Stochastic models for risk estimation in volatile markets: A survey

Stoyan V. Stoyanov, Borjana Racheva-Iotova, Svetlozar T. Rachev, Frank J. Fabozzi

Research output: Contribution to journalArticlepeer-review

28 Scopus citations


Portfolio risk estimation in volatile markets requires employing fat-tailed models for financial returns combined with copula functions to capture asymmetries in dependence and an appropriate downside risk measure. 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 capital allocation with the average value-at-risk measure (AVaR). AVaR is the average loss provided that the loss is larger than a predefined value-at-risk level. We consider in some detail the AVaR calculation and estimation and investigate the stochastic stability.

Original languageEnglish
Pages (from-to)293-309
Number of pages17
JournalAnnals of Operations Research
Issue number1
StatePublished - Mar 2010


  • Average value-at-risk
  • Conditional value-at-risk
  • Downside risk
  • Fat-tailed distributions
  • Risk budgeting
  • Stable distributions


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