Ornstein–Uhlenbeck processes time changed with additive subordinators and their applications in commodity derivative models

We characterize Ornstein–Uhlenbeck processes time changed with additive subordinators as time-inhomogeneous Markov semimartingales, based on which a new class of commodity derivative models is developed. Our models are tractable for pricing European, Bermudan and American futures options. Calibration examples show that they can be better alternatives than those developed in Li and Linetsky (2012)  [6]. Our method can be applied to many other processes popular in various areas besides finance to develop time-inhomogeneous Markov processes with desirable features and tractability.