Forward rate & volatility

The fixed rate is priced against a forward-looking estimate of the floating rate, not today's spot rate — and that estimate behaves differently depending on how full the pool is.

Forward floating rate F(T)

Below the kink, the forward rate is simply the smoothed moving average of recent floating rates. Above it, the model expects a spike and mean-reverts the forecast toward a long-run spike rate.

z = κ·T
damping = (1 − e^−z) / z
F(T) = θ + (r_sma − θ) × damping

below U_kink: κ=0 → F=r_smaabove U_kink: mean-reverts to θ_spikeAaveV3Adapter.sol:252

Volatility σ

Sample standard deviation of the recent floating-rate history, annualised.

σ = stdev(rate_history, n−1) × sqrt(365)

rate history ring buffer√365 annualisationPricing.sol:133

Regime boundary parameters

U_kink — utilisation that flips the spike regime: 0.90κ_spike — mean-reversion speed: 40 / yrθ_spike — long-run spike rate: 9.0%r_floor — hard floor on the forward rate: 0.10%