that arrive from outside the system. The combination of risk-sensitive behavior rules and the coordinated actions implied … Gaussian. We illustrate such endogenous extreme events through the pricing density resulting from dynamic hedging of options … and the flash crash of May 2010 …

We provide ready-to-use formulas for European options prices, risk sensitivities, and P&L calculations under Lévy …

risks. Portfolios hedging macro uncertainty have historically earned zero or even significantly positive returns, while … a simple extension of the long-run risk model …