Constant Function Market Makers
Reserve functions, marginal price and payoff-specific construction.
#Reserves and trading functions
A CFMM admits trades that keep a reserve function at or above a specified level. In equality form, trades move reserves along an invariant surface.
ψ(x, y) = kp_pool = (∂ψ/∂x) / (∂ψ/∂y)#Generic and payoff-specific
| CFMM | Starting point | LP exposure |
|---|---|---|
| Constant product | x × y = k | Derived from the constant-product curve |
| Constant mean | Weighted reserve product | Determined by weights and rebalancing |
| RMM | Target payoff V | Recovered to match or approximate V in its domain |
#Value after arbitrage
V(c) = inf { cᵀR : ψ(R) ≥ k }External prices c value feasible reserves R. Arbitrage moves the pool toward the reserve state that minimizes value at those prices, producing the LP value function.
- Replicating Market Makers
Angeris, Evans and Chitra's primary paper on constructing CFMM trading functions from target payoff functions.