Risk, Return, and Ross Recovery

Abstract

Carr was asked to share his thoughts on the current state of derivatives theory and practice. His response was to write a discussion and extension of one of the most provocative and potentially important new ideas in the field: Ross’s recent paper on extracting both the risk-neutral density and the empirical density from a set of market option prices. This feat has long been regarded as impossible, so demonstrating that it is not is a major achievement. Carr and Yu detail how the proof is done and then present an alternative route to the same result, but starting from what may be considered a more tractable assumption that a numeraire portfolio exists.