Despite the use of VaR as a means to control risk, using VaR can have the opposite effect. VaR is used by bank and insurance regulators more than any other risk measure. A value-at-risk (VaR) constraint on the probability that future firm equity value will be less than a floor, when the floor is...

This paper provides implied measures of higher-order dependencies between assets. The measures exploit only forward-looking information from the options market and can be used to construct an implied estimator of the covariance, co-skewness, and co-kurtosis matrices of asset returns. We...

We study whether prices of traded options contain information about future extreme market events. Our option-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...

This paper provides implied measures of higher-order dependencies between assets. These measures exploit only forward-looking information from the options market and can be used to construct an implied estimator of the full covariance, co-skewness, and co-kurtosis matrices of asset returns. In...

We present an easily implemented, fast, and accurate method for approximating extreme quantiles of compound loss distributions (frequency and severity) as are commonly used in insurance and operational risk capital models. The Interpolated Single Loss Approximation (ISLA) of Opdyke (2014) is...

We solve a moment problem to compute the best upper and lower bounds on the expected value E[φ(X)], subject to constraints E[X^i] = μ_i for i = 1, 2,...,n. By setting φ(x)=I_(-\inf,t], the indicator function for the event X ≤ t, we calculate the bounds on Pr(X ≤ t) = E[I_(-\inf,t]]. The...

The paper discusses how to assess risk by computing the best upper and lower bounds on the expected value E[φ(X)], subject to the constraints E[Xⁱ] = µ_i for i = 0, 1, 2, . . . , n. φ(x) can take the form of the indicator function φ(x) = 𝕀_(−∞,K](x) in which the bounds on Pr(X ≤ K)...

Stop-loss and limited loss random variables are two important transforms of a loss random variable and appear in many modelling problems in insurance, finance, and other fields. Risk levels of a loss variable and its transforms are often measured by risk measures. When only partial information...

In this paper, we investigate dependent risk models in which the dependence structure is defined by an Archimedean copula. Using such a structure with specific marginals, we derive explicit expressions for the pdf of the aggregated risk and other related quantities. The common mixture...

The literature proposes several alternatives for estimating compound distributions, which are widely used for risk quantification in the banking and insurance industries. In this paper, we evaluate the accuracy and time-efficiency of different approaches for estimating quantiles of compound...