Before revision: The realised characteristics for Discretisation-Invariant (DI) swaps satisfy the aggregation propertywhen restricted to multivariate processes that are ]  deterministic functions of martingales. Hence DI swaps have model-free fair values, in that a no-arbitrage assumption for forward prices is sufficient to derive exact option replication portfolios with neither jump nor discrete monitoring errors.
After revision: The realised characteristics for Discretisation-Invariant (DI) swaps satisfy the aggregation propertywhen restricted to multivariate processes that are ] deterministic functions of a multivariate martingale. They are initially characterised as solutions to a second-order system of PDEs, then those pay-offs based on martingale and log-martingale processes alone form a vector space. Hence there exist an infinite variety of other variance and higher-moment risk premia that are less prone to bias than standard variance swaps because their option replication portfolios with neither jump nor discrete monitoring errors.