Before revision: Extensive research illustrates the jump and discretisation errors that affect the valuation of standard swap contracts. We introduce a vector space of price and return characteristics that allow to define swapswhich can be valued exactly, assuming only that the market is free of arbitrage. Although fair-value swap rates are independent of monitoring frequency, the associated risk premiums are not.
After revision: 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 are independent of monitoring frequency, the associated risk premiums are not.