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Covered-Call RMM

A trading function shaped around covered-call value.

#Target payoff

A covered call rises with the underlying below strike and flattens above strike. Its concave, nondecreasing terminal shape motivates the RMM construction.

V_T(S_T) = min(S_T, K) + P
Covered-call payoff compared with long stockLong stock rises continuously. The covered-call line rises until the strike, then stays flat.Stock price at expiry (S_T)Position valueStrike KLong stockCovered callCapped region
Illustrative terminal geometry. Premium shifts the covered-call line upward; fees are excluded.

#Inverse construction

The RMM inverse problem seeks a reserve set whose minimum external-market value equals the target payoff.

Simplified research notation
ψ_V(R) = inf_c [cᵀR − V(c)]

RMM-01 uses Black-Scholes structure and time-dependent parameters so arbitrage-driven reserve changes approximate a covered-call replicating portfolio as expiry approaches.

#Replication error

  • Blocks and trades are discrete.
  • Arbitrage can arrive late or face limited capital.
  • Fees widen the no-arbitrage band.
  • Realized volatility can diverge from the model input.
  • Rounding and terminal handling leave residual error.
  1. Replicating Market Makers

    Angeris, Evans and Chitra's primary paper on constructing CFMM trading functions from target payoff functions.

  2. Replicating Portfolios: Constructing Permissionless Derivatives

    Primitive research describing RMM-01 and onchain structured-product constructions.

  3. Primitive rmms-py

    Open-source Python simulation toolkit for covered-call RMM behavior, arbitrage and fee experiments.

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