Volatility and Correlation of Traded Forward Contracts

[cmdty]

The documentation, and implementation in MultiFactorModel, only derive the integrated covariance of (log of) forwards at a uniform granularity, which will generally be the highest possible granularity of traded contracts assumed by the model, and the granularity at which physical storage nomination occurs. For example for natural gas, when valuing storage with day-ahead nomination, the granularity will be daily. However, for calibration and simulation purposes it would be useful to approximate the covariances for contracts at the actual traded granularity, e.g. monthly, quarter, seasonal and yearly.

One approach would be to use moment-matching, i.e. find the parameters of a single GBM (Geometric Brownian Motion) which matches the moments of a basket of GBMs.

For 1 and 2 factor models, something like Jamshidian Trick could be used to calculate the PV of options, which in turn could be used to back out the implied volatility of the traded contract which are implied by a specific set of model parameters.