Stochastic models for risk estimation in volatile markets: A survey

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

doi:10.1007/s10479-008-0468-1

Stochastic models for risk estimation in volatile markets: A survey

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

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

28 Scopus citations

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.

Original language	English
Pages (from-to)	293-309
Number of pages	17
Journal	Annals of Operations Research
Volume	176
Issue number	1
DOIs	https://doi.org/10.1007/s10479-008-0468-1
State	Published - Mar 2010

Keywords

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

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10.1007/s10479-008-0468-1

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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.",

keywords = "Average value-at-risk, Conditional value-at-risk, Downside risk, Fat-tailed distributions, Risk budgeting, Stable distributions",

author = "Stoyanov, {Stoyan V.} and Borjana Racheva-Iotova and Rachev, {Svetlozar T.} and Fabozzi, {Frank J.}",

note = "Funding Information: Acknowledgements Prof. Rachev gratefully acknowledges research support by grants from Division of Mathematical, Life and Physical Sciences, College of Letters and Science, University of California, Santa Barbara, the Deutschen Forschungsgemeinschaft and the Deutscher Akademischer Austausch Dienst.",

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AU - Fabozzi, Frank J.

N1 - Funding Information: Acknowledgements Prof. Rachev gratefully acknowledges research support by grants from Division of Mathematical, Life and Physical Sciences, College of Letters and Science, University of California, Santa Barbara, the Deutschen Forschungsgemeinschaft and the Deutscher Akademischer Austausch Dienst.

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AB - 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.

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KW - Conditional value-at-risk

KW - Downside risk

KW - Fat-tailed distributions

KW - Risk budgeting

KW - Stable distributions

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Stochastic models for risk estimation in volatile markets: A survey

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Keywords

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