s Uniswap V3 pools. The model combines elements of time-weighted holding (for token holders) and time-weighted liquidity provision (for LPs), using a sigmoid function to incentivize long-term commitment. The model draws heavily from the research paper “Retroactive Airdrops are Exotic Options” by Tarun Chitra ([1]), adapting its concepts to our specific needs. This proposal includes a summary of the relevant parts of that paper, three detailed examples of the LP reward calculations, and clearly defines eligibility.

1. Background and Motivation (Referencing )

Chitra [1:1] argues that these airdrops can be viewed as exotic options, specifically random start perpetual American options. This perspective provides a powerful framework for understanding their valuation and designing effective distribution mechanisms.

  • Exotic Options Analogy: The paper highlights that users participating in activities that might earn them a future airdrop are essentially paying an “option premium” (in the form of opportunity costs, fees, or impermanent loss) for the right to receive tokens. However, unlike traditional options, the reward amount and the “expiry date” (airdrop time) are unknown.
  • Staking Protocols and Options: The model in [2] incorporates elements of both staking protocols ([3], [4]) and options pricing. Users “stake” their capital (either by holding tokens or providing liquidity) to earn a share of the future token distribution.
  • Agent-Based Modeling: Chitra [1:2] proposes an agent-based model to simulate airdrop dynamics, allowing for the analysis of different distribution strategies and their impact on user behavior.
  • Random Start Perpetual American Options: The paper argues these options are the best fit.

2. Proposed Model (Adaptation of [1:3])

Our proposed model adapts the core ideas of [1:4] to create a combined reward system for both token holders and liquidity providers:

Eligibility:

To be eligible for the airdrop, a user must have either:

  1. Held FOLD tokens: For a minimum duration (to be determined by governance, e.g., 1 month) before the snapshot block. The holding period will determine reward.
  2. Provided liquidity to designated Uniswap V3 pools: For a minimum duration (to be determined) before the snapshot block.

Airdrop Calculation (Two Paths, Same Underlying Principle):

  • For Token Holders:

    Airdropped Tokens = Token Balance * Sigmoid( 5 * (Months Held / Max Months - 0.5) )
    • Token Balance: The amount of [TOKEN_NAME] held at the snapshot block.
    • Months Held: The number of months the tokens have been continuously held (up to Max Months).
    • Max Months: A predefined maximum holding period (proposed: 48 months).
    • Sigmoid(x) = 1 / (1 + exp(-x)): The standard sigmoid function.

  • For Liquidity Providers:

    Airdropped Tokens = Capital * Sigmoid( 5 * (Months Held / Max Months - 0.5) )
    • Capital: The liquidity (L) provided to the Uniswap V3 pool.
    • Months Held: The number of months the liquidity has been continuously provided.
    • Max Months: A predefined maximum holding period (proposed: 48 months).
    • Sigmoid(x) = 1 / (1 + exp(-x)): The standard sigmoid function.

Payoff Calculation (For Liquidity Providers Only): This remains the same.

Payoff = max(e^(-r * tau_s) * (Position Value + Airdrop Value) - Initial Investment Value, 0)

Hurdle Rate (For Liquidity Providers Only) : This remains the same

Hurdle Rate = (phi + 1) * (Initial Investment Value / Airdropped Tokens)

Rationale:

  • Unified Eligibility: Simplifies the airdrop process and broadens participation.
  • Time-Weighted Rewards: Both token holders and LPs are rewarded for long-term commitment, using the same sigmoid function for consistency.
  • Incentivizes Holding and LPing: Encourages both holding of the governance token and providing liquidity to the protocol’s pools.
  • Based on Established Research: Grounded in the theoretical framework presented in [1].

3. Parameters for Governance Vote:

Parameter Proposed Value Description
max_months 48 Maximum holding period (in months) for the sigmoid function.
risk_free_rate 0.03 Risk-free interest rate (used in payoff calculation for LPs).
airdrop_token_price [To be determined] The price of the airdrop token.
airdrop_time [To be determined] The time the airdrop will occur.
sigmoid_scale 5 Scaling factor for the sigmoid function (controls steepness).
sigmoid_shift 0.5 Shift factor for the sigmoid function (controls midpoint).
snapshot_block [To be determined] The Ethereum block number for the snapshot of token holdings and liquidity positions.
eligible_pools [List of pools] Uniswap V3 pools eligible for the airdrop (e.g., [USDC/ETH 0.3%, DAI/ETH 0.05% ]).
[TOKEN_NAME] [Token Symbol] The governance token that must be held to qualify (e.g., “GOV”).
token0_price 1 Price of token 0, assuming it is a stablecoin.
min_holding_duration [To be determined] Minimum duration (e.g., in months) for both token holding and liquidity provision to be eligible.

Draft Script for Calculation

References:

  1. Chitra, T. (2022). Retroactive Airdrops are Exotic Options. Available at [link to arXiv or other publicly accessible location]. ↩︎ ↩︎ ↩︎ ↩︎ ↩︎

  2. Chitra, T. (2019). Competitive equilibria between staking and on-chain lending. arXiv preprint arXiv:2001.00919. ↩︎

  3. 2 ↩︎

  4. Chitra, T., & Evans, A. (2020). Why stake when you can borrow? Available at SSRN 3629988. ↩︎

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2

Thank you Sam.

I request the consideration of two edge cases:

  • xfold should be treated as fold
  • sending xfold or fold between two self-owned wallets does not interrupt holding period

Thank you

1 Like