Abstract

The price of derivatives (and hence of structured products) can be calculated as the discounted value of expected future payoffs, assuming standard hypotheses on frictionless and complete markets and on the type of stochastic processes for the price of the underlying. However, the probabilities used in the pricing process do not represent "real" probabilities of future events, because they are based on the assumption that market participants are risk-neutral. This paper reviews the relevant mathematical finance literature, and clarifies that the risk-neutrality hypothesis is acceptable for pricing, but not to forecast the future value of an asset. Therefore, we argue that regulatory initiatives that mandate intermediaries to give retail investors information on the probability that, at a future date, the value of a derivative will be higher or lower than a given threshold (so-called "probability scenarios") should explicitly reference probabilities that take into account the risk premium (so-called "real-world" probabilities). We also argue that, though probability scenarios may look appealing to foster investor protection, their practical implementation, if based on the right economic approach, raises significant regulatory and enforcement problems.

Any errors or omissions are the responsibility of the authors. We thank Carlos Alves, Andrea Beltratti, Giuseppe Corvino, Francesco Corielli, Steffen Kern, Victor Mendes and Roberto Renò for very useful comments, though the responsibility for any mistakes and for the opinions expressed remains our own. The ideas and positions in the paper are personal views of the authors and cannot be attributable to Consob.
This version of the paper has been published as ESMA Working Paper No. 1, 2015.