### Abstract

Value-at-Risk (VaR) has become the universally accepted risk metric adopted internationally under the Basel Accords for banking industry internal control, capital adequacy and regulatory reporting. The recent extreme financial market events such as the Global Financial Crisis (GFC) commencing in 2007 and the following developments in European markets mean that there is a great deal of attention paid to risk measurement and risk hedging. In particular, to risk indices and attached derivatives as hedges for equity market risk. The techniques used to model tail risk such as VaR have attracted criticism for their inability to model extreme market conditions. In this paper we discuss tail specific distribution based Extreme Value Theory (EVT) and evaluate different methods that may be used to calculate VaR ranging from well known econometrics models of GARCH and its variants to EVT based models which focus specifically on the tails of the distribution. We apply Univariate Extreme Value Theory to model extreme market risk for the FTSE100 UK Index and S&P-500 US markets indices plus their volatility indices. We show with empirical evidence that EVT can be successfully applied to financial market return series for predicting static VaR, CVaR or Expected Shortfall (ES) and also daily VaR and ES using a GARCH(1,1) and EVT based dynamic approach to these various indices. The behaviour of these indices in their tails have implications for hedging strategies in extreme market conditions.

Original language | English |
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Pages (from-to) | 355-369 |

Number of pages | 15 |

Journal | The North American Journal of Economics and Finance: a journal of financial economics studies |

Volume | 26 |

DOIs | |

Publication status | Published - 2013 |

Externally published | Yes |

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### Bibliographical note

Cited By :16Export Date: 1 January 2018

Correspondence Address: Allen, D.E.; School of Accounting Finance and Economics, Edith Cowan UniversityAustralia; email: d.allen@ecu.edu.au

Funding details: ARC, Australian Research Council

Funding text: We thank the Australian Research Council for funding support. We are grateful to the reviewers for helpful comments.

References: Bingham, N.H., Goldie, C.M., Teugels, J.L., (1987) Regular variation encyclopedia of mathematics and its applications, vol. 27, , Cambridge University Press, Cambridge, UK; Chavez-Demoulin, V., Embrechts, P., An EVT primer for credit risk (2011) The oxford handbook of credit derivatives, pp. 500-532. , Oxford University Press, A. Lipton, A. Rennie (Eds.); Coles, S.G., (2001) An introduction to statistical modelling of extreme values, , Springer, London; Danielsson, J., de Vries, C., Value-at-risk and extreme returns (2000) Annales d'Economie et de Statistique, 60, pp. 239-270; Davison, A.C., Smith, R.L., Models for exceedances over high thresholds (with discussion) (1990) Journal of the Royal Statistical Society, pp. 393-442. , Series B, 52; Embrechts, P., Klüppelberg, C., Mikosch, T., (1997) Modelling extremal events for insurance and finance, , Springer, Berlin; Embrechts, P., (1999) Extreme value theory in finance and insurance, , Department of Mathematics, ETH (Swiss Federal Technical University), Zurich, (Manuscript); Engle, R.F., Manganelli, S., CAViaR: Conditional autoregressive value at risk by regression quantiles (2004) Journal of Business & Economics Statistics, 22 (4), pp. 367-381; Franke, J., Härdle, K.W., Hafner, C.M., (2008) Statistics of financial market: An introduction, , Springer-Verlag Berlin Heidelberg; Giesecke, K., Goldberg, L.R., Forecasting extreme financial risk (2005) Risk management: A modern perspective, , Elsevier, Amsterdam, M. Ong (Ed.); Gilli, M., Këllezi, E., An Application of extreme value theory for measuring financial risk (2006) Computational Economics, 27 (2), pp. 207-228; Gouriéroux, C., (1997) ARCH models and financial applications, , Springer, New York; Jesus, R., Ortiz, E., Cabello, A., Long run peso/dollar exchange rates and extreme value behavior: Value at Risk modeling (2013) The North American Journal of Economics and Finance, 24, pp. 139-152; Jondeau, E., Rockinger, M., The tail behavior of stock returns: Emerging versus mature markets (1999) Documents de Travail 66: Banque de France; Koenker, R.W., Bassett, G., Regression quantiles (1978) Econometrica, 46 (1), pp. 33-50; Kuan, C.H., Webber, N., (1998) Valuing interest rate derivatives con-sistent with a volatility smile, , University of Warwick, (Working Paper); Longin, F.M., The assymptotic distribution of extreme stock market returns (1996) Journal of Business, 69, pp. 383-408; Loretan, M., Phillips, P., Testing the covariance stationarity of heavy-tailed time series (1994) Journal of Empirical Finance, 1 (2), pp. 211-248; Manganelli, S., Engle, R.F., (2001) Value at risk models in finance, , European Central Bank, Working Paper; McNeil, A., Frey, R., Estimation of tail related risk measure for heteroscedastic financial time series: An extreme value approach (2000) Journal of Empirical Finance, 7, pp. 271-300; McNeil, A.J., Frey, R., Embrechts, P., (2005) Quantitative risk management: Concepts, techniques and tools, , Princeton University Press, Princeton, New Jersey; McNeil, A.J., (1999) Extreme value theory for risk managers internal modelling and CAD (Vol. II), pp. 93-113. , RISK Books; Mills, C.F., (1927) The behaviour of prices, , National Bureau of Economic Research, New York; Morgan, J.P., Riskmetrics (1996) Technical Document; Neftci, S.N., Value at risk calculations, extreme events, and tail estimation (2000) Journal of Derivatives, pp. 23-37; Onour, I.A., Extreme risk and fat-tails distribution model: Empirical analysis (2010) Journal of Money, Investment and Banking; Reiss, R.D., Thomas, M., (1997) Statistical analysis of extreme values with applications to insurance, finance, hydrology and other fields, , Birkhäuser Verlag, Basel; Sheedy, E., Can risk modeling work? (2009) Journal of Financial Transformation, 27, pp. 82-87; Straetmans, S., Extreme financial returns and their comovements (1998), Ph.d. dissertation, Tinbergen Institute Research Series, Erasmus University Rotterdam; Taleb, N., (2007) The black swan: The impact of the highly improbable, , Penguin, London; Turner, L., (2009) The turner review: A regulatory response to the global banking crisis, , FSA, London; Vervaat, W., Functional central limit theorems for processes with positive drift and their inverses (1972) Zeitshrift fur Wahrscheinlichkeitstheorie, 23, pp. 245-253

### Keywords

- CVaR
- ES
- EVT
- VaR