Implications of parameter uncertainty on option prices

Abstract:
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 under-priced whereas another investor may find the very same option

over-priced. 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.