VIX波動度Wavelet-CEV模型之研究-----使用狀態轉換架構與小波分析方法

Abstract

本研究針對芝加哥選擇權交易所﹝CBOE﹞所訂定的波動度指標﹝VIX﹞，對波動度直接做模型配適。應用狀態轉換模型(Regime Switching)的概念以及分段線性模型﹝piecewise linear model﹞的架構，採用Wavelet—CEV變異數模型檢視有關參數的性質及波動度模型的配適效果。一般而言，波動度平均值在牛市時較低、熊市時較高，而收斂速度則是在牛市時較大、熊市時較小。Wavelet 之分析方法可處理異常之大波動，使波動度模型之參數估計較為準確，也在結構分析上協助對波動度狀態的瞭解。

The purpose of this research is to model the volatility index, VIX, formulated by CBOE using the concept of Regime Switching and piecewise linear structure. I adopt the Wavelet analysis to inspect the properties of CEV parameters in the stochastic volatility model. Generally speaking, volatility is relatively high in the bear market and low in the bull market. The converging rate on average is higher in the bull market than that in the bear market. Wavelet analysis which can deal with the unusual structure change in the market enables the parameter estimation to be correctly specified.