# Synthetic AMM

**The AMM allows traders to buy & sell Impermanent Gain Options before maturity.**

The AMM is called "*Synthetic"* because it uses the liquidity of the Earn Vaultâ€”no AMM-specific liquidity is needed.

It ensures traders can trade without any negative impact on either the protocol balance or the Earn Vault payoff.

The AMM achieves it by:

determining the

**correct price to trade**Impermanent Gain Options.correctly rebalancing Earn Vault liquidity every time a trade happens (Delta Hedging).

## Pricing

You can find an in-depth description of the pricing formulas here.

## Bonding Curve

A bonding curve is a mathematical function that links the price of an asset to its supply.

Smilee Synthetic AMM enables trading volatility-based products, whose price is itself a function of volatility. Therefore, Smilee Bonding Curve can be easily defined as a function that adjusts the implied volatility used to price such volatility-products when their supply changes.

To capture change in supply, Smilee uses the utilization rate of Impermanent Gain options weighted by its vega (i.e., the measurement of an option price sensitivity to changes in implied volatility) and adjusted it over time through a time decay parameter.

As a result, when utilization rate grows (i.e., traders are buying), option prices grow, because the Synthetic AMM uses an higher implied volatility and, conversely, when utilization decreases (i.e., traders are selling) prices decrease. Moreover, if utilization rate remains stable, implied volatility decays over time making options more attractive for buyers.

You can find an in-depth description of the Smilee Bonding Curve here.

The Synthetic AMM is just a conceptual component implemented at the smart contract level within the mathematics of Vaults.

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