Discretisation-Invariant Swaps

Extensive research illustrates the jump and discretisation errors that affect the valu-ation of standard swap contracts. We introduce a vector space of price and return characteristics that allow to define swaps which 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. A historical analysis based on 16 years of S&P500 data demonstrates the diversity of the risk exposures attainable through trading these swaps, as well as floating-floating swaps that trade differential risk premiums and maturities