Assessment and Propagation of Input Uncertainty in Tree-based Option Pricing Models

Abstract: This paper aims to provide a practical example on the 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 provide three alternative frameworks to calibrate option pricing tree models, propagating parameter uncertainty into the resulting option prices. We finally compare our methods with classical calibration-based results assuming that there is no options market established. These methods can be applied to pricing of instruments for which there is not an options market, as well as a methodological tool to account for parameter and model uncertainty in theoretical option pricing.