AMM TWAP with Price Floor Protection

This approach combines AMM TWAP pricing with a protective price floor. The floor can be implemented in two ways:

• ZCB Floor: Sets a lower bound using the ZCB model with a relatively high APY.

• Linear Discount Floor: Leveraging linear discount's tendency to underprice the market value.

This approach allows protocols to choose between stronger price protection (linear) or better market alignment (ZCB) while maintaining TWAP's market responsiveness. The price at time $t$is given by:

With Linear Discount Floor:

$$P_t=Max( \frac{\sum P_t \times \Delta t}{\sum \Delta t},1 - d \times \frac{T - t}{T})$$

With ZCB Floor:

$P_t=Max( \frac{\sum P_t \times \Delta t}{\sum \Delta t},\frac{1}{(1 + r)^T})$

where $P$_t is the AMM-observed spot price over each sampling interval, $Δt$ is the elapsed time of that interval, and the sums run over all samples in the averaging window ending at $t$. In the linear floor, $T$ denotes the total term (so $T$ - $t$ is the time remaining) and in the ZCB floor, $T$ denotes the time to maturity (years).

This design leverages the natural tendency of deterministic models to underprice PTs, creating a protective lower bound that ensures stability. Meanwhile, when market conditions are favorable and trading prices exceed this floor, the TWAP component allows the PT to track higher market prices, enabling better capital efficiency. This balance helps protect against downside risk while maintaining upside potential.