Time-changed Ornstein-Uhlenbeck processes and their applications in commodity derivative models

Lingfei Li*, Vadim Linetsky

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

40 Scopus citations

Abstract

This paper studies subordinate Ornstein-Uhlenbeck (OU) processes, i.e., OU diffusions time changed by Lévy subordinators. We construct their sample path decomposition, show that they possess mean-reverting jumps, study their equivalent measure transformations, and the spectral representation of their transition semigroups in terms of Hermite expansions. As an application, we propose a new class of commodity models with mean-reverting jumps based on subordinate OU processes. Further time changing by the integral of a Cox-Ingersoll-Ross process plus a deterministic function of time, we induce stochastic volatility and time inhomogeneity, such as seasonality, in the models. We obtain analytical solutions for commodity futures options in terms of Hermite expansions. The models are consistent with the initial futures curve, exhibit Samuelson's maturity effect, and are flexible enough to capture a variety of implied volatility smile patterns observed in commodities futures options.

Original languageEnglish (US)
Pages (from-to)289-330
Number of pages42
JournalMathematical Finance
Volume24
Issue number2
DOIs
StatePublished - Apr 2014

Keywords

  • Bochner subordination
  • Commodity derivatives
  • Commodity futures
  • Commodity options
  • Energy derivatives
  • Jumps
  • Mean reversion
  • Ornstein-Uhlenbeck
  • Stochastic volatility
  • Time change

ASJC Scopus subject areas

  • Accounting
  • Finance
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Applied Mathematics

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