Application of Modified POT Method with Volatility Model for Estimation of Risk Measures

Marcin Fałdziński



The main aim of this paper is the presentation and empirical analysis of the new approach which combines volatility models with Peaks over Threshold method that comes from extreme value theory. The new approach is applied for estimation of risk measures (VaR and ES) in financial time series. For the empirical analysis the financial risk model evaluation was conducted. In this paper the POT method was compared with standard volatility models (GARCH and SV) in case of the conditional modeling.


Extreme Value Theory, Peaks over Threshold, Value-at-Risk, Expected Shortfall

Full Text:



Alexander, C. (2008), Market Risk Analysis vol. IV: Value-at-Risk Models, John Wiley & Sons Ltd., New York.

Angelidis, T., Degiannakis, S. (2006), Backtesting VaR Models: An Expected Shortfall Approach, Working Papers, University of Crete, Athens University of Economics and Business.

Artzner, P., Delbaen, F., Eber, J. M., Heath, D. (1997), Thinking Coherently, Risk, 10, 68–71.

Artzner, P., Delbaen F., Eber J.M., Heath, D. (1999), Coherent Measures of Risk, Mathematical Finance, 9, 203–228. DOI:

Brooks, C., Clare, A.D., Dalle Molle, J.W, Persand, G. (2006), A Comparison of Extreme Value Theory Approaches for Determining Value at Risk, Journal of Empirical Finance, 12, 339–352.

Christoffersen, P.F. (1998), Evaluating Interval Forecasts, International Economic Review, 3. DOI:

Dowd, K. (2005), Measuring Market Risk Second Edition, John Wiley & Sons Ltd., New York.

Embrechts, P., Klüppelberg, C., Mikosch, T. (2003), Modelling Extremal Events for Insurance and Finance, Springer, Berlin.

Fałdziński, M. (2008), Model warunkowej zmienności wartości ekstremalnych (Conditional Extreme Value Volatility model), in Zieliński Z. (ed.), Współczesne trendy w ekonometrii (Contemporary Trends in Econometrics), Wydawnictwo Wyższej Szkoły Informatyki i Ekonomii, Olsztyn.

Fałdziński, M. (2009), On The Empirical Importance Of The Spectral Risk Measure With Extreme Value Theory Approach, Forecasting Financial Markets and Economic Decision-Making FindEcon, Łódź, submitted.

Haas, M. (2001), New Methods in Backtesting, Financial Engineering Research Center, Bonn.

Harmantzis, F.C., Miao, L., Chien, Y. (2006), Empirical Study of Value-at-Risk and Expected Shortfall Models with Heavy Tails, Journal of Risk Finance, 7, No.2, 117–126.

Kuester, K., Mittnik, S., Paolella, M.S. (2006), Value-at-Risk Prediction: A Comparison of Alternative Strategies, Journal of Financial Econometrics, 1, 53–89. DOI:

McNeil, J.A., Frey, F. (2000), Estimation of Tail-Related Risk Measures for Heteroscedastic Financial Time Series: an Extreme Value Approach, Journal of Empirical Finance, 7, 271–300.

Osińska, M., Fałdziński, M. (2008), GARCH and SV models with application of Extreme Value Theory, in Zieliński Z. (ed.), Dynamic Econometric Models, Volume 8, UMK, Toruń.

Szegö, G. (2004), Risk measures for the 21st century, John Wiley & Sons Ltd., West Sussex, UK.

ISSN (print) 1234-3862
ISSN (online) 2450-7067

Partnerzy platformy czasopism