Model-Free Discretisation-Invariant Swaps and S&P 500 Higher-Moment Risk Premia

We derive a general multivariate theory for realised characteristics of `model-free discretisation-invariant swaps', so-called because the standard no-arbitrage assumption of martingale forward prices is sufficient to derive fair-value swap rates for such characteristics which have no jump or discretisation errors. This theory underpins specific examples for swaps based on higher moments of a single log return distribution where exact replication is possible via option-implied `fundamental contracts' like the log contact. The common factors determining the S&P 500 risk premia associated with these higher-moment characteristics are investigated empirically at the daily, weekly and monthly frequencies.