Temporal’s vAMM creates a real-time, continuous yield curve enabling custom duration YT / PT positions while cumulating liquidity into a single pool per asset.

1. Pricing

Temporal’s vAMM introduces a ‘notional interest’ (NI) variable, so that yield at any given duration (d) is priced in terms ofon a constant product basis:

PTd×NId=kPT_d ×NI_d = k

Trades change the balances of PT and NI, and consequently, the yield. This concentrates liquidity around the bootstrapped yield range.

YT is priced by the same vAMM pool as per the formula:


Cumulative PT and NI values with durations d are used to compute yield at ‘d’. This cumulation prevents liquidity fragmentation across durations.

Impact of a trade of duration ‘d’ is spread over the curve with durations d. This optimizes yield-curve behavior limiting arbitrage opportunities over the curve.

2. Liquidity Provision

LPs provide liquidity to a single pool for a given asset; for example, LPs deposit stAtom into a single pool which transacts YT, PT and stAtom

Liquidity serves any duration of YT / PT trade between min and max durations for the given pool

LPs can exit at any time without being locked

3. Minimal Impermanent Loss

Temporal’s vAMM design makes Impermanent Loss (IL) a negligible concern by shifting the AMM curve to push PT price towards its underlying value as time passes. Mitigating time-dependent IL.

Additionally, IL from swaps is mitigated as well, since both the LP’d assets are very highly correlated (e.g. PT-stAsset / stAsset). If liquidity is provided until maturity, the LP’s position is equivalent to that of holding the underlying asset. This is because as the maturity date nears, PT appreciates towards the underlying asset.

IV. AMM Features

  • Capital Efficiency – single pool, no liquidity fragmentation across durations.

  • Custom Durations – choose any duration for YT / PT with daily maturities.

  • Concentrated Liquidity – liquidity consolidated into rough yield ranges to boost capital efficiency.

  • Low IL – price automatically converges to the underlying asset over time.

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