Publication: Dalgacık bazlı uç değer teorisi ile parametrik olmayan volatilite modellemesi
Abstract
Dalgacık bazlı uç değer teorisi, parametrik olmayan volatilite modellemesi, genelleştirilmiş pareto dağılımı, dalgacıklar ÖZET DALGACIK BAZLI UÇ DEĞER TEORİSİ İLE PARAMETRİK OLMAYAN VOLATİLİTE MODELLEMESİ Bu tezin amacı, riske maruz değer öngörüsünde dalgacık bazlı uç değer teorisini geliştirmektir. Döndürmeli en yüksek örtmeli ayrık dalgacık dönüşümü genelleştirilmiş pareto dağılımında eşik değer olarak önerilerek dalgacık bazlı genelleştirilmiş pareto dağılımı, dalgacık bazlı koşullu genelleştirilmiş pareto dağılımı, dalgacık bazlı beklenen kuyruk kaybı ve dalgacık bazlı koşullu beklenen kuyruk kaybı modelleri geliştirilmiştir. Dalgacık bazlı uç değer teorisi modellerinin örneklem dışı öngörü performansı değişen varyans, simülasyon ve bootstrap ve uç değer teorisi modelleri ile karşılaştırılmıştır. Karşılaştırma modeli olarak değişen varyans modellerinden GARCH, EGARCH, GRJ-GARCH, APARCH, IGARCH, FIGARCH, FIEGARCH, FIAPARCH, HYGARCH, GRJ-normal karma GARCH ve asimetrik normal karma GARCH modelleri eklenmiştir. Ayrıca, Riskmetrics-EWMA, Cornish-Fisher ve markov rejim değişim GARCH modelleri ile riske maruz değer hesaplanmıştır. Dağılım seçiminin önemini test etmek amacı ile GARCH modelleri normal dağılım yanında student-t ve çarpık student-t dağılımları ile de modellenmiştir. Uygulama olarak, İMKB-100 endeksi seçilmiş ve örneklem dışı öngörü için 15.01.2001-20.03.2009 tarihleri arasındaki günlük 2048 gözlem kullanılmıştır. Önerilen dalgacık bazlı uç değer teorisi ve karşılaştırma modellerinin öngörü performansı aşım sayısı, kök ortalama hata kare, Kupiec(1995), Lopez(1998) ve Christoffersen(1998) geriye dönük testleri ile test edilmiştir. Ampirik bulgular, dalgacık bazlı uç değer teorisi modellerinin gerek aşım sayısı gerekse kuyruk testlerine göre daha iyi öngörü performansı sağladığını göstermektedir. Wavelet based extreme value theory, nonparametric volatility modelling, generalized pareto distribution, wavelets
NONPARAMETRIC VOLATILITY MODELLING WITH WAVELET BASED EXTREME VALUE THEORY The aim of the present thesis is to develop wavelet based extreme value theory for value-at-risk forecasting. Circularly shifted maximal overlap discrete wavelet transform is offered as threshold in generalized pareto distribution and wavelet based generalized pareto distribution model, wavelet based conditional generalized pareto distribution model, wavelet based expected shortfall model and wavelet based conditional expected shortfall model are developed. The out-of-sample forecasting performance of the wavelet based extreme value theory models are compared with conditional volatility, simulation and bootstrap and extreme value theory models. GARCH, EGARCH, GRJ-GARCH, APARCH, IGARCH, FIGARCH, FIEGARCH, FIAPARCH, HYGARCH, GRJ-normal mixture GARCH, asymmetric normal mixture GARCH are selected for comparison of volatility models. Besides, value-at-risk is calculated by using Riskmetrics-EWMA, Cornish-Fisher and markov regime switching GARCH models. GARCH models are also tested with student-t and skewed student-t distribution beside gaussian distribution in order to test the importance of selecting distributions. For application, ISE-100 index is selected and 2048 data is used for the period between January 15, 2001 and March 20, 2009 as out-of-sample forecasting. The forecasting performance of the wavelet based extreme value theory suggested in the present thesis and comparison models are tested with backtesting models of violations number, root mean squared errors(RMSE), Kupiec(1995), Lopez(1998) and Christoffersen(1998) tests. Empirical evidence shows that wavelet based extreme value theory provides better forecasting performance based on not only number of violations but also tail loss tests.
NONPARAMETRIC VOLATILITY MODELLING WITH WAVELET BASED EXTREME VALUE THEORY The aim of the present thesis is to develop wavelet based extreme value theory for value-at-risk forecasting. Circularly shifted maximal overlap discrete wavelet transform is offered as threshold in generalized pareto distribution and wavelet based generalized pareto distribution model, wavelet based conditional generalized pareto distribution model, wavelet based expected shortfall model and wavelet based conditional expected shortfall model are developed. The out-of-sample forecasting performance of the wavelet based extreme value theory models are compared with conditional volatility, simulation and bootstrap and extreme value theory models. GARCH, EGARCH, GRJ-GARCH, APARCH, IGARCH, FIGARCH, FIEGARCH, FIAPARCH, HYGARCH, GRJ-normal mixture GARCH, asymmetric normal mixture GARCH are selected for comparison of volatility models. Besides, value-at-risk is calculated by using Riskmetrics-EWMA, Cornish-Fisher and markov regime switching GARCH models. GARCH models are also tested with student-t and skewed student-t distribution beside gaussian distribution in order to test the importance of selecting distributions. For application, ISE-100 index is selected and 2048 data is used for the period between January 15, 2001 and March 20, 2009 as out-of-sample forecasting. The forecasting performance of the wavelet based extreme value theory suggested in the present thesis and comparison models are tested with backtesting models of violations number, root mean squared errors(RMSE), Kupiec(1995), Lopez(1998) and Christoffersen(1998) tests. Empirical evidence shows that wavelet based extreme value theory provides better forecasting performance based on not only number of violations but also tail loss tests.