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Stochastic models for risk estimation in volatile markets: a survey

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  • Stoyan Stoyanov
  • Borjana Racheva-Iotova
  • Svetlozar Rachev
  • Frank Fabozzi

Abstract

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. Copyright Springer Science+Business Media, LLC 2010

Suggested Citation

  • Stoyan Stoyanov & Borjana Racheva-Iotova & Svetlozar Rachev & Frank Fabozzi, 2010. "Stochastic models for risk estimation in volatile markets: a survey," Annals of Operations Research, Springer, vol. 176(1), pages 293-309, April.
    • Handle: RePEc:spr:annopr:v:176:y:2010:i:1:p:293-309:10.1007/s10479-008-0468-1
    DOI: 10.1007/s10479-008-0468-1
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    4. Young Shin Kim, 2022. "Portfolio optimization and marginal contribution to risk on multivariate normal tempered stable model," Annals of Operations Research, Springer, vol. 312(2), pages 853-881, May.
    5. Michele Leonardo Bianchi & Gian Luca Tassinari, 2018. "Forward-looking portfolio selection with multivariate non-Gaussian models and the Esscher transform," Papers 1805.05584, arXiv.org, revised May 2018.
    6. Johan Dahlin & Mattias Villani & Thomas B. Schon, 2015. "Bayesian optimisation for fast approximate inference in state-space models with intractable likelihoods," Papers 1506.06975, arXiv.org, revised Jun 2017.
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    8. Jianxu Liu & Quanrui Song & Yang Qi & Sanzidur Rahman & Songsak Sriboonchitta, 2020. "Measurement of Systemic Risk in Global Financial Markets and Its Application in Forecasting Trading Decisions," Sustainability, MDPI, vol. 12(10), pages 1-15, May.
    9. Wu, Xu & Zhang, Linlin & Li, Jia & Yan, Ruzhen, 2021. "Fractal statistical measure and portfolio model optimization under power-law distribution," The North American Journal of Economics and Finance, Elsevier, vol. 58(C).
    10. Kenichiro Shiraya & Tomohisa Yamakami, 2023. "Constructing Copulas Using Corrected Hermite Polynomial Expansion for Estimating Cross Foreign Exchange Volatility," Papers 2301.10044, arXiv.org.
    11. Vladik Kreinovich & Monchaya Chiangpradit & Wararit Panichkitkosolkul, 2012. "Efficient algorithms for heavy-tail analysis under interval uncertainty," Annals of Operations Research, Springer, vol. 195(1), pages 73-96, May.
    12. Shiraya, Kenichiro & Yamakami, Tomohisa, 2024. "Constructing copulas using corrected Hermite polynomial expansion for estimating cross foreign exchange volatility," European Journal of Operational Research, Elsevier, vol. 314(3), pages 1195-1214.
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