Abstract

Classical models in mathematical finance, even if highly complex, typically share important methodological weaknesses: failure to account for model uncertainty and failure to incorporate market information in a consistent manner. In the wake of financial crisis these have been much debated.

In response, an increasingly active field of research focuses on model-free super/sub-hedging using the underlying and Vanilla options. Explicit results often rely on pathwise inequalities and embedding techniques while pricing-hedging duality is obtained using martingale optimal transport methods. However, the resulting prices and hedges are often too expensive to be practically relevant.

In this talk I show how to interpolate between the two worlds. I argue that quoted option prices should be incorporated through distributional constraints while beliefs, or past data, are most naturally included through pathwise restrictions. The resulting framework is robust and flexible. It allows for realistic outputs while quantifying the impact of making assumptions. I will present abstract results about pricing-hedging duality and then discuss examples of restrictions on future realised volatility and future option prices.

Based on joint works with Sergey Nadtochiy (University of Michigan) and Zhaoxu Hou and Peter Spoida (University of Oxford).