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Modelling conversion options with a mean reversion motion

Author

Listed:
  • Carlos L. Bastian-Pinto

    (PUC-Rio, IAG)

  • Luiz E. T. Brandão

    (PUC-Rio, IAG)

Abstract

Commodity prices are generally better modeled by a long-term Mean Reverting Process, than by a Geometric Brownian Motion stochastic diffusion process, which is more generally used to value real options, since it is simpler to use. In this article we model two correlated uncertain variables using a mean reversing process bivariate lattice to value the switch option between outputs available to ethanol and sugar producers, using the same source: sugarcane. The model results show that the switch option adds a signi cant value for the producer income. The article also shows that when modeled by a geometric brownian motion, the switch option yields significantly higher values than with a mean reverting model, for the option itself as much as for the base case without flexibility. This confirms that the stochastic model chosen can influence significantly the option value.

Suggested Citation

  • Carlos L. Bastian-Pinto & Luiz E. T. Brandão, 2007. "Modelling conversion options with a mean reversion motion," Brazilian Review of Finance, Brazilian Society of Finance, vol. 5(2), pages 97-124.
    • Handle: RePEc:brf:journl:v:5:y:2007:i:2:p:97-124
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    More about this item

    Keywords

    real options; mean reverting model; switch options; commodity prices;
    All these keywords.

    JEL classification:

    • C34 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Truncated and Censored Models; Switching Regression Models
    • M21 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics - - - Business Economics
    • Q42 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy - - - Alternative Energy Sources

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