Implications of Parameter Uncertainty on Option Prices

Financial markets are complex processes where investors interact to set prices. We present a framework for option valuation under imperfect information, taking risk neutral parameter uncertainty into account. The framework is a direct generalization of the existing valuation methodology. Many investors base their decisions on mathematical models that have been calibrated to market prices. We argue that the calibration process introduces a source of uncertainty that needs to be taken into account. The models and parameters used may differ to such extent that one investor may find an option underpriced; whereas another investor may find the very same option overpriced. This problem is not taken into account by any of the standard models. The paper is concluded by presenting simulations and an empirical study on FX options, where we demonstrate improved predictive performance in sample and out of sample using this framework.