The purpose of this thesis is to identify the best volatility model for Value-at-Risk(VaR) estimations. We estimate 1 % and 5 % VaR figures for Nordic indices andstocks by using two symmetrical and two asymmetrical GARCH models underdifferent error distributions. Out-of-sample volatility forecasts are produced usinga 500 day rolling window estimation on data covering January 2007 to December2014. The VaR estimates are thereafter evaluated through Kupiec’s test andChristoffersen’s test in order to find the best model. The results suggest thatasymmetrical models perform better than symmetrical models albeit the simpleARCH is often good enough for 1 % VaR estimates.

Στην εργασία αυτή προσεγγίζεται μια μέθοδος ιδιαίτερα γνωστή στον χρηματοπιστωτικό τομέα, με την οποία γίνεται αποτίμηση της αξίας σε κίνδυνο, Value at Risk, που είναι εκτεθειμένες μετοχές και χαρτοφυλάκιο, σύμφωνα με την συσχέτιση των αποδόσεων των περουσιακών τους στοιχείων, αλλά και το συστηματικό κίνδυνο αυτών σε σχέση με τις γενικές τάσεις της αγοράς. Χρησιμοποιώντας τις αποδόσεις 3 μετοχών, αλλά και ενός χαρτοφυλακίου μετοχών απο το Χρηματιστήριο Αξιών Αθηνών, ο βασικός στόχος της παρούσας διατριβής είναι να γίνει μια συγκρτική ανάλυση της αξίας σε κίνδυνο (VaR) για έναν επενδυτή με θέση αγοράς σε διάφορα επίπεδα εμπιστοσύνης και για δύο υποδείγματα δεσμευμένης ετεροσκεδαστικότητας (GARCH και E-GARCH). Για αυτή την συγκριτική ανάλυση, χρησιμοποιείται μια μεθοδολογία για τον έλεγχο των αποτελεσμάτων των παραπάνω υποδειγμάτων, γνωστή ως έλεγχος Kupiec. / In this Theses, we present an application well-known in the financial sector, Value at Risk, with which we measure the risk of stocks and portofolios. Using the returns of 3 stocks and a portofolio from the Greek Stock Exchange Market, the basic goal of the present theses is to make a comparative analysis of the value at risk for an investor with long rading position in various confidence levels and for two generalized autoregressive conditional heteroskedasticity models (GARCH and E-GARCH). For this comparative analysis, a methodology is used to backtest the results of the GARCH models, known as Kupiec Test.

The role of risk management has gained momentum in recent years most notably after the recent financial crisis. This thesis uses a quantitative approach to evaluate the theory of value at risk which is considered a benchmark to measure financial risk. The thesis makes use of both parametric and non parametric approaches to evaluate the effectiveness of VAR as a standard tool in measuring risk of stock portfolio. This study uses the normal distribution, student t-distribution, historical simulation and the exponential weighted moving average at 95% and 99% confidence levels on the stock returns of Sonny Ericsson, Three Months Swedish Treasury bill (STB3M) and Nordea Bank. The evaluations of the VAR models are based on the Kupiec (1995) Test. From a general perspective, the results of the study indicate that VAR as a proxy of risk measurement has some imprecision in its estimates. However, this imprecision is not all the same for all the approaches. The results indicate that models which assume normality of return distribution display poor performance at both confidence levels than models which assume fatter tails or have leptokurtic characteristics. Another finding from the study which may be interesting is the fact that during the period of high volatility such as the financial crisis of 2008, the imprecision of VAR estimates increases. For the parametric approaches, the t-distribution VAR estimates were accurate at 95% confidence level, while normal distribution approach produced inaccurate estimates at 95% confidence level. However both approaches were unable to provide accurate estimates at 99% confidence level. For the non parametric approaches the exponentially weighted moving average outperformed the historical simulation approach at 95% confidence level, while at the 99% confidence level both approaches tend to perform equally. The results of this study thus question the reliability on VAR as a standard tool in measuring risk on stock portfolio. It also suggest that more research should be done to improve on the accuracy of VAR approaches, given that the role of risk management in today’s business environment is increasing ever than before. The study suggest VAR should be complemented with other risk measures such as Extreme value theory and stress testing, and that more than one back testing techniques should be used to test the accuracy of VAR.

Submitted by Fabiola Costa (famedina06@hotmail.com) on 2010-08-24T14:18:56Z No. of bitstreams: 1 Dissertacao_Fabiola_Medina_Costa.pdf: 981365 bytes, checksum: 368c8b3a6a54c3a8e7c0f62130bcf2a3 (MD5) / Approved for entry into archive by Vitor Souza(vitor.souza@fgv.br) on 2010-08-24T14:39:21Z (GMT) No. of bitstreams: 1 Dissertacao_Fabiola_Medina_Costa.pdf: 981365 bytes, checksum: 368c8b3a6a54c3a8e7c0f62130bcf2a3 (MD5) / Made available in DSpace on 2010-08-24T17:42:48Z (GMT). No. of bitstreams: 1 Dissertacao_Fabiola_Medina_Costa.pdf: 981365 bytes, checksum: 368c8b3a6a54c3a8e7c0f62130bcf2a3 (MD5) Previous issue date: 2010-05-28 / This paper proposes the historical simulation model to calculate the VaR, considering return ajusted by the realized volatility measured from intraday returns. The database consists of five most liquid share among the different segments of Bovespa Index. For the proposed methodology we used two of the empirical theories of the empirical literature - adjusted historical simulation and realized volatility. The Kupiec tes and Christoffersen test are used to analized and veryfy the proposed methodology performance. / O presente trabalho propõe para o cálculo VaR o modelo de simulação histórica, com os retornos atualizados pela volatilidade realizada calculada a partir de dados intradiários. A base de dados consiste de cinco ações entre as mais líquidas do Ibovespa de distintos segmentos. Para a metodologia proposta utilizamos duas teorias da literatura empírica – simulação histórica ajustada e volatilidade realizada. Para análise e verificação do desempenho da metodologia proposta utilizamos o Teste de Kupiec e o Teste de Christoffersen.