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Assessment and propagation of input uncertainty in tree‐based option pricing models

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  • Henryk Gzyl
  • German Molina
  • Enrique ter Horst

Abstract

This paper aims to provide a practical example of assessment and propagation of input uncertainty for option pricing when using tree‐based methods. Input uncertainty is propagated into output uncertainty, reflecting that option prices are as unknown as the inputs they are based on. Option pricing formulas are tools whose validity is conditional not only on how close the model represents reality, but also on the quality of the inputs they use, and those inputs are usually not observable. We show three different approaches to integrating out the model nuisance parameters and show how this translates into model uncertainty in the tree model space for the theoretical option prices. We compare our method with classical calibration‐based results assuming that there is no options market established and no statistical model linking inputs and outputs. These methods can be applied to pricing of instruments for which there is no options market, as well as a methodological tool to account for parameter and model uncertainty in theoretical option pricing. Copyright © 2008 John Wiley & Sons, Ltd.

Suggested Citation

  • Henryk Gzyl & German Molina & Enrique ter Horst, 2009. "Assessment and propagation of input uncertainty in tree‐based option pricing models," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(3), pages 275-308, May.
    • Handle: RePEc:wly:apsmbi:v:25:y:2009:i:3:p:275-308
    DOI: 10.1002/asmb.736
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