# Premiums / Rebates

Premiums and rebates reflect changes in the exchange's liabilities

## Indifferent Pricing

For each new trade, the AMM charges premium or provides rebate such that the risk level after accepting the trade is kept at the same level as before. In particular, we define premium / rebate $\pi$ as

where $X_{t+\tau}$($X'_{t+\tau'}$) is the liability before (after) accepting the trade, and $\rho$ is EVaR of each liability. Note that $\pi > 0$ implies that the trader pays premium, whereas $\pi < 0$ implies that the trader receives rebate.

For example, consider the state where the market is long-heavy (or the AMM has a net short exposure). For any additional long order, the AMM charges premium since $\rho(X_{t+\tau'}') > \rho(X_{t+\tau})$. If any trader opens a short position to decrease the long-short imbalance, they will receive rebate.

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