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A joint affine model of commodity futures and US Treasury yields


  • Chin, Michael

    () (Bank of England)

  • Liu, Zhuoshi

    () (Bank of England)


We derive a general joint affine term structure model of US government bond yields and the convenience yields on physical commodities. We apply this framework separately to oil and gold. Our results show clear links between bond and commodity markets, since bond factors play a significant role in the pricing of the convenience yield term structure. Our framework allows us to decompose the term structure of futures prices into expectations of future spot prices and risk premia components. We estimate that the risk premium in oil futures has been negative over the 1980s and 1990s, and turned positive in the mid-2000s, consistent with a declining role for supply shocks in the oil market over this period. In contrast, we estimate that the gold risk premium is mostly positive throughout the sample period.

Suggested Citation

  • Chin, Michael & Liu, Zhuoshi, 2015. "A joint affine model of commodity futures and US Treasury yields," Bank of England working papers 526, Bank of England.
  • Handle: RePEc:boe:boeewp:0526

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    Cited by:

    1. Constantino Hevia & Ivan Petrella & Martin Sola, 2018. "Risk premia and seasonality in commodity futures," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(6), pages 853-873, September.

    More about this item


    Commodity futures; gold; oil; risk premium; convenience yields; affine term structure model; Treasury yields;

    JEL classification:

    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • Q02 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - General - - - Commodity Market
    • Q40 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy - - - General

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