Shortfall deviation risk: an alternative for risk measurement

Expected Shortfall: a natural coherent alternative to Value at Risk

We discuss the coherence properties of Expected Shortfall (ES) as a financial risk measure. This statistic arises in a natural way from the estimation of the “average of the 100p% worst losses” in a sample of returns to a portfolio. Here p is some fixed confidence level. We also compare several alternative representations of ES which turn out to be more appropriate for certain purposes.

Expected Shortfall: a natural coherent alternative to Value at Risk

Shortfall risk measure for general semimartingales

In this talk, we focus on a convex risk measure which is induced by the shortfall risk, which is defined as the weighted expectation by some loss function of the positive part of the difference between a claim and a portfolio value at the maturity of our market. The convex risk measure concerned in this talk expresses the least cost to suppress its shortfall risk below the threshold being deter...

Binomial Approximations of Shortfall Risk for Game

We show that the shortfall risk of binomial approximations of game (Israeli) options converges to the shortfall risk in the corresponding Black–Scholes market considering Lipschitz continuous path dependent payoffs for both discrete and continuous time cases. This results are new also for usual American style options. The paper continues and extends the study of [6] where estimates for binomial...

Backtesting Expected Shortfall: Accounting for Tail Risk

The Basel Committee on Banking Supervision (BIS) has recently sanctioned Expected Shortfall (ES) as the market risk measure to be used for banking regulatory purposes, replacing the well-known Value-at-Risk (V aR). This change is motivated by the appealing theoretical properties of ES as a measure of risk and the poor ones of V aR. In particular, V aR fails to control for “tail risk”. In this t...