This paper introduces a novel method for pricing commodity index derivatives consistently with market prices of derivatives on single commodities. We discuss the Black, mean-reversion and local volatility pricing models with special attention paid to the parameterization of volatility surfaces....

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...