Calibration of One- and Two-Factor Models For Valuation of Energy Multi-Asset Derivative Contracts

We study historical calibration of one- and two-factor models that are known to describe relatively well the dynamics of energy underlyings such as spot and index natural gas or oil prices at different physical locations or regional power prices. We take into account uneven frequency of data due to weekends, holidays, and possible missing data. We study the case when several one- and two-factor models are used in the joint model with correlated model factors and present examples of joint calibration for daily natural gas prices at several locations in the US and for regional hourly power prices.