An Empirical Modeling of Index Volatility with Wavelet Analysis

Abstract

本文定義一市場波動度測度Realized integrated variance, 並檢視S&P 500, Nasdaq以及FTSE 100三個市場的Realized integrated variance的特性. Realized integrated variance數學的定義為某一段時間內市場日報酬率的變異數, 在傳統的理論架構中, 例如GARCH, 將Realized integrated variance視為其波動度測度Spot volatility的近似值. 本文認為, 市場參與者參與市場的時機乃根據可以觀察得到的Realized integrated variance, 而非Spot volatility. 再者, 由於若干連結波動度的衍生性金融產品的出現, Realized integrated variance成為可以直接交易的標的. 因此有必要直接刻畫Realized integrated variance的性質. 首先, 我們發現波動度是一非穩態(nonstationary)的Jump-decaying的時間序列. 在將市場分割成booming和slumping不同的段落之後, 我們發現波動度時間序在這2種時間的特性有顯著的差異. 其次, 由波動度所呈現的市場特性, 可能因為1997之後大量使用選擇權等避險工具而有所改變.

This paper examines the realized integrated variance of the daily return rate series of S&P 500, Nasdaq and FTSE 100 respectively. The realized integrated variance is defined to be the statistical variance of the market index return rates within a certain time window. In stead of regarding the realized integrated variance as an empirical approximate of the latent spot volatility as formally defined in a mathematical framework, such as GARCH, we treat it as a direct “observable” volatility measure and try to model its dynamics straightforward. First, we find the volatility series is a stochastic jump-decay process rather than being all-over-the-time stationary in each market. Also, under switching booming and slumping market conditions, the volatility series exhibits significantly different dynamic characteristics. Secondly, some major market structures, related to volatility mechanism, might have changed due to the hefty usage of options for hedging volatility risk after 1997.