Carr and Wu's (2020) framework in the oil ETF option market

Xiaolan Jia, Edwin Ruan*, Jin E. Zhang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


This paper studies the information inferred from the Carr and Wu's (2020) formula based on a new option pricing framework in the United States Oil Fund (USO) options. We first document the term structure and dynamics of the risk-neutral variance and covariance rates which lead to a "U"-shaped implied volatility smile with a positive curvature. We then investigate the return predictability of the innovations in the risk-neutral variance and covariance rates (DRNV and DRNC) and their term structures (TRNV and TRNC) and find that DRNC is a significant and robust predictor to forecast daily, weekly and monthly USO excess returns in both statistical and economic terms based on in-sample and out-of-sample tests.
Original languageEnglish
Article number100334
JournalJournal of Commodity Markets
Publication statusPublished - Sept 2023


  • Crude oil
  • Risk-neutral covariance
  • Implied volatility smile
  • Return predictability
  • Option pricing


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