This paper introduces a model-free decomposition of S&P 500 forward market index returns in terms of realized and implied dispersion, downside, and tail risk using option portfolios. The decomposition lends itself by construction to learn about the different sources of risk in the market return,...

We study optimal execution with "self-exciting" price impact, where persistent trades not only incur price impact but also increase the execution costs for successive orders. This model is motivated by an equilibrium between fundamental sellers, market makers, and end users. For risk-neutral...