functions in closed-form, which help with pricing and risk measure calculations. In a numerical example, we demonstrate the … implied volatility surface (up to 100%) and on two risk measures: value at risk and expected shortfall where an increase of up …

The forward-looking nature of option market data allows one to derive economically-based and model-free risk measures … classical risk measures for the S&P500 Index. Delivering good results both at short and long time horizons, the proposed option …-implied risk metrics emerge as a convenient alternative to the existing risk measures …

measures of risk. Furthermore, Qα(X ; p) is the optimal value in a certain minimization problem, the minimizers in which are … problems. In finance, Q0(X;p) and Q1(X ; p) are known as the value at risk (VaR) and the conditional value at risk (CVaR). The … sensitivity to risk. The problems of the effective computation of the bounds are considered. Various other related results are …

The computation of various risk metrics is essential to the quantitative risk management of variable annuity guaranteed … produce closed-form approximation of the risk measures for variable annuity guaranteed benefits. The techniques are further … developed in this paper to address in a systematic way risk measures for death benefits with the consideration of dynamic …

We investigate how the spectral risk measure associated with holding stocks rather than a risk-free deposit, depends on … the holding period. Previous papers have shown that within a limited class of spectral risk measures, and when the stock … price follows specific processes, spectral risk becomes negative at long periods. We generalize this result for arbitrary …

results for maturity-randomized first-passage probabilities and allows for a derivation of diffusion and single jump risk …The present article deals with intra-horizon risk in models with jumps. Our general understanding of intra-horizon risk … quantifying market risk by strictly relying on point-in-time measures cannot be deemed a satisfactory approach in general. Instead …

for market risk. The Committee has focused, among other things, on the two key areas of moving from Value-at-Risk (VaR) to … Expected Shortfall (ES) and considering a comprehensive incorporation of the risk of market illiquidity by extending the risk … measurement horizon. The estimation of the ES for several trading desks and taking into account different liquidity horizons is …

-VaR, as objective measures of downside risk for financial prospects. We establish the connections of the VaRs with the first … alternative risk measures that are associated with the weaker behaviour assumptions underlying the VaRs …