Robust option pricing with volatility term structure -- An empirical study for variance options

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.