ATLAS Math: Risk Based Valuation

General

The risk based portfolio valuation provides a conservative estimate of portfolio value under adverse conditions.

• Market participants must maintain a positive risk based valuation at all times.

• If the valuation becomes negative, the account is subject to liquidation.

• The exchange operator defines two risk parameters per token:

  • Risk Price

  • Risk Slippage

Adjusted Token Balance

For each token, define the adjusted balance:

$$\text{Adjusted Balance(token)} = \text{Token Balance} - \text{Borrowed Quantity with Interest} + \text{Lent Quantity with Haircut}$$

where:

$$\text{Lent Quantity with Haircut} = \text{Lend Quantity} \times 0.98$$

• tokenBalance = user’s holdings of the token

• borrowedQuantityWithInterest = borrowed amount plus 10 days of interest

• lendQuantity = total amount lent to others

📌 For efficiency, lending values are aggregated as the sum of all borrowed positions with the maximum 10-day interest rate.

Margin & Portfolio Valuation

The risk-based valuation of the portfolio is:

$$\text{Risk Based Valuation} = \text{Adjusted Bal(BaseToken)} + \sum_{\text{Non-base tokens}} \text{Token Value}$$

Token Value

For each non-base token:

$$\text{tokenValue} = \min(\text{tokenValue}_{high}, \text{tokenValue}_{low})$$

where:

$$\text{tokenValue}_{high} = \text{adjustedBal(token)} \times \text{adjustedTokenPrice}_{high} + \text{aggregatePerpValue}_{high}$$

$$\text{tokenValue}_{low} = \text{adjustedBal(token)} \times \text{adjustedTokenPrice}_{low} + \text{aggregatePerpValue}_{low}$$

Adjusted Token Prices

The adjusted token prices are computed as:

$$\text{adjustedTokenPrice}_{high} = \text{price}_{mark} \times \Big(1 + \text{riskPrice} - \text{riskSlippage} \times \text{sign}(\text{adjustedBal(token)})\Big)$$

$$\text{adjustedTokenPrice}_{low} = \text{price}_{mark} \times \Big(1 - \text{riskPrice} - \text{riskSlippage} \times \text{sign}(\text{adjustedBal(token)})\Big)$$

Adjusted Perp Values

For perpetual positions, we compute high and low valuations:

$$\text{aggregatePerpValue}_{high} = \sum_{\text{perp positions}} \text{perpValue}(\text{markPrice} \times (1 + \text{riskPrice}))$$

$$\text{aggregatePerpValue}_{low} = \sum_{\text{perp positions}} \text{perpValue}(\text{markPrice} \times (1 - \text{riskPrice}))$$

Perpetual Position Valuation

The perp value at a given price is:

$$\text{Perp Value(price)} = \text{PNL from price movement + Funding Fees at that price}$$

SDKs & Optimization

ATLAS Math: Risk Based Valuation have the above formulas built in, so you can test and simulate margin requirements for different position sets.