Stochastic models for risk estimation in volatile markets: a survey

The problem of portfolio risk estimation in volatile markets requires employing fat-tailed models for financial instrument returns combined with copula functions to capture asymmetries in dependence and a true downside risk measure for risk estimation. In this survey, we discuss how these three essential components can be combined together in a Monte Carlo based framework for risk estimation and risk budgeting with the average value-at-risk measure (AVaR). We consider in detail the questions of AVaR calculation and estimation and also stochastic stability of AVaR when combined with heavy-tailed scenarios.