Mean reversion of stochastic convenience yields for CO2 emissions allowances: Empirical evidence from the EU ETS

Convenience Yields and Risk Premiums in the EU‐ETS—Evidence from the Kyoto Commitment Period

“…So far, less attention has been directed toward the relationship between EUA spot and futures prices, convenience yields, and deviations from the cost‐of‐carry relation in the EU‐ETS. Exceptions include the studies by Chang et al (); Chevallier (); Gorenflo (); Madaleno and Pinho (); Milunovich and Joyeux (); Trück et al (); Uhrig‐Homburg and Wagner () that are highly related to the work conducted in this paper. In the following, we will briefly review the findings and some of the limitations of these studies.…”

“…More recently, Gorenflo () suggests that the cost‐of‐carry hypothesis between spot and futures prices holds for the trial period, while for the Kyoto commitment period there are deviations from the cost‐of‐carry relationship. Chang et al (), based on the cost‐of‐carry model, examine the properties of convenience yields for emissions allowances futures contracts with maturities from December 2010 to December 2014. The authors suggest that convenience yields for emissions allowances exhibit a time‐varying trend, are mean‐reverting, while the standard deviation in the convenience yield declines with an increase in time‐to‐maturity.…”

“…The authors suggest that convenience yields for emissions allowances exhibit a time‐varying trend, are mean‐reverting, while the standard deviation in the convenience yield declines with an increase in time‐to‐maturity. Note that unlike Chang et al (), Gorenflo (), and Madaleno and Pinho (), where an assumption about a constant average risk‐free rate is made, in our analysis we use the actually observed daily risk‐free rates for each maturity to obtain more precise estimates of the convenience yield. Finally, Trück et al () investigate the relationship between spot and futures prices within the EU‐ETS during the pilot trading and first Kyoto commitment period.…”

“…Gorenflo () suggests that the cost‐of‐carry hypothesis between spot and futures prices holds for the trial period, whereas for the Kyoto commitment period there are deviations from the cost‐of‐carry relationship. Chang et al () suggest that convenience yields for Phases II and III futures contracts exhibit a time‐varying trend, are mean‐reverting, while the standard deviation in the convenience yield declines with an increase in time‐to‐maturity. Most recently, Trück et al (), analyzing the behavior of spot and futures contracts, find that during Phase II the market has changed from initial backwardation to contango with significant negative convenience yields.…”

“…To the best of our knowledge, we provide the first study to consider the relationship between carbon emission spot and futures prices for the entire first Kyoto commitment period from 2008 to 2012. Also, unlike previous studies by Chang et al (), Gorenflo (), and Madaleno and Pinho (), where an assumption about a constant average risk‐free rate is made, we use actually observed daily risk‐free rates for each maturity of the futures contracts to determine a more precise estimate of the convenience yield. We are also the first to thoroughly examine the impact of key factors such as interest rate levels, surplus allowances, and factors related to the dynamics of EUA spot prices on convenience yields and risk premiums in the EU‐ETS.…”