-implied conditional expectation of market loss due to tail events, or tail loss measure, predicts future market returns, magnitude, and … probability of the market crashes, beyond and above other option-implied variables. Stock-specific tail loss measure predicts … cares about the left tail of her wealth distribution benefits from using the tail loss measure as an information variable to …

before. We show, for the one-dimensional case, the equivalence of the set correlation functions and the extremal coefficient …

Shortfall (ES), take into account both the frequency and the severity of losses. Under VaR a single confidence level is assigned … regardless of the size of potential losses. We allow for a range of confidence levels that depend on the loss magnitude. The key … ingredient is a benchmark loss distribution (BLD), i.e.~a function that associates to each potential loss a maximal acceptable …