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Multi-factor models and the risk premiums: a simulation study

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Abstract

The estimation of commodity spot price models often involves the estimation of risk premiums. We show in a simulation study that the market prices of risk cannot be accurately estimated using two popular estimation techniques; the Kalman filter and an iterative routine. Risk premium parameters may be dependent on the starting value for the iterative routine, and cannot be accurately estimated using the Kalman filter technique. We conclude with a short analysis of results from the spot price model literature by examining the implied volatility term structure from other published research papers.

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Notes

  1. \(\xi \) is initialized with an arbitrarily chosen value of 3. The initial value of the state variables do not influence the estimation of the model parameters.

  2. While the price of financial assets usually are observed without measurement error, the model can be slightly misspecified, giving rise to an error term. Regardless of the economical interpretation of the error term, the variance of the innovation in this experiment is given such a low value that it does not affect the estimated model parameters. We set \(\sigma _f = 0.001\).

  3. To better isolate the problems that occur in the estimation of the risk premium parameters the initial configuration of the model parameters is fixed at their true value.

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Authors and Affiliations

  1. Department of Industrial Economics and Technology Management, Norwegian University of Science and Technology, 7491 , Trondheim, Norway

    Arne Andresen & Johan M. Sollie

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  1. Arne Andresen
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  2. Johan M. Sollie
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Correspondence to Johan M. Sollie.

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Andresen, A., Sollie, J.M. Multi-factor models and the risk premiums: a simulation study. Energy Syst 4, 301–314 (2013). https://doi.org/10.1007/s12667-013-0080-6

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