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Whitepaper 2: Automated Market Making of the Collateral Rebalancing Pool



Simulation of ALEX’s AMM of Collateral Rebalancing Pool during high market volatility

Two-Asset Collateral Pool: Rationale

AMM: Geometric Mean Market Maker

Rebalancing Set-up and Collateral Pool Valuation

Dynamic Rebalancing

Flight to Quality


Collateral Pool Key Parameters

Contract Initialization

  • Loan-to-Value (LTV): The ratio of the loan amount to the value of the collateral (“collateralize asset(s)”). For example, if LTV is set to be 80%, a loan amount equivalent to 80 BTC requires 100 BTC as collateral. There is generally no objectively correct LTV ratio; the LTV ratio depends on the quality of the collateralize asset, as well as the market condition when the loan is taken out. Collateralization Ratio (CR) is the inverse of LTV.
  • Tenor: The length of time remaining before the loan expires.
  • Strike Price: In the Black-Scholes model, strike price refers to the price at which the contract holder can purchase the underlying security when exercising a call option, or sell the underlying security when exercising a put option. In ALEX, the strike price determines the initial split of the risky and the riskless asset. For example, for an at-the-money option, in which strike price is set to be equal to the spot price, there would be an equal split of between two assets in the pool (i.e. ~50%).
  • Implied Volatility: In the Black-Scholes model, implied volatility is the volatility estimate of an underlying security. A crude approximation of implied volatility is historical volatility. In practice, implied volatility is usually backed out from the observed option price.
  • Risk-free Interest Rate: In the Black-Scholes model using risk-neutral valuation, the risk-free interest rate equals the expected return. The risk-free interest rate is usually assumed to be 0%, as future direction of the underlying security is unknown.

Pool Rebalancing

  • Rebalancing Frequency: Theoretically, continuous rebalancing is preferred for price continuity. In practice, ALEX updates the weights periodically to avoid over-calibration.
  • Smoothing Factor of Exponential Moving Average (EMA): EMA is an averaging method that places more weight on more recent observations. Assume y(t) is the observation value of y at time t, and that {y}(t) is the corresponding moving average, where α is the smoothing factor. Then:

Flight to Quality

  • Conversion Threshold: This is the LTV level when the risky asset in the collateral pool is completely converted to the riskless asset to prevent the loan from under-collateralization.
  • Reserve Premium: The reserve premium is collected on behalf of a reserve fund. The reserve fund serves as the protocol’s last resort. In the extreme event that market turmoil dries up liquidity and ALEX cannot convert all risky assets quickly enough to cover the loan amount, the protocol would cover the difference. The reserve premium is thus another mechanism to guarantee continuity of borrowing and lending activity on ALEX.



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