  The robust option pricing problem is to find upper and lower bounds on fair
prices of financial claims using only the most minimal assumptions. It
contrasts with the classical, model-based approach and gained prominence in the
wake of the 2008 financial crisis, and can be used to understand the extent to
which a model-based price is sensitive to the underlying model assumptions.
Common approaches involve pricing exotic derivatives such as variance options
by incorporating market data through implied volatility. The existing
literature focuses largely on incorporating implied volatility information
corresponding to the maturity of the exotic option. In this paper, we aim to
explain how intermediate data can and should be incorporated. It is natural to
expect that this additional information will improve the robust pricing bounds.
To investigate this question, we consider variance options, where the bounds of
the informed robust pricing problem are known. We proceed to conduct an
empirical study uncovering a surprising finding: Contrary to common belief, the
incorporation of more information does not lead to an improvement of the robust
pricing bounds.
