Using option market data we derive naturally forward-looking, nonparametric and model-free risk estimates, three desired characteristics hardly obtainable using historical returns. The option-implied measures are only based on the first derivative of the option price with respect to the strike...

We discuss risk measures representing the minimum amount of capital a financial institution needs to raise and invest in a pre-specified eligible asset to ensure it is adequately capitalized. Most of the literature has focused on cash-additive risk measures, for which the eligible asset is a...

We study capital requirements for bounded financial positions defined as the minimum amount of capital to invest in a chosen eligible asset targeting a pre-specified acceptability test. We allow for general acceptance sets and general eligible assets, including defaultable bonds. Since the...

This paper provides a coherent method for scenario aggregation addressing model uncertainty. It is based on divergence minimization from a reference probability measure subject to scenario constraints. An example from regulatory practice motivates the definition of five fundamental criteria that...

We address the problem of risk sharing among agents using a two-parameter class of quantile-based risk measures, the so-called Range-Value-at-Risk (RVaR), as their preferences. The family of RVaR includes the Value-at-Risk (VaR) and the Expected Shortfall (ES), the two popular and competing...

The recursive prediction and filtering formulas of the Kalman filter are difficult to implement in nonlinear state space models. For Gaussian linear state space models, or for models with qualitative state variables, the recursive formulas of the filter require the updating of a finite number of...

We consider dynamic sublinear expectations (i.e., time-consistent coherent risk measures) whose scenario sets consist of singular measures corresponding to a general form of volatility uncertainty. We derive a càdlàg nonlinear martingale which is also the value process of a superhedging...

A major obstacle for research in international asset pricing and corporate finance has been a lack of reliable and publicly available data on international common risk factors and portfolios. To address this gap, we provide a step-by-step description of how appropriately screened data from...