We add to the discussion on risk management by proposing an innovative measure of Value at Risk (VaR), which relaxes some statistical assumptions. We provide a VaR based on time-varying moments of the best-fitting probability distribution function. This risk measure can capture the cross-effects associated with contagion and integration through the estimation of a multivariate autoregressive moving average–generalized autoregressive heteroskedasticity (ARMA–GARCH). We implement an empirical exercise to account for the risk management of some of the main worldwide financial sector indices of G20 economies. According to Basel back-testing and back-testing that deals with the frequency and conditionality of losses exceeding VaR, this innovative VaR seems to perform better than Basel VaR.
AndersonT., & DarlingD. (1952). Asymptotic theory of certain goodness-of-fit criteria based on stochastic processes. Annals of Mathematical Statistics, 23, 193–212.
3.
CampbellS. (2005). A review of backtesting and backtesting procedure. Finance and Economics Discussion Series, Divisions of Research e Statistics and Monetary Affairs, Federal Reserve Board, Washington D.C.
4.
CappielloL., EngleR., & SheppardK. (2006). Asymmetric dynamics in the correlations of global equity and bond returns. Journal of Financial Econometrics, 4, 537–572.
5.
ChangC., Jiménez-MartínJ., MaasoumiE., McAleerM., & Pérez-AmaralT. (2015). Choosing expected shortfall over VaR in Basel III using stochastic dominance. TI 2015-133/III Tinbergen Institute Discussion Paper.
6.
ChristoffersenP. (1998). Evaluating interval forecasts. International Economic Review, 39, 841–862.
7.
CornishE., & FisherR. (1937). Moments and cumulants in the specification of distributions. Revue de l’Institut International de Statistique, 5, 307–320.
8.
DanielssonJ. (2013). The new market regulations. VoxEU.org.
9.
DanielssonJ., & de VriesC., 1998. Value-at-risk and extreme returns. Annales d’Economie et de Statistique, ENSAE, 60, 239–270.
10.
DickeyD., & WayneF. (1979). Likelihood ratio statistics for autoregressive time series with a unit root. Econometrica, 49, 1057–1072.
11.
EngleR. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50, 987–1007.
12.
FamaE. (1965). The Behavior of Stock Market Prices. Journal of Business, 38, 34–105.
13.
FasoloA. (2006). Interdependence and contagion: An analysis of information transmission in Latin America’s stock markets. Working Papers Series 112, Central Bank of Brazil, Research Department.
14.
HullJ., & WhiteA. (1998). Value at risk when daily changes in market variables are not normally distributed. Journal of Derivatives, 5, 9–19.
15.
JarqueC., & BeraA. (1981). Efficient tests f or normality, homoscedasticity and serial independence of regression residuals: Monte Carlo evidence. Economics Letters, 7, 313–318.
16.
KleinI., & FischerM. (2003). Kurtosis ordering of the generalized secant hyperbolic distribution: A technical note. Working Paper Friedrich-Alexander-Universität Erlangen-Nürnberg, No. 54/2003
17.
KolmogorovA. (1933). Sulla determinazione empírica de uma legge di distribuzione. Giornale dell’ Institutp Italiano degli Attuari, 4, 83–91.
18.
KupiecP. (1995). Techniques for verifying the accuracy of risk management models. Journal of Derivatives, 3, 73–84.
19.
LeeS., & LeeT. (2009). Value-at-risk forecasting based on Gaussian mixture ARMA–GARCH model. Journal of Statistical Computation and Simulation, 81, 1131–1144.
20.
LevyP. (1925). Calcul des probabilities.
21.
LienD., YangX., & YeK. (2014). Alternative approximations to value-at-risk: A comparison. Communications in Statistics - Simulation and Computation, 43, 2225–2240.
22.
LiuW. (2010). Estimation and testing of portfolio value-at-risk based on L-comoment matrices. Journal of Futures Markets, 30, 897–908.
23.
LonginF., & SolnikB.1995. Is the correlation in international equity returns constant: 1960–1990? Journal of International Money and Finance, 14, 3–26.
24.
LonginF., & SolnikB. (2001). Extreme correlation of international equity markets. The Journal of Finance, 56, 649–676.
25.
LopezJ. (1999). Methods for evaluating value-at-risk models. Federal Reserve Bank of San Francisco Economic Review.
26.
MandelbrotB. (1963). The variation of certain speculative prices. Journal of Business, 36, 394–419.
27.
MatosP., JucáI., CruzR., & MacedoA. (2015). BRIC’s risk management based on an innovative VaR. The Empirical Economics Letters, 14, 697–704.
28.
MatosP., OquendoR., & TrompieriN. (2016). Integration and contagion of BRIC financial markets. Journal of Applied Economics and Business, 4, 23–48.
29.
PenaV., RiveraR., & Ruiz-MataJ. (2006). Quality control of risk measures: Backtesting VAR models. Journal of Risk, 9, 39–54.
30.
PrauseK. (1999). The generalized hyperbolic model: Estimation, financial derivatives and risk measures(PhD thesis). University of Freiburg.
31.
PuigM., & RiveroS. (2014). Causality and contagion in EMU sovereign debt markets. International Review of Economics and Finance, 33, 12–27.
32.
RajwaniS., & KumarD. (2016). Asymmetric Dynamic conditional correlation approach to financial contagion: A study of Asian markets. Global Business Review, 7, 1339–1356.
33.
RippelM., & JánskýI. (2011). Value at risk forecasting with the ARMA–GARCH family of models in times of increased volatility. Working Papers IES 2011/27, Charles University Prague.
34.
SillittoG. (1969). Derivation of approximants to the inverse distribution function of a continuous univariate population from the order statistics of a sample. Biometrika, 56, 641–650.
35.
SmirnovN. (1933). Sur les écarts de la courbe de distribution empirique. Recueil Matématique, 6, 3–26.
36.
SrivastavaA., BhatiaS., & GuptaP. (2015). Financial crisis and stock market integration: An analysis of select economies. Global Business Review, 16, 1127–1142.
37.
VaughanD. (2002). The generalized hyperbolic secant distribution and its application, communications in statistics. Theory and Methods, 31, 219–238.
38.
WestK., & ChoD. (1995). The predictive ability of several models of exchange rate volatility. Journal of Econometrics, 69, 367–391.
